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Integrating ELD Standards into K12 Math and Science

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Theories supporting all lesson models used in MS Credential Program 22(1)

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NGSS & STEM Curriculum for Grades K-8 | KnowAtom

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Designed for Next Generation Science Standards, KnowAtom’s K-8 STEM curriculum offers hands-on materials, professional development, and more.

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A required part of this site couldn’t load. This may be due to a browser extension, network issues, or browser settings. Please check your connection, disable any ad blockers, or try using a different browser.

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IXL | Math, Language Arts, Science, Social Studies, and Spanish

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IXL is the world’s most popular subscription-based learning site for K–12. Used by over 17 million students, IXL provides personalized learning in more than 17,000 topics, covering math, language arts, science, social studies, and Spanish. Interactive questions, awards, and certificates keep kids motivated as they master skills.

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Science Video Fieldwork #1:

https://www.youtube.com/watch?v=1AdcmWoJvz0

Science Video Fieldwork #2:

https://www.youtube.com/watch?v=ZxRLV3qUev4

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Math Video Fieldwork #1:

https://www.youtube.com/watch?v=rB13osq_e10 Math Video

Math Video Fieldwork #2:

https://www.youtube.com/watch?v=t13JZRqaZx4

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Before During After Lesson Plan Template (1)

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CalTPA Passing Standards for 2024–2025 Operational Administration

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CalTPA Passing Standards for 2024–2025 Operational Administration

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At its June 2019 meeting, the Commission approved the following passing standards for the redeveloped CalTPA:

Cycle 1 (8 rubrics): A final cut score of 19 points with one score of 1 allowed

Cycle 2 (9 rubrics): A final cut score of 21 with one score of 1 allowed

These passing standards will apply to all CalTPA cycles submitted on or after August 23, 2019.

Candidates who do not meet the passing standard on one or both cycles may seek remedial support from their preparation programs and have the opportunity to retake the appropriate cycle(s) in accordance with the CalTPA Retake Policy . See PSA 19-06 for more information.

At its December 2023 meeting, the Commission approved a secondary passing standard for the following performance assessments: CalTPA, EdSp CalTPA, and edTPA. See PSA-24-02 for more information about the secondary passing standard.

Close

https://www.ctcexams.nesinc.com/testview.aspx?f=html_frag/caltpa_testpage.html

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CalTPA is offered in the following credential areas*:

and the following Single Subjects:

Industrial and Technology Education

Mathematics

Music

Physical Education

Science

Social Science

Theatre

Performance assessment consisting of two instructional cycles:

Instructional Cycle 1: Learning About Students and Planning Instruction

Instructional Cycle 2: Assessment-Driven Instruction

*Translations or transcripts are NOT required for the following:

concurrent bilingual candidates who are in a placement where a language other than English is exclusively used for instruction, or who are in a placement where both English and another language are used for instruction
NOTE: Analysis and reflection narratives must be primarily in English

candidates registered for the World Languages assessment

candidates using American Sign Language (ASL) in a classroom setting with students who are deaf or hard of hearing

candidates using Braille instructional materials in a classroom setting with students who are visually impaired

For all other candidates, any evidence in a language other than English must be accompanied by a translation.

Your Session is about to expire in seconds.
To continue your session, select Stay Signed In.

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CalTPA is offered in the following credential areas*:

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https://achievethecore.org/page/2736/introductory-materials-on-the-common-core-state-standards?utm_source=chatgpt.com

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Achievethecore.org :: Introductory Materials on the Common Core State Standards

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Teachers answer the top questions parents have about the Common Core and what it means for their child.

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The Math Learning Center – Virtual Manipulatives
Interactive tools for various math concepts.
https://www.mathlearningcenter.org/resources/apps​

Didax – Free Virtual Manipulatives
A collection of virtual manipulatives for classroom use.
https://www.didax.com/math/virtual-manipulatives.html​

Scholastic – Using Manipulatives
Guidance on incorporating manipulatives into math instruction.
[https://www.scholastic

10 Math Manipulatives to Enhance Student Learning
https://www.prodigygame.com/main-en/blog/math-manipulatives

Teaching Resources: Using Manipulatives in Mathematics Learning
[https://www.teachermagazine.com/au

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CRA (Concrete, Representational, Abstract) Model

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CRA (Concrete, Representational, Abstract) Model

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1. Edutopia: Using the CRA Framework in Elementary Math
This article discusses how the CRA framework can be implemented in elementary classrooms, emphasizing the progression from hands-on manipulatives to abstract reasoning.

edutopia.org

2. PaTTAN: Concrete-Representational-Abstract (CRA)
The Pennsylvania Training and Technical Assistance Network provides detailed guidance on the CRA instructional sequence, including practical examples and strategies for educators.

pattan.net

3. K5 Math Spot: What is the CRA Math Model?
This blog post offers an overview of the CRA model, explaining how to transition students through concrete, representational, and abstract stages to build deep mathematical understanding.

k5mathspot.com

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CA Standards for the Teaching Professional (CSTPs)

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TPES - QUICK CHART (with TPE 7)

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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NGSS Elementary Science

https://www.nationalacademies.org/our-work/conceptual-framework-for-new-science-education-standards

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The National Research Council's (NRC) Framework describes a vision of what it means to be proficient in science; it rests on a view of science as both a body of knowledge and an evidence-based, model and theory building enterprise that continually extends, refines, and revises knowledge. It presents three dimensions that will be combined to form each standard:
Dimension 1: Practices
The practices describe behaviors that scientists engage in as they investigate and build models and theories about the natural world and the key set of engineering practices that engineers use as they design and build models and systems. The NRC uses the term practices instead of a term like "skills" to emphasize that engaging in scientific investigation requires not only skill but also knowledge that is specific to each practice. Part of the NRC's intent is to better explain and extend what is meant by "inquiry" in science and the range of cognitive, social, and physical practices that it requires.

Although engineering design is similar to scientific inquiry, there are significant differences. For example, scientific inquiry involves the formulation of a question that can be answered through investigation, while engineering design involves the formulation of a problem that can be solved through design. Strengthening the engineering aspects of the Next Generation Science Standards will clarify for students the relevance of science, technology, engineering and mathematics (the four STEM fields) to everyday life.
Dimension 2: Crosscutting Concepts
Crosscutting concepts have application across all domains of science. As such, they are a way of linking the different domains of science. They include: Patterns, similarity, and diversity; Cause and effect; Scale, proportion and quantity; Systems and system models; Energy and matter; Structure and function; Stability and change. The Framework emphasizes that these concepts need to be made explicit for students because they provide an organizational schema for interrelating knowledge from various science fields into a coherent and scientifically-based view of the world.
Dimension 3: Disciplinary Core Ideas
Disciplinary core ideas have the power to focus K-12 science curriculum, instruction and assessments on the most important aspects of science. To be considered core, the ideas should meet at least two of the following criteria and ideally all four:

Have broad importance across multiple sciences or engineering disciplines or be a key organizing concept of a single discipline;

Provide a key tool for understanding or investigating more complex ideas and solving problems;

Relate to the interests and life experiences of students or be connected to societal or personal concerns that require scientific or technological knowledge;

Be teachable and learnable over multiple grades at increasing levels of depth and sophistication.

Disciplinary ideas are grouped in four domains: the physical sciences; the life sciences; the earth and space sciences; and engineering, technology and applications of science.

Read more about the three dimensions in the NRC Framework online here.

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The National Research Council's (NRC) Framework describes a vision of what it means to be proficient in science; it rests on a view of science as both a body of knowledge and an evidence-based, model and theory building enterprise that continually extends, refines, and revises knowledge.

