ACE Mathematics Newsletter
3 - 8 Mathematics | APR 2019
In this Edition:
Celebrations: Small Group Implementation
Instructional Resources: 6th Six Weeks Instructional Calendars
Instructional Trends in Mathematics: Embracing the Power of Productive Struggle
Announcements: ACE Website
Celebrations
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:
- identify students in need of support
- select student expectation
- 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.)
- create an exemplar & sequence problems
- list common or observed misconceptions
- write diagnostic questions to isolate the misconception(s)
- 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.
Instructional Resources:
Hot off the press: 6th 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
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.
Announcements
ACE Website: www.acedallasisd.com
Accelerating Campus Excellence
Email: jhealey@dallasisd.org
Website: acedallasisd.com
Location: 408 North Haskell Avenue, Dallas, TX, United States
Phone: 972 925 3669
Twitter: @ACEDallasISD