Learning That Lasts: Chapter 4: Reimagining Mathematics Instruction
How can we plan and deliver math lessons that challenge, engage, and empower students so that they love math and become skilled mathematicians?
Reimagining mathematics instruction can be a heavy lift. Most teachers have years of traditional mathematics instruction under their belts by the time they enter their professional careers. Chapter 4 of EL Education’s book Learning that Lasts explores two critical strategies for improving mathematics instruction—changing mindsets about mathematics; and remodeling the basic lesson structure for mathematics. This reimagination leads to mathematics instruction that is more challenging, engaging, and empowering for students as well as teachers.
Almost every school in America is filled with teachers and students who declare, without apparent shame, ‘I am just not a math person,’ or ‘I just don’t get math; I’ve never been good at math.’ What teacher would glibly say, ‘I’m just not a reading person’ or ‘I just don’t get writing?’ Somehow we have decided that it is acceptable to be ‘bad at math’—even if you are a teacher! That culture needs to change, especially in schools
- I can identify ways to promote a mindset that embraces mathematical learning in my classroom (i.e., a growth mindset for mathematics).
- I can describe how Math Workshop 2.0 challenges, engages, and empowers students.
Read: A Different Mindset for Mathematics
Stanford researcher Carol Dweck, author of Mindset: The New Psychology of Success (2006), would say that many teachers and students have a fixed mindset about their ability in mathematics: they assume it is just not an area of strength for them. The first and most important change for a school to make to improve mathematics achievement is a shift in the adult professional culture in the building toward one that embraces mathematical thinking and learning mathematics together.
Accordingly, it is helpful before you start this chapter to review your own “math mindset”—the disposition and experience you bring to learning about mathematics. Let’s do this by telling your “math story!”
Take a few minutes to journal your responses to these questions:
- What was learning about mathematics like for you?
- Would you describe yourself as “good at math?”
- How did your experience as a math student make you feel?
- How does your experience with math now affect/impact your role as a teacher?
Read the Case Study below about how one school, Two Rivers Public Charter School in Washington, DC, approached creating a culture of mathematics.
- How did the school begin the task of building a culture of mathematics?
- What do you think was most critical to the success of the initiative?
- How might your school approach a “mathematics mindset make-over?”
Test your own mindset here.
Then, visit this page on Data Culture from another EL Education PD Pack and examine the graphic on Two Mindsets from Carol Dweck’s work. As you review that graphic, and consider the following questions:
- What is the difference between a growth mindset and a fixed mindset?
- Why is a growth mindset necessary for both teachers and students in learning mathematics?
You can also learn more about Carol Dweck’s research about Growth Mindset at: https://www.youtube.com/watch?v=hiiEeMN7vbQ.
After reviewing all of these resources on Mindset, think about your classroom and your school and consider the following questions:
- How do you help students develop their growth mindset if they believe that other kids are inherently smarter or more talented?
- How do we as adults in a school model (or not) a growth mindset for our students?
Introducing Math Workshop 2.0
Deeper instruction in mathematics enables students to meet the big shifts demanded by new and more challenging standards. These standards require students to grapple with more difficult problems and explain, defend, and critique their mathematical reasoning.
What type of lesson structure best supports students with developing both conceptual understanding and computational fluency? Workshop 2.0, introduced briefly in Chapter 1 of Learning That Lasts, is a highly effective lesson structure that challenges students with higher level problems, engages them in discourse to demonstrate their understanding, and empowers them to be more independent mathematical thinkers. When used effectively in classrooms, teachers have reported the following shifts:
- Students do more of the mathematical thinking and the teacher does less.
- Students do more speaking, writing, and risk taking, and less passive listening.
- Students work on more challenging problems, and do less review and repetition.
- Students often lead their own learning.
- Students and teachers are clearer about what students understand.
Examine the components of Math Workshop 2.0 (on pages 186-188 of Learning that Lasts) and think about what teachers and students are doing during each component:
- Engage and Grapple
Look ahead to your mathematics lessons for next week:
- How do the components of Math Workshop 2.0 differ from your usual lesson planning?
- Choose one upcoming lesson to redesign using the Math Workshop 2.0 lesson structure. Whether you end up teaching this lesson or not, what was the process of designing it this way like? Did it require any shifts in your thinking?
Review and Watch: Math Workshop 2.0 Power Practices
The Math Workshop 2.0 lesson structure provides a clear and concrete structure that allows students to focus on learning mathematical concepts and skills deeply. The beauty of Math Workshop 2.0 is that in can be used in part or as a whole. The five parts of the Math Workshop 2.0 structure are each built around strategies that can engage students in problem solving, challenge their mathematical thinking, and empower them with the tools and language of mathematicians.
Each part of a Math Workshop 2.0 lesson is distinguished by a power practice that makes it particularly effective:
- Finding, Choosing and Using Strong Problems (Engage and grapple)
- Building Rich Mathematical Discourse (Discuss)
- Mini-Lessons that Illuminate Concepts (Focus)
- Individual and Group Practice (Apply)
- Solidify and Assess Understanding (Synthesize)
What follows is an exploration of a few of the Math Workshop 2.0 power practices, which you can view in action in the accompanying videos.
