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Copy of MAL Day 1 Session 1 Virtual Updated December 2021.pdf

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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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HLC/HLA/HLC Progressions Reflection MAL - Google Jamboard

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MAL Day 1 Session 2 Virtual Updated Jan 2022.pdf

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MAL Day 1 Session 3 Updated Jan 22 (1).pdf

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

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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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MAL Day 2 Session 5 Updated February 2022.pdf

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Differentiation Jamboard Session 5

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Differentiation Jamboard Session 5 - Google Jamboard

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Math Menu Subscription — All Learners Network

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ALN provides math teachers with a weekly math menu, complete with everything needed for effective differentiated instruction and engaged student learning.

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MAL Day 2 Session 6 Updated February 2022.pdf

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12.6 x 10 Student Sort - Google Jamboard

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