Overview

Session Summary

In this session you will consider ways to:

  • consider physical classroom set up
  • establish a learning community where students feel safe, take risks, listen to each other, use their mistakes as opportunities to learn and are challenged to think and reason
  • involve students in setting norms and expectations for learning
  • group students in different ways
  • help students see how collaborating and talking math helps them learn math

Getting Started: The Classroom

classroom

When students enter a classroom, they take a look around – this space will be their ‘home’ for the next nine months. How is it set up? Where will they sit? Who will sit by them? Where will they put their ‘stuff’?

This is not only students’ ‘home’, it’s also your home! It requires thought and planning to set up a classroom. There is not one way to do this, but all the questions raised above (and others) do need to be considered as you create the learning community that is your classroom.

Work Setting: Students will be working alone, in pairs, in groups and as a whole group during math class. One lesson could involve students moving from one setting to another. The classroom needs to be arranged in a way that they can easily transition between settings.

  • How can you set up the furniture (desks or tables, shelves, carpet) so students can easily transition from one work setting to another? The student seating needs to be organized so students can easily work in pairs and groups.
  • What part of the room is the best for space where the class can meet for whole group discussion and sharing strategies? What math tools (linking cubes, 100’s chart, number line, anchor chart) will students need in this space?

Wall Space for Strategies, Anchor Charts and Displays

Students need access to math tools such as anchor charts, sentence stems, 100’s chart or number lines.

Classroom Expectations

Teacher Messages

Tools & Anchor Charts

Tools

Where will you display math tools and anchor charts so students have access to these tools as they work at their seats?

 

Anchor Charts

Meaningful Vocabulary Displays

Strategies

Where and how can strategies and student work be displayed so students can refer to them as they work?

Early Grade Strategies
Upper Grade Strategies
Math displays that change with the unit of study.

Student Work

  classroom

Manipulatives and Tools: There are a number of math resources that need to be stored in the classroom. Some materials are frequently used and other materials are used for a limited amount of time. Think about how you’ll store the materials so students have easy access.

Make math manipulatives and tools accessible so students know where to find these and where to put them back after using them. Make your life easier: make them your partners in keeping things in order and handy.

  • What manipulatives do you need for your grade level?
  • What math tools need to be accessible to students on a daily basis?
  • How do you store the materials they are using so they can be easily distributed? classroom
  • Where are materials (e.g, individual whiteboards student books, journals, manipulatives) located so students can easily access them?
  • How will you organize and store the Math Workshop resources for the unit you are working on? How can you store Math Workshop resources for other units so you can access them easily when you need to use them?
  • classroomDo students need some of the tools –such as individual 100 charts, number line, individual white board, marker and eraser – stored at their seat? If so, how will you organize these resources?



Looking ahead…
Once the classroom is set up and the students arrive, the community building and learning can begin. We will address this in Activity 1.

Readings

Readings by Activity (in order as they appear)

Overview

Activity 1

Activity 2: Setting Up the Mathematical Community Cases

The following cases are from the Investigations Implementation Guide.

Activity 3

Video

Related Books

Activity 1: Setting Expectations and Norms

In this activity, you will watch, read, and think about how to set expectations for mathematics learning in your classroom. Setting expectations for math class needs to happen at every grade. You will see how expectations and norms are set in one 5th grade classroom.

Chris Opitz, a teacher at Willard L. Bowman Elementary School, Anchorage School District shared the following…

Social and emotional skills (SEL) and understanding don”t just happen. The ultimate hope is that children come to school with healthy hearts and minds and the skills to communicate and interact effectively. But we all know that this is often not the case. Children come from wildly different backgrounds and experiences, and they bring their diverse skills and struggles to school.

When I think about this daunting task, I have to be a realist. Most people I talk with ultimately realize the importance of SEL skills and knowledge but feel overburdened with the sheer amount of content we are expected to teach in a very limited amount of time. A common statement is, “If I am to get through these math lessons, or this language arts curriculum, when am I supposed to teach the SEL skills? That’s the parents’ job.”

I understand this position and have had those thoughts myself, but my question becomes, “Without SEL skills and knowledge, how can we possibly teach and have students learn effectively?” I believe social interaction is a key ingredient to productive and efficient learning environments.”

Chris Opitz
Cooperative Learning Fits into the Calculation, Edutopia, July, 2009

 

An Ideal Classroom

Scenario: Imagine you are an elementary school student and your teacher has asked you to work in a small group to develop a class working agreement.

Imagine your ideal classroom. Record your ideas for the questions below.

  • How would people act?
  • How would people interact?
  • What will your classroom look like?
  • What would your classroom sound like?

Working Agreement and Classroom Promises

Watch and listen to Lisa, a 5th grade teacher, as she shares how she builds the learning community by establishing a classroom agreement with her students at the beginning of the school year.

All classrooms and grades need to establish expectations for students to work in a safe math learning community. As Lisa shared, the agreement is revisited through the year. Even though the learning environment activity you experienced in this activity takes place in a 5th grade classroom, other grades can use and adapt the idea.

