ACE Mathematics Newsletter
3 - 8 Mathematics | FEB 2019
In this Edition:
Instructional Trends in Mathematics: Embracing the Power of Productive Struggle
Instructional Resources: 5th Six Weeks Instructional Calendars
Featured Item: Small Group Implementation
Professional Development: ACE Team Thursday Recap
Announcements: ACE Website
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.
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.
Differentiating Math Instruction with the MATH Workshop Model
Differentiating instruction is one of the greatest challenges for classroom teachers. Gone are the days of whole group lessons, and assigning the same activities to the entire class. We now teach in a student-centered environment where personalized learning is key.
Fortunately, our students are more engaged and successful than with the former instructional model. Unfortunately, teachers often feel swamped by the prep, coordination, and organization required to maintain quality differentiation. The key to keeping overwhelm at bay is the use of consistent routines and frameworks like math workshop, daily 5, reader’s workshop, and writer’s workshop throughout the day.
WHAT IS M.A.T.H. WORKSHOP?
M.A.T.H. workshop is a framework that allows students to learn new math content each day, practice math strategies in a variety of ways, and reflect on learning through verbal or written sharing. The predictable structure of math workshop makes it easier for students to participate in differentiated activities.
The components of M.A.T.H. workshop include:
Daily math warm up (10-15 minutes)
Mini lesson (10 minutes)
M.A.T.H. practice time (40 minutes)
Share (5-10 minutes)
DAILY MATH WARM UP
This is a time when students are provided spiral review, and routine practice with challenging skills that require repetition to achieve mastery. Your math adoption may have a strong spiral review component that can be utilized, or you may be interested in differentiating your warm up through the use of an activity like Number of the Day.
Your students should be able to complete the daily warm up activities with complete independence to set a positive tone for their workshop session each day.
Each day, students participate in a 5-10 minute lesson, during which new math content is introduced. This is one of two very brief times when all students are potentially working on the same activity simultaneously. This is also a time when students can work through personalized lesson sequences using Khan Academy, Front Row, or your own video lessons recorded.
M.A.T.H. PRACTICE TIME
Following their daily math lesson, students have an extended work session when they practice the new math skills taught that day, build their problem solving skills by solving performance tasks, get hands-on math practice, work on project based learning, complete assessments, use technology to practice math skills, and receive differentiated instruction from you.
How is this possible? These activities are organized into the following categories, stations, or rotations:
M – MEET WITH THE TEACHER
Students receive differentiated instruction from you. You can either schedule specific small groups to work with each day, or formatively assess students as they work, and pull individuals and small groups as needed.
A – AT YOUR SEAT
Students work to build their math reasoning, modeling, and problem solving skills. This is a perfect time for students to work on assignments that match their specific skill level. Student independence is a central focus of at your seat work.
Resources utilized for the at your seat rotation in class should include:
Reteaching, practice, and enrichment sheets from a math adoption for math drill and equation practice.
Problem Solving Task Cards for practice with performance tasks, word problems, math modeling, and writing about math reasoning.
Project based learning units to apply math concepts to real world situations and provide cross-curricular integration.
T – TECHNOLOGY
Students build math fact fluency using math websites or apps, such as IXL, Front Row, Khan Academy, Quick Math, Hungry Fish, and Multiplication.com.
H – HANDS ON
Students build math reasoning and fact fluency as they play math games. Providing students with game cards that have a consistent format boosts independence and engagement.
ORGANIZING STUDENT GROUPS
To maximize efficiency and focus in the classroom, you may want to group students based on a pre-assessment. The groups you form can work through these activities at assigned times to minimize overcrowded at a specific rotation option, and to provide balance in the type of practice students participate in each week.
Students take a moment to reflect on the math progress made that day and share their thoughts verbally, or in writing. This is the second brief time when all students are potentially working on the same activity simultaneously. A few methods for sharing include:
Buddy share out: share a reflection, or the response to a specific question with a math buddy.
Whiteboard share: write a reflection, or sharing response on a whiteboard.
Journal share: write a reflection, or sharing response in a journal.
Exit Ticket: write the response to a specific question on a whiteboard, or on a slip of paper.
Whole class share out: take a moment to reflect silently, then share a reflection with the class.
THE BENEFITS OF M.A.T.H. WORKSHOP
Students are more engaged because they participate in a variety of activities each day. Student achievement is positively impacted because students are engaged in math work that is “just right” for them.
Math prep time is minimal because there is rarely a need to change centers, print materials, or prep elaborate lessons. Teachers receive multiple data points from their interactions with students which allow them to provide ongoing support at their level.
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.