I was recently talking with several math teachers. We were in agreement that it seems students today are profoundly different from students in the past…or at least how we remember them being in the past.
Compared to the “good old days”, the teachers felt students…
- are coming to their respective grade levels less prepared than in the past;
- have less tolerance for productive struggle;
- do not collaborate as well
- are less able to concentrate for any length of time
…and the list continued.
With students seemingly transformed overnight (really…over the course of a pandemic), it is understandable that teachers are left wondering what the heck happened? Why are the instructional strategies we have been using for the past decades suddenly not working with students nowadays?
What is a teacher to do?
In this blog post, I will share how one teacher has embraced the Three Dimensions of Systemic Change that support mathematics instruction found in Chapter 2 of the California Mathematics Framework; and how the students in her classroom have been transformed into engaged mathematicians…literally over night. As a result, she has created an equitable and engaging classrooms that has increased student achievement and given her a new joy for teaching mathematics..
Three Dimensions of Systemic Change that Support Math Instruction
The three dimensions of systemic change that support math achievement in the new CA Math Framework are:
- An Assets-Based Approach to Instruction
- Active Student Engagement Through Investigation and Connection
- Instruction That Centers Cultural and Personal Relevance
Let’s briefly dig into each one.
An Assets-Based Approach to Instruction: This dimension emphasizes the importance of recognizing and valuing students’ existing skills, experiences, and cultural backgrounds as assets to build upon in mathematics instruction. An assets-based approach to instruction acknowledges that students enter the classroom on Day 1 with funds of knowledge that can be utilized to support learning mathematics.
Active Student Engagement Through Investigation and Connection: This dimension focuses on fostering active student engagement by encouraging investigation and making connections in mathematics learning. By engaging students in meaningful mathematical tasks that relate to their lives and interests, educators can promote deeper understanding and interest in math.
Instruction That Centers Cultural and Personal Relevance: This dimension highlights the significance of centering instruction on cultural and personal relevance to reflect the diversity of California’s student population. We can make math instruction culturally relevant and personally meaningful through two simple changes in the daily word problems used for instruction: use students’ names and incorporate their interests in the word problems.
These three dimensions of systemic change in the CA Math Framework aim to provide educators with the tools and strategies needed to promote equity, engagement, and meaningful learning experiences in mathematics instruction, ultimately supporting students in achieving math proficiency and success.
What changes did the teacher make?
Let’s first start by acknowledging where the teacher began. Largely, her teaching strategy could largely be summarized as “I do, You do, We do”.
She discovered that this script as her primary form of instruction was simply not as effective as it used to be. Despite her working harder than ever, she was getting fewer and fewer good results.
Through work with the Merced COE Math Team she was introduced to a different instructional script for her math lessons.
The teacher begins by giving students a story problem to work on using any strategy. Students begin with one or two minutes of pure silence to work on the problem independently before the teacher invites them to continue working on the problem with a partner. While students are working on the problem, the teacher strategically selects and sequences two or three students who will share their strategies. Then the teacher leads the class through a discussion as the two or three students share their thinking. The class is invited to compare and contrast the methods that have been shared on the whiteboard.
How does this new script improve student morale and achievement?
It honors the THREE DIMENSIONS OF SYSTEMIC CHANGE.
By giving the story problem FIRST for students to work on prior to instruction, the teacher is honoring the assets students already have. In effect, she is saying to her students, “I trust you to use whatever knowledge you already possess to attack this problem.” The surprising thing is that students do not have to successfully solve the problem to derive the benefit of assets-based instruction. In this study, students who were given an opportunity to invent their own understanding learned better regardless of whether or not they were successful in their attempt to invent their understanding.
Because students in this new instructional script are not merely mimicking the teacher’s explanation, students are actively engaged in the process of investigating their own understanding and making connections with math concepts they have previously learned. The teacher has noticed that students are freed of the shackles of “follow the teacher” and instead engage in the actual standards for mathematical practice…they are mathematicians! During class discussions, students compare and contrast each other’s strategies.
The teacher is able to elevate cultural and personal relevance simply by selecting a word problem from the lesson in the textbook and rewriting it to include students’ names and their interests. No more bland textbook problems.
Original problem: There are 4 boxes with 6 binders in each one. Three brothers share the binders. How many binders does each brother get?
New problem: There are 4 boxes with 6 cookies in each one. Stasha, Martin, and Diego share the cookies equally. How many cookies does each student get?
So what are the discrete steps for teaching in this way?
- Introduce the story problem to students
- Students work independently on the problem at their desks.
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- Students may use manipulatives, pictures, and/or number sentences to represent the problem.
- While students are working, teacher “teaches between the seats” to support students as needed
- (REMEMBER: it is not important for every student to be successful with this problem.)
- Select two or three students to share their thinking.
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- Strategically sequence the order in which the two or three students will share.
- Arrange the student solution methods from left to right on the whiteboard.
- Allow the class some time to compare and contrast between the various solution methods
- The teacher now teaches a mini-lesson to show students what they will try to do in the NEXT problem.
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- Connect the student-generated solution methods to the lesson objective
- Be explicit about what you want students to try on the next problem.
- Introduce Problem #2 for students to work on.
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- This cycle continues for Problem #2 and possibly Problem #3 (if needed):
Introduce problem → Students work independently → Students share → Teach mini-lesson
- This cycle continues for Problem #2 and possibly Problem #3 (if needed):
To be clear, there are still days in which “I do, You do, We do” might be the preferred instructional script. This might include days where students are provided a day to deliberately practice some sort of procedural fluency that is being built upon days and days of conceptual understanding developed during the “We do, You do, I do” lessons.
For more information on Teaching Through Problem-Solving, read this.
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Love this! Every bit of it!