# data[].attributes.body
Math Common Core Standards

# data[].attributes.body
Syllabus

# data[].attributes.body
Math Lesson Plan Template

# data[].attributes.body
Lesson Plan Info-Class Profile

# data[].attributes.body
Lesson Plan Info-Student Groups

# data[].attributes.body
First Day (May 7th)

# data[].attributes.body
ELD Standards

# data[].attributes.body
Lesson Plan Info-Gradebook

# data[].attributes.body
Math Instructional Strategies

# data[].attributes.body
Information on Math Assessments

# data[].attributes.body
How to Read the Next Generation Science Standards

# data[].attributes.attachment_link.title
How to Read the Next Generation Science Standards

# data[].attributes.body
Grade 1 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 2 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 3 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 4 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 5 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 6 Science Disciplinary Core Ideas

# data[].attributes.body
Grade 6 Earth/Space Science Disciplinary Core Ideas

# data[].attributes.body
Assessment Types

# data[].attributes.body
Math Assessment Commentary (edTPA Task 4)

# data[].attributes.attachment_link.title
Math Assessment Commentary (edTPA Task 4)

# data[].attributes.attachment_link.description
EdTPA Task 4 Students: Number Three, Eight, and Twenty Three

# data[].attributes.body
Syntax in Math and Science

# data[].attributes.body
Assessment Analysis #1: Pre-Assessment

# data[].attributes.body
Assessment Analysis #2: Test Worksheet

# data[].attributes.body
Assessment Analysis #3: Formal Exam

# data[].attributes.body
Assessment Analysis #4: Exit Tickets

# data[].attributes.body
EdTPA Handbook 15

# data[].attributes.body
Science Lesson Plan Template

# data[].attributes.body
Science Standards at a Glance

# data[].attributes.body
Coherence Map

# data[].attributes.attachment_link.description
The Coherence Map shows the connections between Common Core State Standards for Mathematics.

# data[].attributes.body
Assessment Analysis #5: Real-World Map Creation

# data[].attributes.attachment_link.title
Assessment Analysis #5: Real-World Map Creation

# data[].attributes.body
Science Lesson Plan

# data[].attributes.body
Direct Instruction Mathematics Lesson Plan

# data[].attributes.attachment_link.title
Direct Instruction Mathematics Lesson Plan 24

# data[].attributes.body
Direct Instruction Lesson Plan Materials

# data[].attributes.attachment_link.title
Direct Instruction Lesson Plan Materials

# data[].attributes.body
Math Journal: Direct Instruction

# data[].attributes.body
Problem Solving Math Lesson Plan

# data[].attributes.body
Math Journal: Problem Solving

# data[].attributes.body
5E Science Lesson Plan

# data[].attributes.body
Science Journal: 5Es

# data[].attributes.body
TPEs Summary

# data[].attributes.body
TPE Examples

# data[].attributes.body
Attention Behavior Difficulties

# data[].attributes.body
Autism

# data[].attributes.body
Deaf and Hard of Hearing

# data[].attributes.body
Emotional and Behavioral

# data[].attributes.body
Non-Readers

# data[].attributes.body
Orthopedic Impairments

# data[].attributes.body
Physical Impairments

# data[].attributes.body
Sensory Impairment

# data[].attributes.body
SDAIE Strategies

# data[].attributes.body
Weathering and Erosion Experiment Example (4-ESS2-1)

# data[].attributes.attachment_link.authors[].name
The Good and the Beautiful Homeschool Science

# data[].attributes.attachment_link.title
Weathering, Erosion, and Deposition Experiment | Geology | The Good and the Beautiful

# data[].attributes.body
Sculpting Landscapes Demonstration (4-ESS3-1)

# data[].attributes.body
e-Games: Math

# data[].attributes.attachment_link.title
Math Games – Free Online for Grades K–6 | Math Playground

# data[].attributes.attachment_link.description
300+ free math games to build fluency and problem solving. Kid-safe, classroom-ready, no sign-in.

# data[].attributes.body
e-Games: Math

# data[].attributes.body
e-Games: Science

# data[].attributes.attachment_link.description
Eureka! Grab your lab coat and get ready to ace your next science test. Have fun while learning about the water cycle, the skeletal system... and more!

# data[].attributes.body
e-Games: Science

# data[].attributes.attachment_link.readable_text
Enjoy fun science games for kids while learning more about science and technology. There's a range of free online activities to try with something for everyone whether you're interested in animals, plants, chemistry, biology, physics, space, magnets, electricity, forces, light, sounds, gases or other science related topics. Put yourself to the test by trying to complete as many of the interactive challenges as you can, the games start off easy but will be fully testing your technology skills and understanding of the science behind the game in no time.

