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What is something a teacher did in your experience to make you feel like a competent math learner?

What is something a teacher did in your experience to make you feel like a competent math learner?

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Unlock every student’s math potential with our unique and equitable approaches to math instruction and teacher professional development. Join us today!

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High Leverage Concepts | All Learners Network

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Improve your math instruction with high-leverage assessments and classroom tools from ALN! Partner with us to enhance math learning for all students.

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An Introduction

The following documents have been created as a resource for classroom teachers, math interventionists, and special educators who are creating learning opportunities for their students to achieve the concepts targeted by the HLCs. These learning progressions are specific to the grade level All Learners Network HLCs. They do not attempt to include all of the concepts that students are introduced to and practice at individual grade levels. We would encourage teachers to investigate the Common Core State Standards for Mathematics, Achieve the Core's Coherence maps,among many other available resources to find learning progressions for all the grade level standards.

The HLC Learning Progressions identify developing stages along a continuum of concepts, models and skills that lead toward student understanding and application of the HLC. Teachers can intentionally plan lessons based on where a student or students can be placed on the learning progression to help him or her move forward in their learning. These learning progressions are not meant to be used as a checklist. They should be used as reference points to highlight students' progress toward conceptual understanding of grade level mathematics.

The learning progression documents are formatted to show increasing complexity from top to bottom and from left to right. The concepts in each row are sequential and provide a progression of how we believe students develop the high leverage concepts at each grade level. It is important to note that the format does not represent the amount of time necessary for each student to build understanding of the concept. Students will make progress through the learning progression at his or her own pace through the support of targeted learning opportunities provided by the classroom teacher, math interventionist or special educator.

We encourage teachers to read HLC Learning Progressions from previous grades to highlight some of the prerequisite concepts. Knowing the previous grade concepts and helping students make connections from prior knowledge to learning a new concept is critical.

The High Leverage Assessments can help identify areas of strength and areas of need and therefore support the design of instructional strategies.

Finally, there is a common thread throughout all of the Learning Progressions - the use of models. Students should have access to and use of models daily and in all activities which support learning the high leverage concepts, in fact all mathematical concepts. Models support students when building conceptual understanding of important mathematical ideas. Please take the time to review the suggested Models for Intervention and Models for Instruction on all of the HLC Maps.

Learning Progressions

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Additional Resources

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Learning Progressions - All Learners Network

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The following documents have been created as a resource for classroom teachers, math interventionists, and special educators who are creating learning opportunities for their students to achieve the concepts targeted by the HLCs. These learning progressions are specific to the grade level All Learners Network HLCs.

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Launch is how we use the first 5-15 minutes of our math block for purposeful, discussion-rich number sense routines in our classrooms. Learn more!

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The title, Problem Introduction Protocol sounds a bit pretentious. "The way we introduce problems to provide access to everyone" was a mouthful, so we went with PIP.

The Problem Introduction Protocol was a joint effort among all the coaches at the first All Learners convening. We were searching for a way to provide access to problems being used during Main Lesson. Often, students who had trouble would raise their hands almost immediately to declare, "I don't get it." We observed that there was something fundamentally amiss when a student couldn't even begin a problem. As a result, we created an approach for introducing problems that, we thought, would provide an opportunity for everyone to take a stab at the problem. The original version was launched more than a year ago. After gathering some (admittedly thin) data from practitioners, we've come up with the version below.

The Ongoing Cohort of ALN is going to be testing this protocol this fall. We'll report on the results in December. In the meantime, if any educators used it, please let us know in the comments or contact us by email to share what your experience was.

Problem Introduction Protocol

* Read the problem chorally.

* Ask, "What are we trying to figure out?"

* Ask, "What would an answer to that look like?"

* Brainstorm strategies

Read the problem chorally

We do this to accommodate students who might have difficulty with reading and those whose first language is not English. Older kids fuss a bit about reading chorally, but I make them do it anyway. It's important that students get a chance to hear a clear reading of the problem.

In the first few iterations of this approach we had the teacher read the problem to students before the choral reading. I wouldn't discourage this, particularly in one-on-one settings. In general, though, people reported that this was overkill.

Ask, "What are we trying to figure out?"

Step 2 involves determining what kind of answer we're looking for. Many teachers write a statement on the board to summarize student thinking. Some teachers have students write a statement on the paper where they're going to solve. Some (teachers of younger children) will write it on the board and ask students to copy it onto their papers.

Whether you write it or not, students should all be able to articulate what the goal of the problem or task is.

Ask, "What would an answer to that look like?"

This step was a contribution from our Maryland colleagues. It's really helpful. We don't use this step exactly as written. In other words, we don't ask students this question. Instead, we ask about two elements of the problem:

The estimate is usually the result of a teacher question about extreme (and unreasonable) answers. Teachers will ask questions like, "Could it be 1? Could it be 100?" By eliminating unreasonable answers we're helping kids narrow their thinking a bit.

So when you're done with this step, kids should know what the units for the answer will be and what a reasonable solution might look like.