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A Framework for K–12 Science Education | Next Generation Science Standards

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The National Research Council (NRC) of the National Academy of Sciences managed the first of two steps in the creation of the Next Generation Science Standards by developing the A Framework for K-12 Science Education, which was released July 2011.

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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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https://docs.google.com/document/d/1wNV1003ayqpC_zNwbdUbKs6SkEvjDqlE9kwpmNWpYNw/edit?tab=t.0

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NEW K-8 Math Lessons Now Available

Get instant access to hours of fun, standards-based videos, reading material, quiz games, simple DIY activities & more.

Get instant access to hours of fun, standards-based videos, reading material, quiz games, simple DIY activities & more.

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Get instant access to hours of fun, standards-based learning videos, lesson plans, activities, quizzes & more.

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https://www.mollybang.com/Pages/sophiecant.html

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Plus activities teachers can use to help students improve their reading comprehension and understanding of math concepts.

Read-aloud time is typically dedicated to building reading comprehension. Sometimes teachers incorporate some social studies ideas, but rarely does math get to be front and center.

That should change because math and reading don't exist in separate silos. Adults who use math on a daily basis also need to be strong, fluent readers. Likewise, math requires strong logical reasoning skills, which can be honed in tandem with with reading skills. This is why reading about math, as well as using reading as an opportunity to engage with mathematical concepts, should be embraced.

When we blend these disciplines, we invite students to engage with math in a new-and often far more inviting-way. Kids who have struggled with geometry may love the opportunity to write a shape story, for instance-and it might even help them to remember that a square is a type of rectangle but a rectangle is not a type of square.

This far-from-exhaustive list of read-aloud books and related activities can help get teachers started thinking about how to incorporate mathematical reasoning, logic, and concepts into literacy instruction.

, written by John Scieszka and illustrated by Lane Smith, is a hilarious book about a student who, after being told that anything can be a math problem, wakes up to find that she can only see math problems in everything around her.

Activities: Math curse your students-have them go around the school and find math problems. You can extend the lesson by having them solve the problems they find (or pick a few for the class to work on together). For instance, you might pose the problem of needing new classroom supplies. Give students a budget and prices for items and encourage them to decide how to spend the money.

Actual Size

Actual Size, by Steve Jenkins, explains the sizes of different parts of animals, from a gorilla's hand to the world's largest tarantula. It's fantastic for teaching size and scale, and the collage illustrations are beautiful.

Activities: Have students choose an animal they're interested in and build either the whole animal or part of it in its actual size. For example, students could pick an insect and research its dimensions, then draw it accurately on graph paper. For a more elaborate project, students could draw an animal to scale on a large piece of craft paper or with painters tape on the floor; alternatively, they could build it using papier-mâché.

In the engaging tale , written by Mac Barnett and illustrated by Jon Klassen, Triangle tries to trick his friend Square... and a battle of the shapes ensues. This book is part of the Shape Trilogy-don't forget to check out Circle and Square.

Activities: Have students write a shape story with at least one fact about each shape included. For younger students, you might give them part of the story and encourage them to finish it. Or have them write a song or poem about a shape of their choosing.

As an alternative, have your students create a podcast in which they interview a shape. They can ask that shape about its favorite uses (e.g., "I'm a pentagon and my favorite use is a baseball plate"), its best friends ("As a pentagon, I love squares because when we get together it looks like we've made a pencil!"), and so on.

The Map of Good Memories

When Zoe has to flee her hometown because of war, she creates a " map of good memories " in this book written written by Fran Nuño and illustrated by Zuzanna Celej.

Activities: Create a map of good memories with students. Each student can create their own, using a map of their home, school, or hometown. Or you can create a class map and have each student provide a memory for a different place in your town. This activity provides an opportunity to work on map skills such as measurement, scale, and distance. For older students, you might use graph paper to create a scaled map of good memories.

Infinity and Me

In Infinity and Me, written by Kate Hosford and illustrated by Gabi Swiatkowska, Uma looks up at the sky and feels small in the face of so much. This leads her to ponder what infinity means and looks like. This is an unusual book about a fascinating idea.

Activities: To get students thinking about the concept of infinity, sit in a circle and ask students to come up with the largest number they can. Go around until you feel like stopping, and declare the last person the winner. Your students will immediately point out that this is unfair because whoever goes last will win. Suggest another game: Do the same thing, but have students go around trying to say the smallest number they can. The same thing will happen. Discuss with students how a person could possibly win this game. This will spark a great conversation about how numbers can continue infinitely. Sitting in a circle gives students a physical view of infinity as well-you could go around that circle forever.

Another great way to get students thinking about infinity is to have them make a list of all of the things that go on infinitely, such as the number of stars in the universe or the number of times you can cut a rope in half.

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Plus activities teachers can use to help students improve their reading comprehension and understanding of math concepts. Read-aloud time is typically dedicated to building reading comprehension. Sometimes teachers incorporate some social studies ideas, but rarely does math get to be front and center. That should change because math and reading don't exist in separate silos.

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

Research has long linked strong reading skills with improved math achievement -which may seem obvious when it comes to typical math tasks like understanding directions on a test, or parsing word problems.

But literacy skills also support and deepen math understanding in unique and powerful ways.

"Reading and writing are complex, fundamental, integrative learning skills that should be used to their full potential in math class," writes Alessandra King, a middle school math teacher in Bethesda, Maryland. For all students, and especially those who "enjoy reading and writing more than the computational side of math," King says that finding ways to fold literacy into math class gives them "a deeper understanding and stronger appreciation of the usefulness and effectiveness of mathematics."

Blending the disciplines, when the lesson allows for it, also sets students up to "engage with math in a new-and often far more inviting-way," explains educator and tutor Chelsea Miro in an article about math read-alouds. "Kids who have struggled with geometry may love the opportunity to write a shape story, for instance-and it might even help them to remember that a square is a type of rectangle but a rectangle is not a type of square."

Here are six ideas, sourced from teachers and recent research, for merging math and literacy in ways that challenge students' abstract reasoning and build critical thinking and collaborative learning skills.

Explore Picture Books

Early-grade math problems tend to be straightforward and linear-much like the picture books that introduce them to literacy concepts. These shared properties make mathematical reasoning fertile ground for early-grade book authors.

But not all children's books that feature math are created equal. Just like in language arts classes, text selection is important, say educators Kathleen Crawford-McKinney and Asli Özgün-Koca. The trick is to find options that present a rich mathematical problem that students can work through alone or in groups, and then compare their answers to the solution in the book.

In one of their favorite examples, Molly Bang's When Sophie Thinks She Can't, main character Sophie is challenged to form as many different rectangles as possible using 12 tiles. It's a low-threshold, high-ceiling problem, offering a challenge for students across a range of skill levels. For some kids, a related exercise might involve creating their own rectangles using manipulatives and comparing solutions as a class; a more advanced exercise could involve asking them to create squares instead and discussing the differences between shapes.

When designing lessons around picture books, Crawford-McKinney and Özgün-Koca suggest creating content specific questions for students to answer, which will vary by book. But they also favor asking general questions about how math concepts shape the story and how the author establishes this understanding-which can teach students to think more like mathematicians.

For more book ideas, see former elementary school teacher Chelsea Miro's list of favorite books for math read-alouds, including more abstract titles like Kate Hosford's Infinity and Me.

Connect Thinking Through Math Journals

Teachers in subjects like English and science often use journals or logbooks to give students space to record their learning progress, make observations, and brainstorm solutions in a low-stakes format.