Have fun learning online with these cool science games. It's free and easy to use so just scroll down the page, find a game you like the look of and give it a go!

Learning about living things is a very important part of science. Humans like yourself are part of this group and the more you can learn about how your body works the better. There are also lots of games & activities to do with other living things such as animals & plants.

This selection of games & activities include some of the physical processes that control our everyday lives. Find out how electricity works, how our eyes use light to see, how forces such as friction work and the physics behind how the earth sun & moon behave.

The matter that makes up our earth can do weird and wonderful things, find out more with these fun games & activities. Experiment with solids, liquids and gases as you learn more about material properties, melting points, rocks, soils, ice, water & steam.

Solids, Liquids & Gases

Have fun learning about solids, liquids and gases by experimenting with different forms, using different conditions to change them from one form to another.

Detective Science Games for Kids

Use your science skills while playing the role of a detective in a range of fun games and activities that will challenge your knowledge of electricity, friction, magnets, microorganisms, life cycles and other interesting science topics.

# data[].attributes.attachment_link.title
Fun Science Games for Kids - Free Interactive Activities Online

# data[].attributes.attachment_link.description
Enjoy fun science games for kids while learning more about science and technology. There's a range of free online activities to try with something for everyone whether you're interested in animals, plants, chemistry, biology, physics, space, magnets, electricity, forces, light, sounds, gases or other science related topics.

# data[].attributes.body
Fraction Activities w: Manipulatives

# data[].attributes.body
Measurement Activities

# data[].attributes.body
Multiplication Activities

# data[].attributes.body
Algebraic Thinking (Math Activity)

# data[].attributes.body
Proportional Reasoning (Math Activity)

# data[].attributes.body
Proportional Reasoning Example (Math Activity)

# data[].attributes.body
Earthquake Engineering Demonstration (4-ETS1-3)

# data[].attributes.body
Math Fieldwork 1

# data[].attributes.body
Math Fieldwork 2

# data[].attributes.body
Science Fieldwork

# data[].attributes.body
Using Sentence Frames to Help ELs

# data[].attributes.body
Kagan Structures

# data[].attributes.body
UDL Guidelines

# data[].attributes.body
Number Talks Strategy

# data[].attributes.body
Merge Literacy With Mathematics

# data[].attributes.attachment_link.readable_text
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."

# data[].attributes.attachment_link.title
6 Ways to Merge Literacy With Mathematics

# data[].attributes.attachment_link.description
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.

# data[].attributes.body
Standards for Mathematical Practice

# data[].attributes.attachment_link.title
The 8 Standards for Mathematical Practice

# data[].attributes.body
Building Conceptual Understanding in Mathematics

# data[].attributes.attachment_link.title
Building Conceptual Understanding in Mathematics

# data[].attributes.body
PhET Interactive Simulations for Math and Science

# data[].attributes.body
Examples of Science Lesson Plans (NGSS Certified)

# data[].attributes.attachment_link.title
Quality Examples of Science Lessons and Units | Next Generation Science Standards

# data[].attributes.attachment_link.description
To identify and shine a spotlight on emerging examples of quality lessons and units designed for the NGSS, Achieve launched the EQuIP Peer Review Panel for Science (PRP). NextGenScience, the former Achieve science team, continues this work, managing reviews that use the EQuIP Rubric for Science (Ver…

# data[].attributes.body
Mystery Science

# data[].attributes.attachment_link.title
Open-and-go lessons that inspire kids to love science.

# data[].attributes.attachment_link.description
Mystery Science offers open-and-go lessons that inspire kids to love science. The hook, visuals, and activity have all been prepared for you. Less prep, more learning.

