ACE Mathematics Newsletter
3 - 5 Mathematics | SEP 2019 YEAR 4: VOL. 1
In this Edition:
Instructional Trends in Mathematics: Embracing the Power of Productive Struggle in Math
Mathematics Instructional Block: Preview Challenge & Academic Routines
Instructional Planning Tools: Instructional Planning Calendars
Upcoming Professional Development: Math Team Thursday
Announcements: ACE Website
Students exploring concepts with hands-on activities and manipulatives.
Students making connections using pictorial models to facilitate conceptual understanding.
PLCs at Full Strength
Teams planning collaboratively and going deeper into the standards through the lens of CPA.
Routines & PSP
Academic routines & Problem Solving Protocol taking off.
Math Word Walls
Academic vocabulary being reinforced through Math Word Walls.
Small group areas already established and in action to differentiate instruction.
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 ok so 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.
Preview Challenge (Productive Struggle)
Expectations for Implementation
The Preview Challenge is one of the critical components of the Mathematics instructional block that will help us lay the foundation towards teaching conceptually. This segment offers teachers the opportunity to intentionally engage students in a controlled productive struggle by asking them to solve a real-life application problem involving a concept yet to be taught.
The problem posed to students during this segment is used to introduce the day’s lesson. The challenge is not the lesson. The concept the challenge addresses is the topic of the lesson. The problem may or may not be solved during the allotted time and may be used the next day. Teachers monitor students to ascertain the students’ initial performance level with the concept. This information is used to highlight specific aspects of the concept during instruction with which students particularly struggled.
Teachers should revisit the Preview Challenge prior to the end of the lesson, during the We Do segment to ensure the strategy modeled during the I Do is replicated to address the Preview Challenge. Once students have the required skills to solve the problem after the I Do modeling, and successive at bats have taken place during the We Do segment, students are redirected to the challenge question. The intent is to make the learning transparent to students; they now possess the knowledge and skills to answer the question successfully.
Expectations for Implementation
Routines have been consistently used to front-load upcoming student expectations or as a means of spiraling previously taught standards to strengthen student retention of the concepts.
The Second Six Weeks of instruction is a misnomer as there only 5 weeks of instruction (Sept. 30 – Nov. 1), with the Common Assessment administered in week 5. Because of the shortened time period, devoting instructional days to student expectations from the first six weeks that are on the Second Six Weeks Common Assessment is challenging if not impossible. For instance, in grade 3, there are four student expectations from the 1st SW that will be assessed on the 2nd SW CA: SEs 3.2A, 3.2D, 3.4A, and 3.5A. These student expectations are spiraled into instruction during the 2nd SW through a routine, either as a Problem of the Day or by using a suggested routine template.
If routines are omitted from the instructional block, a valuable opportunity to spiral previously taught student expectations is lost. Students need strategically designed spaced opportunities to revisit concepts and strengthen the new neurological connections formed during good, first-pass instruction.
Note the routines listed in each respective Instructional Planning Calendar in the table below:
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.