In math class, however, the journals might look a little different, explains former high school math teacher Nell McAnelly, who used them often with her students. "It is a record of personal experience showing what a student tried, what worked and what didn't, what practices should be continued, and what improvements a student should focus on going forward," she says. "Consequently, journals can promote initiative and confidence, which we know are gateways to learning."

There's still space for written reflections, but also for illustrations, diagrams and charts-making math journals more formal than scrap paper but less polished than an exam paper.

In her experience, students use them to make connections across mathematical ideas and delve into the reasoning behind their answers-much like they might use a journal to analyze a poem or text in language arts. Entries can also be used as discussion prompts for group work, where students can learn directly from one another as they explore new strategies.

Design Math Magazines That Relate to Real-World Topics

In Alessandra King's math classroom, while writing prompt activities are helpful, she prefers assignments that create strong connections between what students are learning in math class and the real world. "Reading and writing are particularly effective in developing a quantitative understanding of the world around us because they can be used to lead students to reflect on everyday experiences," King writes.

To harness the benefits of reading and writing, King has students create math magazines, collaborative publications that they compile with summaries they've written of math-related articles and images from publications like Scientific American, The Economist, the New York Times' Upshot section, and the Atlantic. It's one of her most popular assignments of the year.

King keeps a thick file of articles she's clipped or printed out that touch on math-related topics-from political gerrymandering to fractals in modern art and using machine learning to predict March Madness upsets-and lets students choose ones that pique their interest. They compose a page-long summary of the piece with special emphasis on the math concepts discussed and package their work with related charts or graphics.

At the end of the assignment, everyone's contributions are compiled into a magazine, and King uses a simple rubric to assess their content understanding, clarity of communication, editing, critical thinking, initiative, and creativity.

Identify and Teach Math Vocabulary

When fifth-grade math teacher Kathleen Palmieri discovered that only about 40 percent of her students could accurately define key math vocabulary (of various levels of complexity), she realized she needed to make learning math terms a regular part of her instruction, Palmieri writes in an article for MiddleWeb.

But rather than simply memorizing a list of words, she found that students needed to understand how the mathematical concept worked before the term itself would stick. In other words, if her students didn't know how fractions work, learning the definition probably wouldn't mean much. Additionally, math concepts typically make the most sense when learned in sequential order.

Drawing on ELA vocabulary building skills, Palmieri began asking students to pull out key terms they don't understand at the beginning of a unit for a math glossary that they add to as they learn each concept. Students also used colorful Post-its to create a math word wall that they add to as they learn new words-and can refer to at any time. Lastly, the class regularly decides on a word of the day or even a word of the week, with students responsible for tallying every time they see the word and describing how it's used.

Identify Patterns and Connections Via Word Sorts

Another strategy inspired by ELA instruction, word sorts can easily be adapted to math class to help students recognize patterns and relationships between words. Working alone or in groups, students identify each term in a given vocabulary list and sort terms into categories-either ones created by the teacher (known as closed sorts) or that they come up with themselves (open sorts).

Word sorts can be implemented using mathematical terms, symbols, or even expressions. Students can sort these based on various attributes-say, operation type (addition, subtraction, multiplication, division), geometric shapes (circle, triangle, square), or algebraic properties (commutative, associative, distributive).

To sort a list of mathematical expressions, kids might separate them based on whether they involve addition, multiplication, or both (e.g., the expression 5𝑥+ 3).

Younger students might perform a similar sort by placing the word "rhombus" into multiple categories, including parallelogram, quadrilateral, and two-dimensional, write Miranda L. Sigmon, Kavin Ming, and Daniel Herring-the authors of a 2022 piece on word sorts for the journal Mathematical Teacher.

To drive meaning home, the authors suggest using sentence stems, such as "I think (insert term) goes under the (category name) category because . . ." -which gets students thinking more about the choices they're making. Model a few examples yourself and split students into small groups to encourage genuine discussion and comprehension.

Encourage Collaboration With Math Circles

Inspired by literature circles, a common practice in ELA, history, and occasionally even science classes, math circles involve assigning roles to students that they perform as part of collaborative work in small groups. The goal is to foster math-related group learning, discussion, and advanced collaboration skills like leadership and flexible thinking.

In Patricia Kridler's middle school math classroom, student roles include Situation Summarizer, Vocabulary Master, Idea Guy/Gal, Model Maker, and Computation Kid, Kridler writes in the journal Mathematics Teaching in the Middle School. Since math topics can vary greatly, she often creates new roles depending on the assignment, and asks groups to complete a role worksheet that includes space for every student to share their contributions. After every cycle, she asks students to swap roles.

At first, she assigns simple word problems and lets students take turns in their roles before moving to more complicated or abstract projects that could take several class periods to complete. Typically, students use the role sheets to explain their thinking and their mathematical reasoning in depth, and the Situation Summarizer presents the findings to the entire class.

Math circles allow Kridler to structure a math task "so that all students get to focus on different aspects of how to solve a problem," she writes. "Students also develop the skills necessary to become better independent thinkers. In the process, I am learning much about how students think through problems."

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6 Ways to Merge Literacy With Mathematics

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

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Online manipulatives bring all of the learning and fun without the mess. Our math virtual manipulatives help students grasp abstract concepts through modeling. Literacy virtual manipulatives create a fun space for practicing spelling, rhyming, and more!

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Virtual Manipulatives | Mathematical Modelling | Toy Theater

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Original teaching tools aimed at supporting teachers in the elementary school classroom. Two color counters, 3D dice, probability spinners, graph builders, fraction bars, base ten blocks, and more!

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Unleash your creativity with the world’s best virtual manipulatives!

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https://www.didax.com/math/virtual-manipulatives.html?srsltid=AfmBOooKwx1p1HbdtoQbUwzG2ecdM8A6L3BCyG9tgZcvDiRGsDB_PSt6

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Hands-On Math Goes Digital In and Beyond the Classroom!

Explore Our Collection of FREE Virtual Manipulatives

From Number Lines to Base Ten, Pattern Blocks to Place Value, Disks our collection of free Virtual Manipulatives gives educators and families access to visual and hands-on digital resources that lead to understanding. Students can use these resources in class and at home to practice math concepts, reinforce their growing math understanding, technology they love in the process.

Free Resources & Instructions for Teachers and Families

We've developed these resources for easy access and easy use:

How-To Videos

There's a short video for each of the Virtual Manipulatives in our collection so teachers can use these digital materials easily and confidently with students.

Watch Now

Activities

Activities from the Didax books that teachers use most for easy download. Engaging challenges address core math operations, concepts and skills, from early numeracy all the way to introductory geometry and algebra.

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FAQ

Download this document of FAQ's to answer your Virtual Manipulative questions.

Access Now

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Demonstrate key math concepts in your classroom using our new virtual manipulatives!

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https://www.youtube.com/watch?v=pINopsETHQc

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How to Create Virtual Math Manipulatives in Google Classroom

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https://www.pearsonassessments.com/en-us/Store/Professional-Assessments/Academic-Learning/Group-Mathematics-Assessment-and-Diagnostic-Evaluation/p/100000692

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Group Mathematics Assessment and Diagnostic Evaluation

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Pinpoint areas where K-12 students need instruction with GMADE, the Group Mathematics Assessment and Diagnostic Evaluation math test of individual skills.