Brainstorm Strategies

When I introduce this to teachers I have the habit of saying, "This piece should come with a Surgeon General's Warning: Do Not Narrow the List of Strategies". As students suggest strategies (addition, making a list, drawing a picture, multiplication, etc.) teachers simply respond by saying, "We might be able to use that strategy."

An example of what doesn't work is when teachers say that one strategy is the "right" one: "Yes, this is a division problem." We want to leave the possibility open for children to use whatever makes the most sense to them, even if (right now) it's not the most efficient approach.

One added piece to the brainstorming that seems to work well is to record the strategies on the board. As students are getting started they can refer to these.

What about highlighting important information?

This is a step that we originally included, and one that is recommended by several texts on supporting struggling learners. While we want children to get the important information from the problem, the practice of highlighting or underlining numbers or important facts often translates into students pulling numbers out of the problem and doing some (often inappropriate) arithmetic. The result is a " How Old is the Shepherd? " outcome. For this reason we don't use this step in the protocol. It doesn't mean, of course, that you can't. But if you have students find important information, be sure they have a strategy that makes sense to them and makes sense mathematically.

The Problem Introduction Protocol, then, facilitates reading of the problem, focuses on what the answer is trying to find, gives a decent estimate for a solution, and provides a variety of strategies for getting started. So far it has provided greater access for students to get started with problem solving. As always, we're interested in your experience with this technique. Please let us know how it worked for you.
John Tapper
Published: October 15, 2018

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The Problem Introduction Protocol - All Learners Network

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The title, Problem Introduction Protocol sounds a bit pretentious. "The way we introduce problems to provide access to everyone" was a mouthful, so we went with PIP. The Problem Introduction Protocol was a joint effort among all the coaches at the first All L

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Launch is how we use the first 5-15 minutes of our math block for purposeful, discussion-rich number sense routines in our classrooms. Learn more!

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PZ's Thinking Routines Toolbox | Project Zero

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The Toolbox organizes the Thinking Routines into categories that describe the types of thinking the routines help to facilitate. Some routines appear in more than one category, and some routines have different versions that offer modifications for specific age groups or more specific conceptual challenges.

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How and Why You Should Bring Intentionality to the Opening and Closing of Your Lesson

Social and Emotional Learning (SEL) initiatives have been acknowledged as important for many years, but until recently the discussions remained largely focused on relationship building and behavioral rewards. While these are essential pillars of healthy and equitable schools, the void of research-based instructional and assessment practices hindered implementation at the classroom level and often created frustrations with teachers who wanted to support SEL with their students but were feeling it was at the expense of academic rigor and achievement. In fact, the research has shown that the opposite is true: students who receive systemic SEL instruction in schools average 11 percentage points higher than those who do not and have a greater motivation to learn (Durlak et al., 2011). Studies on SEL initiatives in schools reveal that when woven into instruction, SEL provides opportunities for students to reflect on learning and take greater academic risks.

Studies on SEL initiatives in schools reveal that when woven into instruction, SEL provides opportunities for students to reflect on learning and take greater academic risks.

Luckily, the Collaborative for Academic, Social, and Emotional Learning ( CASEL ) published their answer to this call in their 2019 CASEL 3 Signature Practices Playbook which sought to answer the " but how do I do SEL?". This playbook breaks down the implementation of SEL into a lesson into three steps:

1. 1. Welcoming Opener/Inclusion Activity

2. 2. Engaging Strategies

3. 3. Optimistic Closure

When focusing on staff development, we have found that there was power in developing a shared understanding of the purposeful use of openings and closures as an SEL instructional strategy. This was not because Engaging Strategies were not important, but we found that staff already conceptualized these as tools for interactive learning and connections. The concept of bringing intentionality to the opening and closing of a lesson with SEL, Universal Design for Learning (UDL), and Academic rigor in mind was a new focus. By creating routines and rituals through opening activities, teachers are investing in an orderly classroom that provides predictability for students, therefore, building confidence and a sense of agency and calm. A strong, optimistic closure allows students time to highlight increased understanding, both shared and individual, and supports forward-thinking and reflection on next steps for additional learning.

Welcoming Openers and Optimistic Closures

Given the power of openings and closures, we designed two resources universally (using UDL principles) so that teachers could best remove possible barriers to opening and closing activities. As you will see, both have multiple ways in which students can engage with the activity at hand. Additionally, because the document starts with a focus on the goal of the activity, individual students who might need support in getting their thinking started have access to a variety of sentence starters.

We see this document working in a few ways. First, the teacher could choose the purpose and the stem with the students selecting the format. This would have all students engaging with the same focus but feeling empowered to engage because of the choice in format. Another way this could be used is that the teacher could only dictate the purpose and students would then get to choose the sentence starter (or create their own) and the format. Last, and this might be something that a teacher could work their way through and to as the year progresses, but students could be in full control over their opener or closer-choosing the purpose, stem, and format that best suits them on that day given their progress in the learning and overall disposition. When we talk about creating expert learners, these documents really can help students on this journey. We hope you enjoy!

