ACE Mathematics Newsletter

3 - 8 Mathematics | FEB 2019

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In this Edition:

Celebrations: Small Group Implementation

Instructional Resources: 5th Six Weeks Instructional Calendars

Instructional Trends in Mathematics: Embracing the Power of Productive Struggle

Professional Development: ACE Team Thursday Recap

Announcements: ACE Website

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Small Group Implementation

Small groups are taking off! Teams and teachers launched small groups with fervor and tenacity, strategically grouping students based on goals and performance, making sure differentiation is based on our differentiation tools, and using great questions to ensure conceptual understanding. Teams are also keeping a sharp eye for students not engaged in quality work assignments and how to best ensure students are working with rigorous materials and are able to self-monitor if they are working independently. In order to ensure consistency and effectiveness across our network, ACE has developed a framework to guide you in the process of small group implementation.

Small Group Tables

The expectation for small group tables is for the following to be present and organized:

  • Standard-aligned questions

  • Teacher exemplar

  • Teacher question stems

  • Dry-erase boards/markers

  • Paper & pencils

  • Manipulatives (if applicable)

  • Anchor chart

  • Accessibility Features (if applicable)

  • Designated Supports (if applicable)

Small Group Preparation

Successful small group preparation involves thoroughly analyzing student work. Examining student work and talking directly to students about their work is the most reliable method for determining students’ misconceptions and determining if there is a procedural or conceptual gap.

These are the steps involved in planning a data-based small group session:

  1. identify students in need of support
  2. select student expectation
  3. select standard-aligned problems (standard aligned questions may isolate a particular part of a standard or may break the skill into bite-size pieces that are along the trajectory of understanding the standard to its fullest.)
  4. create an exemplar & sequence problems
  5. list common or observed misconceptions
  6. write diagnostic questions to isolate the misconception(s)
  7. teach/fine tune a specific strategy

Steps 4-6 are really not linear. As you create the exemplar, misconceptions may surface, and questions to ask to identify the gap or a misconception may also surface.

The goal of a small group session is to identify a gap and correct a misconception regarding conceptual or procedural understanding. Therefore teachers should focus on the concept or procedure within the context of a problem – not the problem. Use the problem as a vehicle to address the underlying issue. Then, strategically sequence the problems to be completed based on a learning trajectory geared towards comprehension and mastery of the targeted student expectations.
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Instructional Resources:

This month we would like to highlight planning tools to help you strengthen and accelerate instruction!

Hot off the press: 5th Six Weeks curriculum calendars

When reviewing these calendars, pay close attention to the proposed unpacking of the targeted standards in order to facilitate conceptual understanding. Notice we have left several instructional days open for you to customize them based on your campus data. Please prioritize high leverage SEs based on the STAAR frequency distribution by student expectation for the last three years.

Instructional Trends in Mathematics: Embracing the Power of Productive Struggle

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Productive struggle is a highly effective methodology when it comes to teaching math and other STEM related subjects. Used mostly in the primary level, it involves letting students deal with problems and puzzles on their own, even when they are a bit too advanced for them, and letting them figure out to how to solve them. This, which may seem counterintuitive, is actually intended to let students resort to their own creativity to find possible solutions to problems that do not necessarily have a single way to approach them.

Different studies have led to the conclusion that struggling to make sense of mathematics is an essential part of the learning process, and is the most efficient way to get students to really understand the topics at hand. Unfortunately, struggle is not often perceived as a positive and constructive part of the learning process and, rather, it is treated as failure both by the learner and the teacher. And with curriculums that are designed to move from one topic to the other, regardless of the students’ capacity to master a particular knowledge before moving on, are creating major problems in the study of this field.

Many math courses are taking a dubious approach in which the correct answer is valued more than reasoning and understanding, and where strict formulas are provided in a lecture-like manner, without giving students the possibility to discuss them or to fully understand why they work the way they do. According to some specialists, this leads to students who lack confidence in their abilities, and who – because of this insecurity – are reluctant to put the effort to understand. A problem which is worsened by popular beliefs like that you are either good in mathematics, or that you are not.

Productive Struggle is a methodology that was proposed to end this, and to foster true understanding of math related topics in students of all levels and ages, but especially among younger ones. The goal of this technique is to help students make sense of problems and persevere in solving them, no matter how difficult they find them to be. In order to apply this methodology, teachers present a problem to the class, and give individual students time to think it in on their own. These problems can be framed in any way, but according to recent research studies, problems that have a real-life feel to them are often more meaningful, as students can apply their personal experience, and feel more secure when working out the answer.

After giving students enough time to develop a strategy to resolve the problem and to try it out, fail, and start over, until they figure out an effective way to reach a solution, teachers gather students in small groups, where different solutions are meant to be compared, and used to come up with a better solution based on what the group learnt. Finally, the whole class is meant to discuss the problem, and all the proposed solutions. During the course of the exercises, teachers are not supposed to help students out other than encouraging them, or helping them identify the source of their struggle (are they having trouble identifying how to get started, or how to lay down a strategy? Or are they having a problem applying their line of thought?), or just by pointing out that difficulties are an essential part of learning, and that failing is an option as long as they try.

Only after the whole class has discussed the possible solutions and the different answers, teachers are allowed to draw a map to the solution, and to provide students with tools and tasks that may help them in the future. But, according to experts, it is important that they address that math is hard, and that it is supposed to feel complicated in order for it to be understood, as a means to downsize frustration and encourage students to keep trying.

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Professional Development

ACE Team Thursdays Recap

On our January 31st, 2019 session small group facilitation was explored through the See It, Name It, Do It Model. Participants viewed a small group simulation, the preparation for the facilitation, and then engaged in planning and role playing the same. Assistant principals, campus coaches, and teachers cordially sparred as they determined whether assigned SE specific problems were or were not aligned. After identifying problems, teachers role played small groups and taught each other their instructional strategies.

Everyone was provided a copy of the Time vs. Benefit document that strategically considers student expectations based on the time necessary to teach the standard to mastery and the benefit of achieving mastery in terms of the standard’s frequency on STAAR. This document can be useful when designing instructional calendars for small groups. Participants were also given a check list of components for inclusion when establishing a small group table. Other documents shared included small group implementation Leadership Look Fors and examples of possible teacher feedback regarding questioning and the use of multiple representations.

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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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