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Math Instruction for English Language Learners

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Several years ago, I met a high school math teacher named Hillary Hansen who had just taught her first Basic Math course for English language learners (ELLs). She wanted so much to provide the students with the good foundation they needed, but she felt unable to engage them in her lessons. By the end of the year, she was exhausted and frustrated.That summer she had an opportunity to join a district Sheltered Instruction Observation Protocol (SIOP) cohort to receive professional development and support the needs of ELLs in content classes. She learned about the importance of language acquisition, building background knowledge, increasing student language production, and explicitly teaching academic language. She began the following school year with a new set of tools and a deeper understanding of the instructional scaffolding ELLs need in order to learn the content while also learning English.While Hillary still felt challenged and was working hard, the second year was much more successful for her and her students. She felt she was providing them with the foundation they needed not only to understand the mathematical concepts, but also to successfully interact within a math classroom in order to learn more advanced concepts.As a result of more effective instruction, her students:Understood the content better and were working together to find creative ways to learnIncreased their participation in discussions and learned how to use instructional supports in the classFelt more comfortable with math and asking questions to get the help they neededYou can learn more about some strategies that Hillary and other teachers recommend for teaching ELLs math in the information below, along with reflection tips and ideas for getting to know your students’ math backgrounds.ELL Math Resource CollectionThis resource collection features several ideas for teaching math to ELLs.Reflection QuestionsHow much math instruction have your ELLs received in their prior schooling?How much do their levels of math background vary?What are some of their strengths related to math?What are some of their challenges?What are some practical ways your ELLs are using math in their daily lives?What kinds of strategies have supported their success or engagement in other areas?What are some ways that collaboration or co-teaching might support your ELLs?What are some leadership opportunities you might give ELLs in pair work or small group work?Learn About Students’ Math BackgroundsTeaching ELLs: Tips for Math TeachersPrint PDF >It’s important to remember that ELLs’ math backgrounds may vary significantly. Some students may have had consistent schooling where they developed strong math skills. Others may have limited or no formal schooling, but may have practical skills related to time, money, or other daily topics. If possible, find out whether students have attended school regularly and what kind of experience they have had with math instruction and with math in general. Look for ways to tie instruction to student interests (like sports) and responsibilities at home that involve math, such as helping with family finances, working in family businesses, and holding other jobs. For example, students from migrant farmworker families may be using math related to agriculture, such as weighing or selling produce. Also keep in mind that students may use other numeric and measurement systems students, such as metric system, Celsius, military time, etc.In addition, Pennsylvania educators Sally Lopez and Erin Minick also encourage educators to:Look for leadership opportunities for all students in math classProvide students with opportunities to “teach” others, work together, and demonstrate what they know in multiple waysGroup students intentionally and with sensitivity, avoiding the designation of specific students as “needing more help” in their grouping, partner assignments, or placement in the classroom(Ms. Lopez and Ms. Minick conducted a book study focused on Teaching Math to Multilingual Students, which you can learn more about from their website.)Keep in mind that veteran educators of ELLs also stress the importance of getting to know students as a key part of supporting student success. For example, in this NCELA webinar, Dr. Haiwen Chu, a national expert on mathematics education for English Learners at WestEd, recalls that visiting his high school students’ neighborhoods provided valuable insights on their experiences and familiar topics.See additional ideas for getting to you know your ELLs in 10 Strategies for Building Relationships with ELLs.The Language of MathAlthough it is easy to assume that many ELLs will excel in math class because math is a “universal language” and students may have had prior educational experience that included mathematical instruction, that assumption can lead educators astray. While computational skills may transfer, ELLs may still need support with language-focused tasks, such as solving word problems, learning (and using) math vocabulary, and writing explanations. All of these skills require a language proficiency that sometimes exceeds our expectations. We tend to think of mathematics as a subject that does not require a strong command of language. In reality, however, mathematical reasoning and problem solving are closely linked to language and rely upon a firm understanding of basic math vocabulary (Dale & Cuevas, 1992; Jarret, 1999), especially when considered along with the demands of college- and career-ready standards.Co-Teaching and CollaborationFor many educators, the challenge of bringing language and math instruction together is a relatively new one. ELL teachers who hadn’t taught content areas previously are now being asked to lead or support instruction in the math classroom, and many math teachers who don’t see themselves as language instructors are now responsible for providing effective math instruction to ELLs. When educators collaborate, however, they can better understand each other’s expertise and combine their expertise for the benefit of students.For example, when planning a lesson, a math teacher and an ELL teacher could collaborate to identify both the target content, such as key standards, concepts, or specific topics, as well as key vocabulary, academic language, and the language-focused tasks students will need to complete the lesson. These tasks might include writing out a proof, reading a math problem, explaining how to solve a problem, or writing out numbers as words. The ELL specialist could walk the math teacher through this process several times so that it becomes a more integrated part of the math teacher’s planning over time. After the lesson, the teachers could identify other areas of focus or clarification needed and share these insights with their colleagues.Another tool content teachers can use is language objectives, which help target the language demands of the lesson. You can learn more about them in the videos featuring Mr. Jesus Ortiz below.Teaching Academic VocabularyVocabulary instruction is essential for effective math instruction. Not only does it include teaching math-specific terms such as “percent” or “decimal,” but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word, as well as understanding the concept a vocabulary word describes.The following example, used in a presentation by Dr. Judit Moschkovich of the University of California at Santa Cruz, underscores why vocabulary must be introduced within the context of the content (Moschkovich, 2008): In this problem, the student is instructed to “find x.” The student obviously knew the meaning of the word “find” because they “found” it on the page and circled it. The student even put a note on the page to help the teacher in locating the lost “x”. The student understood the meaning of “find” in one context, but not in the appropriate mathematical context.I recently helped a math teacher create a sheltered lesson, and I was surprised to find that there were some vocabulary words that I didn’t understand. My lack of familiarity with the words hindered my ability to do the math problem and gave me a deeper empathy for ELLs who struggle in the same way with vocabulary and comprehending math assignments.Following is a list of tips for explicitly teaching mathematical academic vocabulary.Teach key academic vocabularyAfter you identify your target content, identify the academic vocabulary words that students will need to understand that content. Some of these key phrases or new vocabulary words may also be helpful to pre-teach in small groups or mini lessons. Think about:Academic vocabulary (equilateral)Words and phrases needed to solve a problem (less than, given, arrange)Common words needed to solve word problems (train station, dolphin, favorite)Homophones (eight/ate, plane/plain, one/won, two/to/too, four/for, some/sum)Words that students are likely to encounter in other settings (formula, prove)Words that represent a numerical value necessary for solving the problem, such as measurement words (foot, feet, meter, pounds, kilometers)After you identify the vocabulary you wish to teach, use scaffolds for academic vocabulary, such as: Visuals: These can include visual representations of concepts, photos, and illustrations of key vocabulary words, posters, and number lines.Realia (real objects) and manipulatives: These might include hands-on objects related to a topic or small items, such as coins or small blocks for counting, sorting, weighing, etc.Graphic organizers: Graphic organizers are tools that allow students to organize information in a visual or hands-on way.Anchor charts: Anchor charts are posters that students and teachers co-create to highlight key concepts and vocabulary that students will need for reference.Offer students the chance to work with objects and images in order to master vocabulary. If there aren’t enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students. For example, Hillary created a Math Word Wall that has three parts: key vocabulary, “in your own words” definitions, and a variety of ways to portray a function. For example, multiplication is portrayed by the following symbols: x, *, and ( ).In addition, it can be helpful to ask students which strategies support their learning. Students often can provide valuable information on what is working for them!For examples of how vocabulary can impact students’ understanding of math problems, see the related video with ESL teacher Anne Formato below.Teach words with multiple meaningsDemonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words, as well as how to use them correctly in a mathematical context. This is also a good opportunity for using visuals and realia. Examples include:YardPlotTableProofAreaEvenPlanePlaceTimesBillQuarterChangeDraw on students’ home languagesUse cognates, which are related words in two languages. English and Spanish have many cognates within academic terms, like fraction/fracción.Use translated words or phrases strategically. For example, New York University has published bilingual glossaries for several topics.Allow (and encourage!) students to use their languages in group work to solve problems, brainstorm, and review material. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language.Increasing Student Language ProductionThe language demands of math are complex. Working with an ELL specialist can be a good starting point for identifying some of the math demands of the lessons you are teaching, as well as for planning how to teach and scaffold those language demands.As I’ve worked with content area teachers in my district to develop Sheltered Instruction lessons and activities to enhance ELL learning, I’ve told them, “If a student doesn’t say it in your class, they’re never going to say it.” This is a bit dramatic, but it’s true to some extent. When students learn new vocabulary, the opportunity to use it must be presented in class, because students are unlikely to try it out on their own — especially academic words like “parallelogram” or “function”!Here are some tips to increase student-to-student interaction with academic language in the math classroom:Have students translate symbols into words, and write the sentence out. Hillary used this strategy to check students’ comprehension of problems before they solved them. For example, 3x + 4 = 16 would be written out, “Three times X plus four equals sixteen.” This helps students process the operations involved in the question and gives them an opportunity to think through how to solve it. It also gives students a chance to familiarize themselves with important vocabulary words. Writing out the answer to a problem is a very important skill to develop because many state math tests require a constructed response to questions.Create a “sentence frame” and post it on the board. Write the format of the sentence you would like students to use in discussion and then hold them accountable for using it. For example, “The answer is _______ degrees because it is a _________ triangle. (Learn more in our sentence frame and sentence stems strategy.)Have students share problem-solving strategies. This involves asking a simple question, such as, “Did anyone else get the answer in a different way?” Then allow enough wait time so students can think through how their problem-solving process was similar or different to the one offered.Allow students to discuss how they are thinking about math. This is a way of redirecting the lesson from teacher-to-student to student-to-student. For example a student might ask a question, “How do you know what kind of triangle it is?” Instead of the teacher answering and going to the board and pointing out the names and different triangles, the teacher can simply ask, “Does someone have an answer? Or “Would someone like to offer help to Mario?” Allow students to share how they think about the math concept and any tips they have for remembering the information.Incorporate writing activities, such as entrance/exit tickets or math journals. This is an excellent way for students to process what they’ve learned and what questions they still have. The journal or exit/entrance ticket prompt could start with simple prompts such as, “One thing I learned today...” “One thing I still don’t understand…” “One way I can get the help I need…” “The answer to this problem is…” “Something that helped me was...