# data[].attributes.body
The GIST Strategy

# data[].attributes.attachment_link.authors[].name
Lindsay Ann Learning - English Teacher Ideas

# data[].attributes.attachment_link.title
How to Write a Nonfiction Text Summary Using the GIST Strategy

# data[].attributes.body
Close to 100 Strategy Instructions

# data[].attributes.body
Seeing Students Learn Science E-Book

# data[].attributes.body
Week 1 PowerPoint

# data[].attributes.body
Week 2 PowerPoint

# data[].attributes.body
Fourth Grade-Science Framework Presentation

# data[].attributes.body
Week 4 PowerPoint

# data[].attributes.body
Week 5 PowerPoint

# data[].attributes.body
Week 6 PowerPoint

# data[].attributes.body
Week 8 PowerPoint

# data[].attributes.body
Week 9 PowerPoint

# data[].attributes.body
Week 10 PowerPoint

# data[].attributes.body
Week 11 PowerPoint

# data[].attributes.body
Use Choice Boards in Math

# data[].attributes.attachment_link.title
The Benefits of Using Choice Boards in Math

# data[].attributes.attachment_link.description
How math choice boards can enable new elementary teachers to meet the needs of their individual learners while employing mathematical rigor. Math instruction can be challenging for new elementary teachers due to the complex nature of the subject, the wide range of student abilities in their classrooms, and the limited time and resources available for instruction.

# data[].attributes.body
Create Better Slides for Math

# data[].attributes.attachment_link.readable_text
When it comes to Google Slides and PowerPoint, less is more-a simple design allows students to focus on the math without distraction.

monkeybusinessimages / iStock

A friend of mine retired recently and left me a present on my desk. It was an unopened package of the plastic sheets we used to use to make slides for the overhead projector. I haven't seen an overhead projector in a classroom for years, but it certainly brought back memories. For a good portion of my career it was the only way to prepare a visual for class.

The old overhead is no more, and its replacement is much more versatile. And as the tools used for projecting images have improved, so has the potential to produce more complex and lively presentations. As someone who spends a lot of time observing and coaching elementary school math teachers, I've seen a rise in the use of PowerPoints and Google Slides, many produced by the publishers of curricula. But we often undercut the power of visuals by trying to make them entertaining. Slide presentations would be so much more effective if we followed one cardinal rule: Keep it simple.

What good slides do and don't do

Good slide shows support the goals of the lesson. They help reinforce oral directions and content. Slides can help a student follow the organization of a lesson, cueing a student about what is coming next and reminding them of predictable classroom routines. They also allow a teacher to include images and video they might not otherwise bring into the classroom without an awkward transition.

However, too often the slides that come from publishers or are crowdsourced from teacher sites have serious flaws. Many are cluttered with irrelevant cartoons and pictures, too much text, and sometimes marketing icons. Worse, in an attempt to be helpful, they often over-scaffold a lesson by giving too much information or suggesting questions that might not be useful in a real discussion. In this way, slides with too much information actually make it harder for a teacher to respond to student thinking because they are built around a script that anticipates a small range of student responses.

There is another, less obvious reason to use unadorned slides. If your slides are simple, you are more likely to use them regularly. Complex slide shows take up teacher preparation time. But slides are an opportunity to rehearse the lesson, which doesn't happen if you don't create them yourself. Less perfect, simpler slides that you make, rather than using ones provided by the publisher, will work better for you.

How to create better slides

Use only a few words: Every slide should be easy to read with as few words as possible. This is especially true of directions. It is good practice to support instructions visually, but if the students can't read the slide, it defeats the purpose. Often the slides I see in class (and sadly at meetings) have text that is too small or too crowded to be easily parsed. The younger the students, the fewer the words and the bigger the type. As a general rule, if you have to use anything smaller than 24-point type, you have too many words on the screen.

Make sure numbers are readable: For math classes, numbers can be especially tricky. Fonts often form numbers in ways that make it hard for younger students to recognize them. Again, the simplest fonts are the easiest to read.

In Google Slides, there's no way to insert an equation unless you download a third-party extension, which makes it more difficult to include properly formatted fractions, exponents, and division symbols. The easiest work-around is simply to take a screenshot of a Google Doc and place it on the screen. Although this involves a little extra effort, it makes the slide easy to read and is worth the time. You don't want students spending their time trying to figure out what's on the screen-you want them to focus on the math.

In this way, slides with too much information actually make it harder for a teacher to respond to student thinking because they are built around a script that anticipates a small range of student responses.

steven goldman

Limit the color scheme to black-and-white: One of the biggest benefits of using slides is that they provide cues to students who need support for their attention. But if our goal is to help students zero in on what's important, we need to keep the slides as simple as possible. Anything that is not relevant on a slide makes it harder for a student to focus on the content. Plain black text on a white background might look boring, but it is not distracting.

