ACE Mathematics Newsletter

3 - 5 Mathematics | OCT 2019 YEAR 4: VOL. 1

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In this Edition:


Instructional Trends in Mathematics: Teaching Towards Conceptual Understanding

Mathematics Instructional Block: I DO (Modelling) & WE DO (Guided Practice)

Instructional Planning Tools: Instructional Planning Calendars & ACP Exemplars

Upcoming Professional Development: Math Team Thursday

Announcements: ACE Website

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Since Summit 2019, we have taken off in Math! ThePreview Challenge and Lesson Cycle have been elevated to new heights and students are engaged in exploring and learning, and loving it!

As we visit campuses we are seeing evidence of Problem Solving Protocol and the Lesson Cycle in all schools. As we continue on our journey check out a little motivation to take our work to the next level.

Instructional Trends in Mathematics: Teaching Towards Conceptual Understanding


Teaching Towards Conceptual Understanding

For decades, the major emphasis in school mathematics was on procedural knowledge, or what is nowadays commonly referred to as procedural fluency. Rote learning was the norm, with little attention paid to understanding of mathematical concepts. Rote learning is not the answer in mathematics, especially when students do not understand the mathematics. In recent years, major efforts have been made to focus on what is necessary for students to learn mathematics, what it means for students to be mathematically proficient. To be mathematically proficient, a student must develop:

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Conceptual understanding is at the forefront for students to become mathematically proficient, since it allows students the opportunity to apply and possibly adapt some acquired mathematical ideas to new situations. Students demonstrate conceptual understanding when they provide evidence that they can recognize, label, and generate examples of concepts; use and interrelate models, diagrams, manipulatives, and varied representations of concepts; identify and apply principles; know and apply facts and definitions; compare, contrast, and integrate related concepts and principles; recognize, interpret, and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding reflects a student’s ability to reason in settings involving the careful application of concept definitions, relations, or representations of either.

To assist our students in gaining conceptual understanding of the mathematics they are learning requires a great deal of planning and execution, it involves using our classroom resources (textbook, supplementary materials, and manipulatives) in ways we had not anticipated or thought of before. If we want to achieve superlative results we may need to be open to challenge our way of thinking and be willing to embrace newly developed instructional strategies based on the latest breakthroughs in neurosciences.

At ACE we will learn and support each other as we build our capacity in teaching conceptually. Getting students to use manipulatives to model concepts, and then verbalize their results, assists them in understanding abstract ideas. Getting students to show different representations of the same mathematical situation is important for this type of understanding to take place. Getting students to use prior knowledge to generate new knowledge, and to use that new knowledge to solve problems in unfamiliar situations is also crucial for long-term sustainable conceptual understanding to emerge. This will also sharpen students' complex problem solving skills which ranks 1st as the top-targeted skill by employers by 2020.

Adapted from: "Balka, Hull & Harbin Miles. What is Conceptual Understanding? (2014) Retrieved from https:

Instructional Resources to Support Teaching Towards Conceptual Understanding

In an effort to continue supporting our collective growth as a professional learning community, we have upgraded our instructional planning calendars for the 2019-2020 school year. One of the most important updates is the inclusion of a new section labeled SE Trajectory. The purpose of this section is to provide a clear picture of the learning progression for a particular standard, indicating the different representations students are to be exposed to in order to scaffold their learning following the Concrete-Pictorial-Abstract learning continuum. In addition to that, we feature the specific Essential Understandings for the targeted SE, making the connection to the critical concepts students should be able to articulate by the end of planned lessons.
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I DO (Model the Concept)

With the direct teach model of instruction, the I DO (Modeling) is one of the most critical components of the Mathematics instructional block that will help us lay the foundation towards teaching conceptually.

An effective I DO should adhere to the following criteria:

1. Aligned to LO & DOL

2. Be completed within 10-15 minutes or less

3. Teacher models replicable steps or thinks aloud with anchor chart

4. Students have an explicit listening/note-taking task

5. Debrief to stamp the understanding

This segment offers teachers the opportunity to intentionally think aloud and model for students the process necessary to understand a learning concept, along with scaffolding the tasks. It is really pivotal that teachers present the concept through the lens of the concrete, pictorial, and abstract learning continuum to ensure students make connections to what they already know and build upon their existing cognitive schema or mental representations.