“Challenge students to create their own math problems. This can be a fun activity if students create a problem similar to the ones you have used in class and they exchange problems with a partner. By creating the problem and checking the answer they are reinforcing their own learning.Teach students how to read, interpret, and summarize data. Provide students with explicit, step-by-step instructions in how to read charts, graphs, tables, and infographics, as well as how to describe what they observe in visual representations of data.Model the kinds of writing students are expected to complete (e.g., written explanations). Students need to see and understand what they are expected to do and produce, such as explaining how they solved a math problem. This is a great opportunity for the “gradual release” strategy -- I do, we do, you do.Try AI tools. Consider using AI tools to rewrite math problems for students at early levels of proficiency or to generate math problems with familiar vocabulary that achieve your target objective. Bilingual Glossaries in Content AreasNew York University has published several bilingual glossaries in multiple languages that cover different content areas, including elementary math, middle school math, Algebra 1 and 2, Calculus, and related math terms.Reading and Understanding Written Math ProblemsWritten word problems present a unique challenge to ELL students and teachers alike. In Reading and Understanding Written Math Problems, Brenda Krick-Morales writes, “Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation — ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered” (Bernardo, 2005).Teacher Xiao-lin Yin-Croft has encountered this pattern in her classroom of bilingual Chinese students in San Francisco. She has developed a very creative way to use her students’ background knowledge of math as a stepping stone for other language learning. She does this by accelerating math instruction at the beginning of the school year and then building on what students have learned in math in reading and other content areas. In Building Bridges for the Future, Xiao-lin explains her strategy:First, we read math word problems; I demonstrate the logical thinking process while translating words into pictures and, finally, into number sentences. Soon, they start to explain their own thinking after reading complicated word problems that involve several steps. They correct each other and argue about which number sentences they should use to arrive at the correct final results. As they sharpen their math skills, I capitalize on their enthusiasm to teach them how to extract the most important information from texts, and move them toward the oral and reading fluency they need to understand and discuss more challenging texts.Even if you aren’t accelerating math instruction, however, there are a number of ways to help students master word problems. Krick-Morales offers suggestions in the previously mentioned article, such as explicit instruction of key vocabulary, daily practice of problem solving, repeated readings of the word problem together as a class, and hands-on activities such as movement, experiments, or drawing to help students comprehend the problem. As students become more familiar with math vocabulary, they will be able to solve problems more easily.Identify key background knowledge in math problemsIt’s important to identify what kinds of background knowledge students will need to understand a math problem. For example, Ms. Lopez and Ms. Minick used this activity with a conference session: Ms. Lopez chose four math problems from her son’s math textbook and asked session attendees to brainstorm the kinds of background knowledge students might have questions about, some of which were relevant to solving the problem and some of which weren’t. Here are some things that attendees came up with:A math problem about a coupon and sales tax at a dog groomer: What is a dog groomer? Why do people take their dogs to get groomed? What is sales tax? What is a coupon? What is “deluxe”? What is an estimate and a discount?A math problem about people receiving a voucher for a free water bottle at a football game: Is football different from soccer? What is a voucher? Does the water bottle come with water inside it?A math problem about a fishing pole on sale: What is “percent off”? What is a sale? What is “regularly priced”? What steps have to be followed to solve this problem?A math problem about calculating a tip in a restaurant: What does “leave a tip” mean? What is a tip? Does the fact that there are four sisters (Emilia and three sisters) impact the outcome of the problem? Why aren’t they using an app like Venmo?As seen from the example above, this can be a powerful area in which math teachers and ELL teachers can collaborate.The Role of Background KnowledgeWhen it comes to background knowledge that impacts students’ understanding of new concepts, students may have relevant experiences to what you are teaching that just need to be drawn out (as in the vignette below). In other cases, students may not have the needed background knowledge. My colleague Hillary found that sometimes her students would get “lost” in a problem simply because they didn’t understand the context. Following are some tips to help in tapping into and building background knowledge of students.Identify connections to your students’ experiences. When planning the lesson, consider whether they might have relevant experiences, and as you introduce the lesson, find out what they know, giving them an opportunity to make connections. They may come up with connections you never had imagined!Modify the linguistic complexity of language and rephrase math problems. Students will understand the problem better if it is stated in shorter sentences and in language they understand. This may be an area in which you wish to experiment with AI tools that can rewrite problems.Guide students to cross out the unnecessary vocabulary in word problems. Doing so allows students to focus on the math function required. For example, one problem Hillary’s students came across referred to a “school assembly.” Even though the meaning of that phrase wasn’t important in the solving of the math problem, students didn’t know it wasn’t important, and the lack of understanding contributed to their confusion.Build knowledge from real world examples. Try to reinforce concepts with examples that students can picture and talk students through the situation. For example, if you need to paint a room, you need to know how much area will be covered so that you know how much paint to buy. Look for familiar ideas or props that can be used to engage students such as recipes, news stories about the economy, or discussion of personal spending habits.Use manipulatives purposefully. This is important at all grade levels. Hillary has found math cubes to be very useful in having students represent the numbers in the problems and then manipulate the cubes to get the answer. She used the cubes and the terms “hot” and “cold” numbers when teaching with the concept of negative numbers. Students would use the red cubes as “hot” or positive numbers and the blue cubes as “cold” or negative numbers. As students laid out the number of hot cubes and cold cubes represented, they could easily see if the answer would be a positive or negative number by which color had the most cubes. A problem such as -2 + 1 = -1 would look like this: The student then removed pairs of cubes — one red, one blue — until they could no longer remove any blocks. The remaining blocks represent the answer. Classroom vignette: A moment of humilityA middle school math teacher was trying to teach points on a grid and vertical/horizontal axis to her ESL students, three boys from Vietnam. She tried many approaches, including visuals, games, simulations, and manipulatives, and was just about to give up after very little progress. Suddenly, a student said, “Oh, I know — same same you drive a boat!” (“The same as you drive a boat!”) It turns out the child had helped his uncle use the stars to navigate a raft when they were fleeing Vietnam and trying to reach refugee camps in Thailand. He explained the concept to the other boys in Vietnamese with gestures and drawings on the board, who knew exactly what he was talking about. The teacher reflected, “I felt so humble. These boys knew a lot more about math than I had given them credit for. I had failed to activate their prior knowledge, and in the process had almost given up.“Source: This vignette is presented in Chapter 4 of Special Education Considerations for English Learners: Delivering a Continuum of Services. Using TechnologyTechnology can also be a powerful tool in math instruction for ELLs. Here are some ways you can play with technology in a math lesson:Look for educational resources that accompany your school’s technology tools and programs. There may be online or software programs available for teachers. For teachers who have an electronic whiteboard in the classroom, there are many resources available on links that can be easily accessed and brought into the classroom.Find out what’s available online. Both PBS Learning Media and Vital NY (Video Teaching and Learning for NYS Educators) on Teachers’ Domain offers an online library of free public media resources. Teachers’ Domain resources include video and audio segments, Flash interactives, images, documents, lesson plans for teachers, and student-oriented activities. (Free registration required.)If students are using a calculator or other device, ensure that they learn how to use it. Based on background and prior educational experience, students might not be familiar with how to use a calculator, graphing calculator, or math apps on devices such as phones or tablets. Give students a chance to practice solving problems with their calculators once you have reviewed different functions. Texas Instruments offers numerous activities and product tutorials in their educational materials.Learn more about how to use AI tools in math. AI tools can be used to generate, differentiate, or rewrite a math problem; create a summary of a lesson plan; and many other tasks. Keep in mind that AI-generated content always need a careful review and edit. (See more in Using AI in Math from Edutopia.)Look for interactive games that offer students a chance to practice their mathematical skills. Nintendo DS has an educational game called Brain Age, which is not language specific. The game provides excellent mathematical training for numbers and tracks results, showing student improvement over time.Books About Math and MathematiciansIn addition, there are lots of books about math and mathematicians that you can incorporate into your classroom and classroom library. You can see a wide range of titles for different ages in our Math Resource Collection.Closing ThoughtsEven if it doesn’t come easily at first, there are ways to get ELLs excited about math. By keeping their language skills and needs in mind when planning mathematical instruction (and by helping your colleagues do the same), you will be taking important steps in helping students master mathematical concepts and skills. You never know — your students may be the next generation of economists, rocket scientists, and math teachers just waiting for the tools they need! Note: I’d like to thank my Minnesota colleagues, Hillary Hansen at Burnsville Senior High School and Kim Olson at Hidden Valley Elementary, as well as Xiao-lin Yin-Croft from San Francisco, for providing many of the helpful math teaching tips in this article. It is inspiring to know that there are talented, creative teachers who are always finding better ways to teach and are willing to share the knowledge.Related VideosHow vocabulary can get in the way of solving a word problemELL Specialist Anne Formato talks about the trouble a student had in understanding a written math problem based on a vocabulary word. Teacher Alejandra Rojas: Why cognates are your “best friend” in math classElementary teacher Alejandra Rojas, who teaches in a dual-immersion program, explains why cognates support vocabulary development in her Spanish-language math class. Teacher Alejandra Rojas: When bilingual students translate for their parentsAlejandra Rojas, a teacher at a dual-immersion school in Arlington, VA, shares some of her experiences as a child and teenager translating for her mother. How to Write Language Objectives: Tips for ELL EducatorsIn this video from Syracuse, NY, Jesus Ortiz, a bilingual teacher, learns how to write a language objective from Areli Schermerhorn, a peer evaluator with expertise in ELL and bilingual education. Teacher Observation Cycle: A Math Lesson on PictographsThis video highlights Mr. Ortiz’s math lesson on pictographs. While the main topic of the video is teacher evaluation, numerous best practices and strategies related to math instruction for ELLs are mentioned in the video. Recommended ResourcesNCELA Teaching Practice Brief: Math (A related podcast is available as well)Supporting English Learners in Math and Science: Effective Instructional Practices and Examples from NCELA’s Teaching Briefs PBS Learning Media: Math LessonsEngageNY: Common Core and MathCommon Core Math and ELLs: Blog PostsDiscovery Education: PuzzlemakerCatherine Snow: Word Generation SMART Notebook Lesson ActivitiesTranslating Word ProblemsColorín Colorado Webcast: English Language Learners in Middle and High School