Eliminate distracting and superfluous imagery: The only images that appear on the screen should be the ones that are absolutely relevant. Everything else detracts from clarity. GIFs, balloons, and floating words do not support attention; they draw attention away from what the student should be focused on.
Courtesy of Steven Goldman
Use a clicker or a remote to advance the slides: Sometimes it's not what's on the slide but how the teacher interacts with the computer that becomes the distraction. Remotes are now inexpensive and require no setup, but they're still a rarity in elementary school classrooms. Without a remote, teachers have to either keep returning to their computer to advance a slide or stand stuck in one place for the whole lesson. A remote makes using slides a more natural part of the class.

It is rare in education for anyone to argue that a teacher should do less or produce something that is less complex, but for slides, the simpler the better. Fewer slides that convey only the necessary information with no fancy transitions or adornment serve the students best. In the classroom, slides are useful tools. They shouldn't be the show.

# data[].attributes.attachment_link.title
Creating Better Slides for Elementary Math

# data[].attributes.attachment_link.description
When it comes to Google Slides and PowerPoint, less is more-a simple design allows students to focus on the math without distraction.

# data[].attributes.body
How Math Autobiographies Build Student Confidence

# data[].attributes.attachment_link.title
How Math Autobiographies Build Student Confidence

# data[].attributes.attachment_link.description
Incorporating a writing task into lessons can help students reflect on their work and see their skills in a new light.

# data[].attributes.body
Set Up High-Impact Tasks in Elementary School Math Centers

# data[].attributes.attachment_link.title
Setting Up High-Impact Tasks in Elementary School Math Centers

# data[].attributes.attachment_link.description
Allowing students to select math centers based on interest instead of skill level provides opportunities for them all to grow.

# data[].attributes.body
Shining a Light on Dyscalculia

# data[].attributes.attachment_link.readable_text
Differentiated Instruction

Here's how to recognize what might be behind a student's difficulty with math as well as strategies for teaching them.

Gary Waters / Ikon Images

With reading research and methodology in the current spotlight, educators are learning more about dyslexia. Now, many are asking for the same support regarding math instruction and dyscalculia, which Dr. Honora Wall, founder of the Dyscalculia Training and Research Institute, defines as "a type of neurodivergence: a difference in brain development or function."

There's much less research, however, about dyscalculia than there is for dyslexia. In Dyscalculia: From Science to Education, cognitive neuropsychologist Brian Butterworth writes that since 2000, the National Institutes of Health has spent $107.2 million in funding for dyslexia research but only $2.3 million on dyscalculia. Consequently, students with dyscalculia are not getting the support they need, due to the lack of teachers' knowledge about the disorder.

Programs and approaches designed for the needs of learners who are dyslexic, such as Orton-Gillingham, Barton, S.P.I.R.E., and Fundations, just to name a few, are readily available. With no equivalent for dyscalculia, educators are scrambling for just the right tools to effectively address the needs of a vulnerable population. The good news is, there are several very concrete ways teachers can support these students.

What dyscalculia is not

It's not dyslexia with numbers. Dyslexia typically involves difficulty learning how to read, which can interfere with math learning. However, dyscalculia impedes a person's ability to make sense of numbers and math concepts in ways that are different from dyslexia.

It's not uncommon. Research suggests, according to Butterworth, that dyscalculia is just as prevalent as dyslexia. In fact, Butterworth maintains that it's estimated that 50 to 60 percent of people with dyslexia also have dyscalculia.

It's not being bad at math. Studies have shown that babies demonstrate an innate understanding of numerosity, as Butterworth says in his book. Dyscalculia is a learning difference that requires specialized teaching and isn't just "being bad at math."

Indicators of dyscalculia

There are several behaviors that can present themselves in learners with dyscalculia. Just as dyslexia and ADHD (attention-deficit/hyperactivity disorder) present themselves on a spectrum, the same is true for dyscalculia. That means that each student brings with them a unique set of strengths and weaknesses. Below are behaviors that are typical for students with dyscalculia.

Difficulties subitizing and estimating: Subitizing is the ability to "see" small numbers without actually counting them. For example, when rolling a die, a young student with dyscalculia will need to count the dots as opposed to automatically seeing that the number rolled was four.

Difficulties with patterns: Students with dyscalculia may have difficulty putting numbers in order from least to greatest or greatest to least. They also may struggle with skip counting or determining what number would come next in a sequence.

Loss of previously acquired skills: Research, according to Wall, hasn't quite determined why this happens, but it is very typical for students with dyscalculia to forget the math they learned, much to the dismay of their teachers. Some lose information quickly, others over time. This is why reference charts and a structured, spiraling curriculum are crucial.

What kind of teaching do dyscalculic learners need?