Teachers explain the reasoning behind the steps being modeled along with helping students see what they should notice and remember. Referencing both conceptual and procedural anchor charts while modeling will help students see what they need to know and be able to do to show understanding of the concept being presented.

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Students may have a clear listening and/or note-taking task as the teacher completes the model to keep students on task and focused on the concept or model being presented. The goal is to provide students with a "learning map" that will support them in making meaningful cognitive connections between what they already know and what they are about to learn. Guided notes and graphic or visual organizers may be suitable tools to incorporate during this component of the lesson cycle.

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In order to assist teachers with the implementation of the I DO, the Instructional Planning Calendars will feature suggested guiding questions to frame the learning. Some questions will address the relevance of the concept to help launch the learning and make it relevant to students, while others will address specific skills needed to internalize the critical essential understandings of the lesson.

WE DO (Guided & Peer Practice)

During this part of the lesson cycle the teacher partners with the students and work through several examples together and then by themselves in order to replicate the process modeled during the I Do portion of the lesson. This allows for a deeper level of learning to develop.

First, students are able to engage in the learning process beyond actively listening. In our society today students are given information overload. Without a chance to apply what they are learning, they may check out immediately. Next, the We Do section allows a teacher to guide and encourage students through the process being taught without leaving them to conquer the new material by themselves. It is the perfect opportunity to scaffold the learning, address any misconceptions, and strengthen cognitive connections before releasing students to work independently.

An effective WE DO should adhere to the following criteria:

1. Aligned to I Do, LO, and DOL

2. Be completed within 20-30 minutes

3. Provide students with at least 2-3 at bats

4. Teacher gives students opportunity to think with multiple response strategies

5. Teacher asks assessing & advancing questions about process & conceptual understanding 6. Teacher monitors for misconceptions to address with the class

During the We Do (Guided) it is critical for the teacher to guide students through the process modeled during the I Do through questioning. Students need to be given the opportunity to think aloud and replicate the steps shown on both conceptual and procedural anchor charts they were exposed to during the I Do. Therefore engagement becomes pivotal and teachers need to infuse several multiple-response strategies such as turn and talk, choral response, whip around, modified whip around, whiteboards, and others, to determine if students are ready to proceed to We Do (Peer Practice), or if additional practice is needed at this time. The learning process is not linear and is driven by student comprehension rate. Teachers are to actively monitor and continuously ask questions to gauge students' internalization of the model.

During the We Do (Peer Practice) students are working with their peers/partners solving similar examples and having additional at bats with the newly presented material. It's the perfect opportunity for teachers to show call students whose work closely mirror the quality and level of the teacher exemplar, as well as those who display misconceptions and need to be addressed in the moment before proceeding any further in the lesson.
Get Better Faster- Show Call Math
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Instructional Planning Tools

The following tools can be found on the ACE website under Instructional Planning Tools.

Instructional Planning Calendars

When reviewing the Instructional Planning Calendars, pay close attention to the proposed unpacking of the targeted standards that support teaching using a conceptual trajectory of content development. Note the instructional resources section for suggested strategies, manipulatives, and anchor charts to incorporate into instruction. The links below can be used to access the grade-specific calendars.

Assessment of Course Performance (ACP)

Assessment of Course Performance Sample Items are provided by the STEM Department, Mathematics, and mirror the student expectations that will be administered on the December assessments. The strategies pictured are recommended but are not the only strategies that can be used. A teacher’s tool box must be filled with multiple test-taking strategies that can be shared with students.

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Upcoming Professional Development

We will be hosting our second Math Team Thursday session of the 2019-2020 school year on November 7th at Chavez from 3:30 - 6:30 pm. Please remember to bring your Taking Action - Implementing Effective Mathematics Teaching Practices book, and complete your reading assignment prior to this session (Chapters 3 & 7). If you did not receive your book during last week's ACE Leadership Training at Edison, you can reach out to one of your Math ILCs (Laquetta Wilson, or Alex Bonet) to request for the book to be delivered to your campus.


ACE Website:

Please visit our revamped Teacher Portal tab on the ACE Website where you will have access to a wide variety of instructional resources and planning tools to create great lessons for our scholars. Instructional Planning Calendars, Common Assessment Exemplars, TEKS Differentiation Tools, Routines, Anchor Charts, and Problem Solving Protocol resources are available for your implementation.
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