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Assessment is at the heart of our teaching practice. We use backward planning and start with the end in mind. We ask ourselves questions like, "what do we want our students to know?" and "what will our students be able to do?" Because assessment is so important, it's no surprise that there are a ton of tech tools for assessment. Trying to find what you're looking for is time-consuming! That's why we've picked the ten best tech tools for student assessment, keeping your goals in mind.

Goal: I want to find out what my students learned

I wish we could read students' minds, but since we can't, we use exit tickets. If you rely on this best practice to plan your next instructional move, you have a lot of options. I love Google or Microsoft Forms. They are easy to use, and you can create multiple choice or short answer questions for students to complete. All the data is there for you.

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Goal: I want to hear from my students and watch them share what they've learned

Flipgrid is a social media-style video discussion platform great for generating class discussion around topics, videos, or links posted to the class grid. Students can video record their responses to share with the teacher or class. It's a great tool for supporting your students to make their thinking visible.

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Goal: I want to do a quick check in during my lesson

Mentimeter lets you add polls, word clouds, Q&As, and more to presentations and create an interactive experience for students, who can vote on/respond to questions and engage with the presentation in real time. This made our list because there's so much variety in the types of formative assessments you can give in real time.

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Goal: I want to see my students' thought process and their answer

Jamboard is a digital whiteboard that is compatible with the GSuite services. It's a game changer for emphasizing the process of learning over the product. Math teachers love how students solve and explain their solution. If you don't use Google, Padlet is our runner up.

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Goal: I want to listen to my students' read to assess fluency

Students read aloud and answer questions on their device (almost any device works). Within 24 hours, you get a running record with scores for accuracy, fluency, and comprehension. A free basic account includes 10 reading assessments/month.

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Goal: I want to include checks for understanding as my students learn

EdPuzzle is a video editor that allows both teachers and students to add voice-overs, comments, resources, and quizzes to existing or self-created online videos. Best part? All the students' answers are gathered for you so you can quickly assess.

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Goal: I want to put checks for understanding in my slides

Pear Deck is an interactive presentation and lesson delivery tool. Students use their devices to follow along with the teacher's slideshow on a classroom screen. Throughout, teachers can pause at points where they've added interactive questions and collect real-time data about student understanding.