CRA Instructional Sequence: In The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths, specialist teacher Ronit Bird agrees with Butterworth that a Concrete Representational Abstract instructional sequence is an approach that moves students from using concrete manipulatives to representational drawings to abstract numbers when learning new concepts and is a best practice for all learners. Dyscalculic learners will need to experience this sequence multiple times and gradually, when developing new skills and understandings.

Visualization: Often the transition from the concrete stage to abstract is a bumpy one. Bird suggests that dyscalculic learners be explicitly taught how to picture numbers and operations in their mind's eye. This is especially true when solving word problems. Drawings, open number lines, and area models are some of the ways she suggests to bridge the concrete and abstract stages.

Quality over quantity: Bird and Butterworth both recommend limiting the demands on a learner's working memory, allowing them to focus on the important skills of a task. Providing reference charts, reading directions, and using rubrics are just some of the ways to reduce the load placed on working memory.

Explicit scaffolding: All learners must have a secure understanding of foundational concepts before building on them. This is especially true for learners with dyscalculia. Making explicit connections to previously taught skills and breaking tasks down into the smallest of steps are essential. This reduces the risk of taking students' background knowledge for granted.

How to plan instruction

Focus on sets: Butterworth asserts that dyscalculics struggle with operations because of a deficit in the understanding of numbers as sets. Instruction needs to focus on supporting concepts such as counting, one-to-one correspondence, part-whole relationships, and cardinality in the early years.

Diagnostics: There are assessments typically used by psychologists to diagnose dyscalculia, including the Wechsler Intelligence Scale for Children, KeyMath-3, Wechsler Individual Achievement Test for Math Fluency, and the Feifer Assessment of Mathematics. Educators, however, must first identify which students need additional support and then specifically which mathematical knowledge is in need of intervention. Acadience Math, the Early Childhood Assessment in Mathematics, Universal Screeners for Number Sense, and the Georgia Numeracy Project are widely used resources.

Feedback: Because a loss of previously acquired skills is a hallmark of the disability, committing mathematical understanding to long-term memory is an arduous process. It is imperative that the information learned be accurate. Wall writes that research suggests that when the brain learns new information, it does not "overwrite" what it has already learned, even if that information is incorrect.

This speaks to the uphill battle that teachers face when having to undo a misconception that a student has committed to memory. In order to avoid this, students who struggle must be given consistent, real-time feedback as they learn. In addition to teacher input, Butterworth recommends adaptive digital platforms and games as great ways to provide feedback consistently.

Manipulatives: Numbers are abstract. Manipulatives make numbers concrete. Using blocks, Cuisenaire rods, ten frames, and counters are just some of the ways students can have hands-on experiences. Dyscalculic learners solidify the concept that numbers are made up of sets of smaller numbers with tactile input from manipulatives.

Joy: Fear of math is a reality for many and is a major obstacle to learning. Years of struggle reinforce math as unenjoyable and a source of anxiety. The frequent use of games modified to students' current levels of understanding can have a disarming effect on those who experience math aversion.

There is still much to learn about dyscalculia. When armed with the right information, however, educators can make small changes to their practice that will have a huge impact on the lives of those with dyscalculia.

# data[].attributes.attachment_link.description
Here's how to recognize what might be behind a student's difficulty with math as well as strategies for teaching them.

# data[].attributes.body
Are We Teaching the Math Kids Need?

# data[].attributes.attachment_link.readable_text
Jo Boaler has spent a lot of time thinking and writing about anxiety-math anxiety, in particular-and its impact on kids' learning trajectories.

Mathematics, she writes in her 2019 book, Limitless Mind: Learn, Lead, and Live Without Barriers, is the subject "with the most damaging ideas held by teachers, students, and parents." It's one of the few academic subjects in which multitudes of students, early on, decide they're not cut out for it: We're either a "math person" or we're not. That notion tends to stick well into adulthood. "It is difficult to know how many people walk around in society harboring damaging ideas about their math ability, but I estimate it to be at least half of the population," she writes.

Boaler, a professor of mathematics education at Stanford University, a best-selling author, and the cofounder of the math education site youcubed.org, has spent decades thinking about how to undo the damage. Her work, closely aligned with Stanford psychology professor Carol Dweck's research on growth mindset, explores what Boaler calls "our most harmful and persistent ideas about innate ability." She's a vocal proponent of changing the way we assess mathematics and modernizing the math curriculum-especially in high school-so that it's more engaging, more inclusive, and more likely to prepare kids for the modern workforce.