Resource:
Durlak, J. A., Weissberg, R. P., Dymnicki, A. B., Taylor, R. D., & Schellinger, K. (2011). The impact of enhancing students' social and emotional learning: A meta-analysis of school-based universal interventions. Child Development, 82, 405-432

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Use This Resource to Meaningfully Integrate SEL Into Your Class

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Social and Emotional Learning (SEL) initiatives have been acknowledged as important for many years, but until recently the discussions remained largely focused on relationship building and behavioral rewards.

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Reforms to Teacher Preparation Imperative for Success in Knowledge Economy, says Carnegie Corporation Expert in Congressional Testimony

Quality teachers have a greater influence on pupil achievement than any other school-based factor. How the nation educates teachers will largely determine the degree to which the United States can participate and succeed in the emerging knowledge economy, Daniel Fallon, Carnegie Corporation of New York's Program Director, Higher Education, told the House Subcommittee on Higher Education, Lifelong Learning and Competitiveness today.

Fallon cited Carnegie Corporation's seven-year initiative to stimulate construction of excellent teacher education programs at selected colleges and universities as an important effort to improve the quality of teaching in the nation's schools. The Annenberg Foundation and the Ford Foundation are also contributing to this ambitious initiative. He noted that the teacher education reform effort, called Teachers for a New Era, is organized around three principles that help schools of education prepare teachers who positively impact pupil learning:

A teacher education program should be guided by a respect for evidence, including attention to pupil learning gains accomplished under the tutelage of teachers who are graduates of the program.

Faculty in the disciplines of the arts and sciences must be fully engaged in the education of prospective teachers, especially in the areas of subject matter understanding and general and liberal education.

Education should be understood as an academically-taught clinical practice profession, requiring: close cooperation between colleges of education and actual practicing schools; master teachers as clinical faculty in the college of education; and residencies for beginning teachers during a two year period of induction.

" The Teachers for a New Era initiative is connecting teacher education programs to working classrooms. The design principles require an ongoing professional relationship between the education school and its recent graduates, and uses pupil learning in the classrooms of those graduates as the primary means of measuring the new teachers' quality," Fallon told the Subcommittee.

Fallon concluded his testimony by describing three early findings emerging from Teachers for a New Era and their potential relevance to the Committee's deliberations:

The first finding concerns difficulties in retrieving the data on particular teachers and particular students necessary for legitimate program improvement purposes in teacher education. Incentives to states and local school districts to construct comprehensive high-quality educational data systems, to entrust these data systems to research institutions, and to make the data available to teacher education programs for purposes of program improvement would accelerate the production of high quality teachers.

The second finding is the success of the implementation of academy-based induction supplemental to district-based induction programs, including reduced teacher turnover and consequent instructional improvements and cost savings. Creating incentives for institutions of higher education to engage in these academy-based induction programs will pay substantial dividends in teacher quality, teacher retention, and pupil achievement.

The third finding is the beneficial impact of an evidence-based continuous-improvement design for teacher education reform on the management of teacher education within a higher education institution and ultimately on the production of high quality teachers. It may beworthwhile, therefore, to consider incentive grants to partnerships between institutions of higher education and school districts that pledge to restructure teacher education in this way.

Carnegie Corporation of New York was created by Andrew Carnegie in 1911 to promote "the advancement and diffusion of knowledge and understanding." As a grantmaking foundation, the Corporation seeks to carry out Carnegie's vision of philanthropy, which he said should aim "to do real and permanent good in the world." The Corporation's capital fund, originally donated at a value of about $135 million, had a market value of $2.52 billion on September 30, 2006. The Corporation awards grants totaling approximately $80 million a year in the areas of education, international peace and security, international development and strengthening U.S. democracy.

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Teacher Quality Most Important School-Based Factor In Boosting Student Achievement | Carnegie Corporation of New York

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Reforms to Teacher Preparation Imperative for Success in Knowledge Economy, says Carnegie Corporation Expert in Congressional Testimony Quality teachers have a greater influence on pupil achievement than any other school-based factor.

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Small Changes in Teaching: The First 5 Minutes

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Small Changes in Teaching: The First 5 Minutes

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High Leverage Concepts — All Learners Network

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What question could you ask based on the pictures of these coins?

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When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas.

By asking "What do you notice? What do you wonder?" we help our students see problems in big-picture ways.

Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to discover multiple strategies for tackling a problem.

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Notice and Wonder - National Council of Teachers of Mathematics

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What is Notice and Wonder? When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas. By asking " What do you notice? What do you wonder?"

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Begin Problem Solving with I Notice I Wonder

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Begin Problem Solving with I Notice I Wonder

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General: Members Only Page - National Council of Teachers of Mathematics

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Educational PolicyBy Robert KaplinskySeptember 27, 201615 Comments

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Want to learn more? Take the free workshop. All 3rd 4th 5th 6th 7th 8th Alg 1 Geom Alg 2 Stat Calc Water Leak Will service arrive in time?Car Ramp How far did the ca…

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Real World 3 Act Math Tasks | Grade 6 Common Core State Standards

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Real World 3 Act Math Tasks that align with the Grade 6 Common Core State Standard for Mathematics.

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12.6 x 10 Student Sort - Google Jamboard

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