Goal: I want my students to give each other feedback

Once you set up your assignment, pick a feedback rubric (or create your own), and select your assignment. Your students take it from there. They submit work, review each others', and then act on the feedback. Best part? There's a teacher overview where you can see it all.

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Goal: I want to give a quiz or test

There are a lot of options with this tool. You can include multiple choice, true/false, and short answer questions. I love how you see students' results in real time, and you can add explanations if students get a question wrong. Students can get instant feedback, or you can make the quiz self-paced or lead it yourself. My favorite feature: Space Race, a group quiz where students "race" to cross the finish line.

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Goal: I want grading to take less time

No matter what grade and subject you teach, grading takes time that we don't have. Enter Floop. This tool is a cloud-based website where students get annotated feedback from you and their classmates. Using any internet-connected device, students upload images of an assignment to the platform, and you put markers in places where you want feedback. Students are able to see and respond to comments, creating a feedback loop.

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Goal: I want one tool that does different types of assessment

Spiral is a free suite of four apps. Use Quickfire to give a formative assessment in real time and hear from all of your students. Discuss makes your slides more interactive for students. Team Up supports student collaboration, and Clip turns public-facing videos into a live chat with questions and quizzes.

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Plus, check out 50 Free Seesaw Activities and Resources For Every Kind of Classroom

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The 10 Best Tech Tools for Student Assessment

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Assessment is at the heart of our teaching practice. We use backward planning and start with the end in mind. We ask ourselves questions like, "what do we want our students to know?" and "what will our students be able to do?"

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To make word problems less confusing, especially for English language learners, change the language, not the math. Here are some ideas.

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English Learners (EL) Academic Language Function Toolkit | Missouri Department of Elementary and Secondary Education

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205 Jefferson St.
Jefferson City, MO 65101Map(link is external)

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The widely adopted ISTE Standards provide a framework for educators to create high-impact, sustainable and scalable learning experiences for all students.

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Ensuring that the technology we bring into math classes fosters active engagement is key.

Incorporating technology in mathematics classrooms enables educators to craft powerful collaborative learning experiences that support problem solving and flexible thinking. With strategic integration of both content-specific and content-neutral technology, students and teachers can construct their learning together in authentic ways that elevate mathematics learning.

Until recently, one of educators' primary concerns around educational technology was the lack of access that existed in many American schools. That gap has decreased, but a new digital divide has emerged: The updated 2017 National Education Technology Plan explains that in today's classrooms many students are using technology as a tool for passive learning rather than engaging in active learning experiences that promote student agency.

The Importance of Content-Specific Pedagogy

In order to create technology-infused experiences that support active mathematics learning, educators must of course have pedagogical content knowledge (PCK)-an understanding of best practices specific to mathematics.

One method a teacher can use to analyze the effectiveness of technology integration is the Technological Pedagogical Content Knowledge (TPACK) framework. This tool supports careful educator reflection on pedagogy, content, and technology not only as separate entities but as overlapping and intersecting domains.
Reproduced by permission of the publisher, ©2012 by tpack.org
For example, when planning to integrate technology into a lesson, educators can take into account the technology knowledge the students will need, the mathematics content knowledge they'll need, and the best practices for teaching both the technology and the math. This process is extremely important because without it, the technology may be integrated in a way that is pedagogically inappropriate for mathematics instruction.

Using PCK to Spot Unhealthy Apps and Websites

Teachers start from their understanding of PCK, or best practices for mathematics instruction, in choosing effective technology tools for the mathematics classroom. We know that mathematics should not be focused on speed or quick answer finding. And timed fact testing is a known trigger of math anxiety, which can lead to low mathematics achievement and mathematics avoidance. Yet math apps and websites that focus on speed and rote memorization are readily available and widely used.

This use of technology can promote fear and stress, and it also sends inaccurate messages about the purpose of mathematics. Math is about thinking deeply, discovering patterns, and making connections. Automaticity with math facts and math skills is critical, but how we get students to automaticity matters. A focus on memorization without understanding promotes a joyless, nonsensical form of mathematics that requires remembering a large amount of seemingly disconnected information.

In addition, technology that simply transfers a gradual release-the "I do, we do, you do" structure-to an online format is a form of passive learning that strips math of student agency and rigor. Although gradually releasing responsibility is an effective model in other content areas, in mathematics this model is best flipped to give students the agency to decide what strategies they want to use and how they might solve a problem.

That's because students should productively struggle with math. We need them to problem solve rather than learn to repeat a specific list of procedures given by the teacher. Problem solving skills are more valuable than memorization, and they're the true work of mathematicians. If we're integrating technology into our classrooms to engage students in real-world experiences, our students must be given opportunities to do real mathematics.

Technology That Fosters Deep Mathematical Thinking

When used appropriately, both content-specific and content-neutral technology can be effective in the math classroom. Research indicates that content-specific apps and websites that focus on math learning with the use of virtual manipulatives are highly effective, and in some cases more efficient than physical manipulatives.

The Math Learning Center, for example, provides several manipulative options, such as rekenreks, geoboards, number lines, and number frames. Apps and websites that provide these types of virtual tools are easy to use, support students with conceptual understanding, and increase student access to math tools.

Content-neutral technology includes tools such as virtual whiteboards, handheld clickers, and student collaboration apps. Virtual whiteboard and websites, such as Explain Everything, promote self reflection, enable students to make their learning visible and share and connect ideas, and have been linked with high-level student thinking and teacher questioning.

But content-neutral technology that promotes fast answering, such as handheld clickers, is associated with decreased cognitive demand, most likely due to the likelihood of being used with minimal student discourse.

Being a Critical Consumer of Technology

The educational technology market is flooded with new apps, tech tools, and gadgets, and in some instances, teachers are commended for increased technology use whether it supports healthy math learning or not. Technology can have a truly positive impact on student learning, but it should not replace teaching or ignore research-based best practices for math instruction.

If we believe that students of mathematics need opportunities for discussing math, creating and connecting visuals, analyzing models, discovering patterns, and making generalizations, the technology that we introduce into our classrooms should match those values.

There was a time when simply getting technology into the hands of our students was a goal, but the time has come to slow down and plan for technology integration that truly supports healthy and productive mathematics learning.

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Ensuring that the technology we bring into math classes fosters active engagement is key.

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Technology Integration in a Science Classroom: Preservice Teachers’ Perceptions - Journal of Science Education and Technology

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The challenge of preparing students for the information age has prompted administrators to increase technology in the public schools. Yet despite the increased availability of technology in schools, few teachers are integrating technology for instructional purposes. Preservice teachers must be equipped with adequate content knowledge of technology to create an advantageous learning experience in science classrooms. To understand preservice teachers’ conceptions of technology integration, this research study explored 15 elementary science methods students’ definitions of technology and their attitudes toward incorporating technology into their teaching. The phenomenological study took place in a science methods course that was based on a constructivist approach to teaching and learning science through science activities and class discussions, with an emphasis on a teacher beliefs framework. Data were collected throughout the semester, including an open-ended pre/post-technology integration survey, lesson plans, and reflections on activities conducted throughout the course. Through a qualitative analysis, we identified improvements in students’ technology definitions, increased technology incorporation into science lesson plans, and favorable attitudes toward technology integration in science teaching after instruction. This research project demonstrates that positive changes in beliefs and behaviors relating to technology integration in science instruction among preservice teachers are possible through explicit instruction.

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Integration of Science, Technology and Engineering

www.youtube.com › watch

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Engineering Integration

Smithsonian Science Education Center |

https://ssec.si.edu › engineering-integration

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April 2024 Editor's Pick

Students reinforce their knowledge that DNA is the genetic material for all living things by modeling it using toothpicks and gumdrops that represent the four biochemicals (adenine, thiamine, guanine, and cytosine) that pair with each other in a specific pattern, making ...