Critics argue that by insisting on math as a joyful, creative exploration, we're doing kids a disservice, and that by reducing or eliminating memorization and math drills, for example, we're setting kids up for a lack of mathematical fluency. But Boaler says that she's got no quarrel with things like math facts and that teachers should help kids develop these-not by "emphasizing facts for the sake of facts, or using timed tests, but by encouraging students to use, work with, and explore numbers," a process that ultimately builds critical number sense and reinforces math facts in a more organic way.

I sat down with Boaler recently for a Zoom discussion about mathematical freedom, anxiety-producing teaching practices, and the systemic changes she says are critical for modernizing math curricula.

Sarah Gonser: In your book Limitless Mind, you say that learning is about identity. Can you explain?

Jo Boaler: Well, we know that when people learn, it's not just about an accumulation of knowledge; it's really about changing who they are as people.

And we've found over the years that the traditional approach to teaching maths-I'm just going to show you methods; you're going to accept them and use them-is incompatible with the identities kids want, particularly around adolescence. Kids want to have their own ideas; they want to be respected as thinkers; they don't want to just be given information that they simply reproduce.

They see it as a subject area where they can't be their full selves, and it's a large part of why people drop out of maths.

Gonser: It's also a subject that causes a lot of very real anxiety. Why is that?

Boaler: I would say it comes from a few different things: It's a subject that is heavily tested; it's a subject that's often taught as right and wrong answers; and there are these widespread myths that you're either born as a math person or you're not. Somehow, you have the right brain, or you don't.

There's lots of micromessaging in classrooms that might get kids to think they can't be successful. Speed is very much at the heart of it. If you ask the class a question and then take the answer from the first kid who raises their hand, you're sending the message that you value speed. And we know that professional mathematicians are not fast; they're some of the slowest thinkers.

Finally, we have stereotyped ideas about who can be good at maths. So if you're a woman or a person of color, you're dealing with that pressure. If you have fixed ideas about who can do maths, a fixed mindset, then that stereotype can really take root.

Gonser: So how can we slow it all down and avoid making math class a place of stress and anxiety?

Boaler: I think a big part of it is A for L-Assessment for Learning-I just think that's so critical. It changes the whole culture of classrooms for kids.

If we assess kids by giving them diagnostic feedback, not grades, and ask them to do their own reflection so that they're able to see themselves progress on this journey-everything changes when assessment is like that in classrooms.

But we also want to change the way content is taught. Kids don't need lots of short questions with one method and one answer. It can be open questions that students think about creatively and visually.

Gonser: You're also an advocate of encouraging struggle and mistakes in classrooms. In Limitless Mind, you describe high achievers who work "at the edge of their understanding, making mistake after mistake in difficult circumstances, correcting mistakes, moving on and making more mistakes." In the classroom, why is that important?

Boaler: The best times for learning are when you're struggling and finding things difficult; that's when your brain is on fire with activity. I think it's really important to share the value of struggle with students. When I teach, I say to students, "I want you to struggle, because that's really good for you." I think it's freeing for students when they know that's a goal. And I think you should keep sharing that, reinforce it during every lesson.

It's really going to involve changing how we assess kids. If kids take a test and they're penalized for making mistakes, that's a counter message-and studies have shown that this mixed message is worse than no message at all. Don't tell them that struggle is good if you're going to mark them wrong when they struggle.

I think it's important that we always let kids resubmit work. And if you're using grading-I'm not a fan of grading myself-but if students don't do well the first time, to allow them to work on it again sends a great message that learning and struggle are valued.

Gonser: Let's talk about broader, more systemic curricular changes. You're a prominent voice in the conversation about re-sequencing math curricula so that it's more than a gateway to higher-level mathematics. What's changed in our world to make this so urgent?

Boaler: Well, we need to modernize not just how we teach it, but the actual content we're teaching in classrooms. The content we teach in maths was created around the 1800s and really hasn't changed since then. It was created at a time when we needed kids to be calculators. And so learning arithmetic, calculating things quickly-that was important.

But the world has changed dramatically. In high school, in particular, we're teaching a wide array of methods for kids to do by hand that they'll never use in their lives again. You will never go into a workplace and have people, by hand, go through synthetic division. So we're spending too many hours giving kids this outdated content that they're so turned off by. For what reason?

Gonser: What should we be teaching instead?

Boaler: So I'm very excited about bringing data science into mathematics. I am one of the five writers of a new framework in California where we are highlighting data science as a really important part of maths.