Finding, Choosing and Using Strong Problems
Students often have a disconnect between the concepts and skills in mathematics class (beyond simple arithmetic) and their lives within and outside of school. If we can create genuine connections between mathematics and life for students by choosing problems that relate to the content of other academic classes, or relate to school, community, or national and world issues, we can ignite a sense of purpose in students.
Watch the video Going Deep with Kindergartners with Problem-Based Math to see how teacher Anne Simpson chooses a “real-life” problem to empower and engage her kindergarten students in grappling with concepts in mathematics. As you watch, consider the following questions:
- What made this problem challenging and engaging for Simpson’s young learners?
- How did Simpson empower students to lead their own learning in this lesson?
- How does the gallery walk protocol help students think about their own learning and synthesize as a group?
- What makes this “real-life” problem engaging for the students?
- As you examine an upcoming lesson, how can you include a “real-life” problem to challenge, engage, and empower your students?
Building Rich Mathematical Discourse
Effective mathematics classrooms have one thing in common—they provide opportunities for rich mathematical discourse. Students can discuss mathematical concepts and patterns with sophistication. The Math Workshop 2.0 lesson structure builds this into the second phase of the lesson, requiring students to share their work from the grapple problem.
The capacity of students to discuss mathematics deeply and insightfully is a product of deliberate structures, strategies, and mathematical culture established by the teacher. This culture must be an emotionally and socially safe place in which students can ask questions and suggest ideas without fear of judgment.
Watch the video Teaching Students to Prove their Mathematical Thinking through Questions, Charts, and Discourse to see what discourse looks like and sounds like in a third grade classroom that has built a culture of strong mathematical discourse. As you watch, consider the following questions:
- How does the teacher challenge students to use multiple strategies and to think as mathematicians?
- How does the debrief structure in this classroom engage students in thinking about their own thinking?
- As you think of your classroom culture, what conditions are present to support students in asking questions and suggesting ideas?
Mini-Lessons that Illuminate Concepts
The mini-lesson occurs after students have had a chance to grapple with a problem and you have had a chance to observe their thinking. The keys to an effective and engaging mini-lesson are:
- Focus sharply on the learning target(s).
- Plan everything ahead of time: main points, vocabulary, examples, visuals.
- Be ready to adjust the plan to connect to student ideas, language, and questions observed during the grapple and discuss sections of the workshop.
The mathematical concepts and strategies you present in your mini-lesson should connect to the ideas and questions students raised while grappling with problems. It is empowering for students to learn that their mathematical thinking parallels established conventions and algorithms. Labeling the “idea” with a student’s name (e.g.,“Alicia’s approach”) can be even more empowering!
Watch the video Using a Problem-Based Task with Fourth Graders to Create Deep Engagement in Math to see how Jessica Proffitt asks her students to grapple with their ideas and figure mathematical concepts out for themselves. As you watch, consider the following questions:
- How does the task Proffitt chose invite students to discover deep mathematical concepts?
- What elements of Math Workshop 2.0 can you identify in this lesson?
- How does Proffitt engage students in the problem and prepare them to dig into rigorous mathematical thinking?
Review: The Critical Moves of Reimagining Mathematics Instruction
Following a new lesson structure like Workshop 2.0 is a high-leverage
next step to challenge, engage, and empower students to be skilled and facile
mathematicians. The Who, What and Why of Reimagining Mathematics Instruction, from chapter 4 of Learning That Lasts, describes the critical moves and entry points for reimagining mathematics instruction.
As you consider The Who, What, and Why of Reimagining Mathematics Instruction, choose one critical move to focus and reflect on. Then consider the following questions:
- What would be different in your classroom if this critical move were happening?
- What action steps could you take to implement this critical move?
- How could you involve your administration in supporting you?
The Power of Belief - Mindset and Success: Watch this video to learn more about how to develop the growth mindset necessary to create a culture of mathematical literacy.
Marilyn Burns’s Website: Math Solutions: Review this website for a variety of supports for creating a culture of mathematics, especially mathematical discourse.
The Standards for Mathematical Practice, annotated for the K–5 classroom: This document provides two different ways of adapting the language of the Common Core practice standards to the K–5 setting.
Two Rivers Public Charter School Website—Learn with Two Rivers: Two Rivers Public Charter School in Washington, DC has a website to share best practices with other schools. The Problem-based Tasks in Math page supports many Math Workshop 2.0 practices.
- Looking back at your “math mindset” story, what changes could you make to ensure that you and your students feel confident that everyone can grow and succeed at mathematics with effort and focus?
- What time, structures, and resources are available at your school for you to develop and deepen your own conceptual understanding of mathematics? What concrete steps could you take to initiate change?
- What steps can you commit to to bring one or more components of the Math Workshop 2.0 (and their accompanying “power practices”) to your classroom?
For School Leaders…
- What collaborative structures exist at your school for educators to develop formative and summative assessments that measure conceptual understanding of mathematics? How could you make that a priority?
- How can you support and encourage teachers to share mathematics with the broader community through newsletters, schoolwide mathematics events, and displaying and celebrating mathematics publicly on the walls and at community meetings?
- How can you make improvement in mathematics and problem-solving a schoolwide focus for staff as well as students? Read the case study on pages 219-220 of Learning that Lasts to see how Two Rivers Public Charter School in Washington, DC accomplished this. How might you create a similar plan at your school?