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Ignite STEM learning in K-12 - TeachEngineering

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Free, K-12, NGSS standards-aligned STEM lessons and hands-on activities for teaching elementary, middle and high school science, engineering design and math. Search by concepts or specific Next Generation Science Standards (NGSS) to Ignite STEM learning in K-12.

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Engineering is a systematic and often iterative approach to designing objects, processes, and systems to meet human needs and wants (National Assessment Governing Board, 2010). It’s important for students to understand how science can be utilized to solve real-world problems through engineering. Students have ample opportunities to build their engineering design skills throughout Smithsonian Science for the Classroom.

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Science Manipulatives " Toy Theater | Learn * Create * Play

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Over 1.1 billion simulations delivered

160interactive simulations

97language translations

3001teacher-submitted lessons

Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. PhET sims are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery.

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Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. PhET sims are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery.

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Interactive STEM Simulations & Virtual Labs | Gizmos

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Unlock STEM potential with our 550+ virtual labs and interactive math and science simulations. Discover engaging activities and STEM lessons with Gizmos!

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Best Virtual Science Tools - Proximity Learning

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Explore how Proximity Learning brings hands-on science to online classrooms with interactive experiments and real-time engagement for K–12 success today.

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5 Math Formative Assessment Examples That Work Wonders! | ClassPoint

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Explore these 5 innovative Math Formative Assessment Examples and Techniques to transform the way you teach and conduct assessments in your math classes!

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Resources for Implementing Three-Dimensional Science Assessments
As educators, districts, and states implement new science standards, they are faced with creating and implementing new three-dimensional assessments to help monitor student progress and provide feedback to students, parents, and teachers. Achieve has worked with teachers, states, and researchers to develop a variety of tools and resources to help design and implement assessments that are worth students' and teachers' time.
Task Annotation Project in Science: The Task Annotation Project in Science (TAPS) was launched to provide an answer to the questions "what does it look like to ask students to demonstrate progress toward three-dimensional standards?" and "what are the most important features of high-quality science tasks?" This suite of resources includes annotated examples of assessment tasks for elementary, middle, and high school as well as a series of short resources that highlight the major takeaways across the whole project.

Tennessee District Science Network Task Library: In early 2019, NextGenScience launched the Tennessee District Science Network (TDSciN), a group of six districts in Tennessee working collaboratively to improve their science programs and move towards the vision of science education reflected in the Tennessee Academic Standards for Science. As part of this work, teachers from each district collaborated in cross-district educator workgroups to develop a library of assessment tasks. These tasks and accompanying resources can deepen educators' understanding of classroom tasks that measure student proficiency in today's science standards.

Science Cognitive Complexity Framework: This framework offers a new approach to capturing and communicating the complexity of summative assessment items and tasks designed for three-dimensional standards. The complexity framework can be used to assess the degree to which an assessment task asks students to intellectually engage in and make use of disciplinary core ideas, science and engineering practices, and cross-cutting concepts in service of sense-making. The new framework allows for both the analysis of individual items or tasks and the holistic analysis of multi-component tasks or item clusters.

A recording of an introductory webinar on the science framework is available here.

Science Assessment Criteria: This document describes the most important features of statewide summative assessments designed for three-dimensional standards based on A Framework for K-12 Science Education, such as the NGSS.

Science Assessment Task Screening Tools: These two tools are intended to assist educators in evaluating science assessment tasks to determine whether they are designed for three-dimensional science standards based on the Framework for K-12 Science Education, such as the Next Generation Science Standards.

Transforming Science Assessment: Challenges and Recommendations for States: This brief describes some key challenges associated with developing assessments for new three-dimensional science standards and recommendations for states to consider.

Transforming Science Assessment: Systems for Innovation: This series of resources is designed to provide state education leaders with 1) information about how states are currently pursuing statewide assessment systems in science; 2) analyses of what features influence different approaches, with an eye to supporting state leaders as they make their own decisions regarding science assessment systems; 3) detailed state profiles that highlight how and why some states have made decisions regarding designing and enacting different examples of systems of assessment; and 4) a how-to guide for policymakers looking to enact systems of assessment in science.

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As educators, districts, and states implement new science standards, they are faced with creating and implementing new three-dimensional assessments to help monitor student progress and provide feedback to students, parents, and teachers. Achieve has worked with teachers, states, and researchers to develop a variety of tools and resources to help design and implement assessments that are worth students' and teachers' time.

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These two tools are intended to assist educators in evaluating science assessment tasks to determine whether they are designed for three-dimensional science standards based on the Framework for K-12 Science Education, such as the Next Generation Science Standards.

The Science Task Prescreen can be used to conduct a quick review of assessment tasks to identify any "red flags" - challenges commonly found in science assessment tasks - and determine whether a task is worth diving into more deeply.

The Science Task Screener is used to take that deeper dive into evaluating science assessment tasks. The purpose of the Science Task Screener is

1. to determine whether classroom assessment tasks are high quality, designed to elicit evidence of three-dimensional performances, and designed to support the purpose for which they will be used; and

2. to provide a group of reviewers with a common set of features to ground conversations about what it "looks like" for students to demonstrate the kinds of performances expected by three-dimensional standards.

The Screener builds off the criteria in Category III of the EQuIP Rubric for Science by more clearly specifying features for the assessment tasks embedded in lessons and units.

An FAQ about the Science Task Prescreen and Screener is available here.

If you have questions or are interested in professional development opportunities related to evaluating science assessment tasks, please contact nextgenscience@wested.org.

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These two tools are intended to assist educators in evaluating science assessment tasks to determine whether they are designed for three-dimensional science standards based on the Framework for K-12 Science Education, such as the Next Generation Science Standards.

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As states and districts across the country have begun to implement new science standards in classrooms, they have turned to the question of how to best assess student learning in order to provide actionable information to student, teachers, and families. The criteria described here are intended to be a useful resource for anyone developing and/or evaluating statewide summative assessments aligned to their Framework-based three-dimensional science standards. The criteria balance the requirements of statewide summative assessments with the vision represented by new science standards by focusing on the most important shifts and innovations and defining qualities of three-dimensional learning and performance.

Each criterion includes a high-level summary of what it is included as well as detailed descriptors of what kind of evidence developers can provide and evaluators can look at to make judgements about how well a given statewide summative assessment represents three-dimensional science standards.

Achieve developed this document with extensive input from experts and practitioners in the science and assessment fields. It is grounded in our collective and evolving understanding of how best to assess multi-dimensional standards, in the research that defines what all students should know and be able to do in science, and in lessons learned from early state processes in developing three-dimensional assessments. Regardless of each state's approach, this document is intended to be a useful resource for anyone developing and/or evaluating statewide summative assessments aligned to their Framework-based three-dimensional science standards.

Download the criteria here, and find the FAQs here.

Provide feedback on the criteria
The criteria represent the collective input, guidance, and efforts of many states, science education researchers, and assessment experts across the country. As their work continues, subsequent versions of the criteria will build on and incorporate their experience and be updated to include examples and scoring guidance. States, practitioners, researchers, and assessment developers are invited to share feedback and suggestions for how to improve subsequent versions of the criteria by emailing ngss@achieve.org and including "Assessment Criteria" in the subject line.

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Criteria for Procuring and Evaluating High-Quality and Aligned Summative Science Assessments

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As states and districts across the country have begun to implement new science standards in classrooms, they have turned to the question of how to best assess student learning in order to provide actionable information to student, teachers, and families.