Now, it's hard to do that because the Common Core Standards really didn't include data science, and they need to be updated. But what we've done is try and bring a data science perspective to the current standards. This data science initiative is very exciting, not only because it gives teachers of all grades interesting content to work with, but it also helps kids become data literate, which is something they really need in this world.

There are more data points in the world than there are stars in the galaxies right now; the world is filled with data. So even little kids need to prepare to become data literate.

Gonser: You're also leading the charge on changing the high school math sequence, streamlining the algebra-geometry-algebra sandwich so there's room for a data science class-can you tell me more about that?

Boaler: In the high school years, something very exciting is happening. For generations, really, there's been this race to get to calculus because it can get you into college.

It's built on a very inequitable system. Because there are so many courses before calculus in middle school and high school, it's effectively meant we're pushing kids out of the calculus track in sixth grade, which is awful. The content is also not very up-to-date and not very engaging.

There's recently been a dramatic change in California: The UC and Cal State systems will now accept data science as a third-year course instead of Algebra 2. This is amazing and important because Algebra 2 is a course that is the end of the road for most kids, and now they can take data science instead.

Gonser: Why is Algebra 2 the end of the road for so many kids?

Boaler: Because it's so procedural and uninteresting that the vast majority of kids, after they've done Algebra 2, don't take any more maths. Data science is completely different. As we're rolling it out, we're communicating: This can be a course in high school that any student can take. You don't have to be advanced in middle school, and yet it can lead to a high-level STEM career. I see that completely changing who ends up going into STEM.

Gonser: What do you say to critics who argue this is a change that will water down the curriculum, make it less rigorous?

Boaler: It's totally rigorous, actually. Mathematics is a very broad subject. There's no reason that we should say, "Let's just value this part, which is calculus." The mathematics of data science involves matrices and probability and statistics and linear algebra-which is beyond what's often taught in calculus.

Gonser: My last question comes from an Edutopia reader, a teacher, who asks: "What's your greatest piece of advice for early math educators?"

Boaler: My biggest piece of advice is to really spend time trying to change kids' mindsets and ideas about themselves, because that will pay huge dividends. If you encourage struggle, if you remind kids that they can learn anything, we now know there are no limits to what people can learn.

Kids should know that if the kid next to them is solving something more quickly, it doesn't matter. We know that kids enter school with a growth mindset, and that drops with each passing year. And part of that is kids looking at other kids and thinking, "Oh, they can do it better than me." We have to counter those ideas and couple that with math that's open and creative. When you do that, things change.

# data[].attributes.attachment_link.description
Every child possesses vast mathematics potential, says Jo Boaler, Stanford University mathematics professor and best-selling author-but for them to access it, we need to rethink how we teach math.

# data[].attributes.body
Highly Engaging Science for Students in Special Education

# data[].attributes.attachment_link.readable_text
By integrating age-appropriate modifications, special education teachers can design high-interest, standards-aligned science units.

Many high school special education teachers have access only to materials geared toward young students, which makes it difficult to provide all students with an age-appropriate science experience. However, teachers can provide a high-level integrated science experience for students with significant disabilities. Chelsie, the science expert, and Sara, the special education expert, spent a year developing this comprehensive model to make science accessible to each student in the high school setting.

To illustrate the process, we've designed a high-interest unit about squirrels to explore this question: How do traits of a species and their environment impact survival? Special education teachers know that these types of cross-curricular lessons require careful planning, modification of standards-based lessons, and the integration of assistive technology. When teachers are intentional about practicing cross-curricular skills to learn science, students gain valuable knowledge and skills.

3 Steps to Adapting Science Content

1. Standards-based integrated unit planning. First, you need to obtain all alternative assessment standards applicable to your state. Our squirrel-themed unit identified three science standards from the Iowa Core Essential Elements Standards to drive the learning. Having a small number of standards makes the task seem manageable and cognitively appropriate for students. To build a unit around the standards, look for themes that align with student interests.

For this unit, the focus is on squirrels. Squirrels are of high interest to students and an animal they can easily identify. While learning about the genetics of squirrels, students are reading and writing, as well as conducting research that requires calculations and modeling. This model uses a science concept that requires cross-content skills to support new science learning.

As this is an integrated unit, it is important to review other content standards. Alternative math and English language arts standards are vital to support the lessons and tasks being developed. To further enhance the lessons in your unit, infuse 21st Century Skills and alternative social studies standards. Integration of several different core standards into one lesson of the squirrel unit allows the teacher to monitor different skills during a single task or activity. This multistandard approach maximizes instructional minutes.

Current individualized education program (IEP) goals can be targeted as well. Teachers are tasked with not only addressing student IEP goals but also designing and delivering specially designed instruction. By keeping student goal areas in mind as you create your own unit, you will be able to provide meaningful and engaging lessons without losing valuable instructional minutes.

For example, another lesson in the unit targets students with reading comprehension goals. We were able to modify a text not only to be used for the lesson but also to monitor progress. There are several opportunities for students to engage with media in the mode of video, pictures, charts, and varied readings that are age-appropriate and may also be used for comprehension progress monitoring.

2. Modifications. Modifications should support the student's communication needs and will be age-appropriate. Sometimes modifications to media and other sources become more juvenile. This can be common, especially for students on the alternative assessment. We sought to find age-appropriate materials and make the necessary modifications to those materials rather than finding materials at their instructional level.

As you explore the unit, notice that there are modifications made to some tasks, and the teacher handbook makes further suggestions on modifications for each lesson. Use your judgment, and make additional modifications that hold true to the targeted standards. This specific unit was written at the high school target level but offers assessment points at each level in the Dynamic Learning Maps.

Modifications of quality sources, rather than the use of elementary or juvenile sources, will allow students to verbalize, write, or draw responses to questions at a high level. Another modification to consider when using age-appropriate sources is to allow for a choice of response styles. For example, if an exemplar text only has a written response, that does not mean you discard it. Instead, consider whether the student needs generated responses, fewer choices, visuals, oral responses, or other alternatives to access the text.

As you continue to create, consider using class and small group discussions. Incorporate model building, hands-on activities, and movement. Modifications will not change the achievement target but allow for differentiation for your students and their learning needs. For example, the Hungry Squirrels game could be played at many different scales using 2D and 3D materials, with sound added to the materials, or adjusted for students' physical abilities.

3. Integration of assistive technology. Finally, assistive technology is an important part of how students can access science lessons and demonstrate their knowledge. This is a low-technology supported unit. The low-technology focus was intentional to support accessibility for most classrooms.

We created a communication board specific to the unit using subscriptions and symbols we had access to. We also included sensory bins for students who would benefit from a sensory break that is tied to the unit's theme. If you have low-vision students, additional prompts and color contrast for multimedia and online content can increase accessibility.

Following these three steps, teachers can create an age-appropriate, carefully planned, modified, standards-based unit with integration of assistive technology that is engaging for all students.

# data[].attributes.attachment_link.title
Highly Engaging Science for Students in Special Education

# data[].attributes.attachment_link.description
By integrating age-appropriate modifications and assistive technology, teachers can design engaging standards-aligned science units.

# data[].attributes.body
Make Science Connections Across the Curriculum

# data[].attributes.attachment_link.readable_text
When P.S. 249, the Caton School, in Brooklyn, New York, saw that attendance on Fridays was consistently low, the staff came up with Super Science Fridays-an immersive science day when hands-on activities and cross-curricular investigations would give students an incentive to come to school and help get them reinvigorated and excited about learning. Students wear lab coats and think like scientists, and throughout the day the regular blocks for math, writing, and reading all relate to the science content they are studying. As a result, attendance and engagement improved-and so did science learning.

# data[].attributes.attachment_link.title
Making Science Connections Across the Curriculum

# data[].attributes.attachment_link.description
Dedicating a day each week to integrating science into every subject helped an elementary school boost attendance, learning, and fun.

# data[].attributes.body
Use Crosscutting Concepts to Boost Students' Scientific Thinking

# data[].attributes.attachment_link.title
9 Tips for Using Crosscutting Concepts to Boost Students' Scientific Thinking

# data[].attributes.attachment_link.description
Introducing elementary students to ideas that apply across disciplines enhances their understanding of the sciences as an interconnected whole.

# data[].attributes.body
Spark Curiosity and Solve Real-World Problems

# data[].attributes.attachment_link.title
Sparking Curiosity and Solving Real-World Problems

# data[].attributes.attachment_link.description
See how students apply their literacy skills to explore science problems outside classroom walls.

# data[].attributes.body
A Project-Based Approach to Teaching Elementary Science

# data[].attributes.attachment_link.title
A Project-Based Approach to Teaching Elementary Science

# data[].attributes.attachment_link.description
New research reveals that when science, reading, and math come together in rigorous hands-on projects, student collaboration, engagement, and achievement can soar.