Notebook

Jot down in your notebook any ideas you are thinking of using or adapting for setting norms and expectations in your classroom.

From the Field

I am also very cognizant of the cultural backgrounds of my students. It is critical for me to create a learning environment where students feel safe to share thoughts and make mistakes as we all learn together.

It is important for me to support ELL’s development of the English language through careful planning that engages students in group work or partner work where they talk through representations and story contexts with one another.” p.6


Lisa Nguyen
5th grade teacher


Positive Norms to Encourage in Math Class By Jo Boaler


How to Teach Math as a Social Activity Chris Opitz, Edutopia

Activity 2: The Math Community Across the Grades

In this activity you will read cases written by teachers from different grade levels. In their classrooms learning is central, mistakes are opportunities, and all children are supported in learning math.

Read

Read at least two of the cases below.

Setting Up the Mathematical Community Cases

Notebook

In your notebook respond to the questions at the end of two of the cases you read. Specify which cases you read using Grade and the name of the case.

From the Field

Praise and Perception

… in a 1998 study at Columbia University with Claudia Mueller, Dweck investigated the relevance of the types of praise that teachers offer students in conveying mindset. This study, conducted with fifth grade students, shows that when teachers use personal praise (for their intelligence), it tends to put students in a fixed mindset, whereas using process praise (for their effort or procedure) tends to foster a growth mindset.”

Cindy Bryant
Growth Mindset and the Common Core Math Standards, Edutopia

Read the message a teacher posted to start her math lesson. She begins by praising for the class’s determination, motivation and their willingness to share their strategies, based on their previous day’s work. Her praise is connected to behaviors, rather than a comment that’s detached such as “You’re all awesome”.

 

Read more about the use of praise below.


Praise Children for Effort, Not Intelligence, Study Says, New York Times


How Not to Talk to Your Child: The inverse power of praise

Introducing Sam and Charlie

Sam struggles in math. Sam has trouble understanding the information in a word problem, and representing it is therefore challenging. The issue is often related to language. For Sam, every problem is a new problem. Sam doesn’t think about the “what do I know that can help me here?”


Charlie is always eager to be the first to share the answer to a problem and his strategy. The answer is most often correct, though Charlie resists using any tools (number line, arrays, 100 Chart). I worry that Charlie is bored and wonder how to challenge him. When I think about whom to pair with Charlie, I most always find a student who is average because Charlie is very competitive, yet is also a good helper when he realizes someone needs help.

Journal

Describe your own Sam and Charlie in your journal

Activity 3: Mindsets and Mathematical Practices

In this activity you will look at the mathematical practices and how they impact student learning in the math classroom. You will also learn about Carol Dweck’s work with mindsets and how they impact learning outcome.

The Standards for Mathematical Practices

The Common Core mathematics standards include both content and process standards. Content standards include the mathematical knowledge and skills students should learn. The process standards (Mathematical Practices) specify the mathematical ways of thinking students should develop while learning mathematics content. These Mathematical Practices build on the NCTM Process Standards and the five strands of mathematical proficiency outlined in the National Research Council’s (Adding It Up: Helping Children Learn Math).

NCTM Process Standards

NCTM Principles and Standards

NCTM Process Standards

  • problem solving
  • reasoning and proof
  • communication
  • representation
  • connections.

Adding It Up Strands for Mathematical Proficiency

  • Conceptual Understanding classroom—comprehension of mathematical concepts, operations, and relations
  • Procedural Fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
  • Strategic Competence—ability to formulate, represent, and solve mathematical problems
  • Adaptive Reasoning—capacity for logical thought, reflection, explanation, and justification
  • Productive Disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

NOTE: These five strands are interwoven and interdependent. How students acquire mathematical proficiency and how teachers develop that proficiency in their students are also interwoven.

CCSS Mathematical Practices (MPs)

Mathematical Practices describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise.”

(CCSSM, p. 8)

Read

Read The following document provides K-5 examples of the Mathematical Practices. Standards for Mathematical Practice: Commentary and Elaborations for K–5

Notebook

Think about Mathematical Practices examples for your grade level. Choose a grade level to focus on if you are not a classroom teacher. Record the examples in your notebook.

The Impact of Growth Mindsets and Teacher Beliefs

Read and listen to Carol Dweck as she shares her findings about Growth Mindsets. Then read and reflect on a chart developed by NCTM that describing unproductive and productive beliefs about teaching and learning mathematics.

Growth Mindset

What are growth and fixed mindsets? How do you develop a growth mindset?

In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

Carol Dweck

Learn more as Carol Dweck shares her research on growth mindset.

Notebook

What is your ‘yet’? Think of a growth mindset you want to set for you as a teacher and for your students. Record your thoughts in your notebook.

Read

Read How to Encourage Students by Carol Dweck from article Revisits the ‘Growth Mindset, Education Week, September 2015

Teaching and Learning Beliefs

Teachers’ beliefs influence their teaching and learning. Our believes teaching and learning are often formed from their school and/or family mathematics experiences.

Read

Read Beliefs About Teaching and Learning Mathematics from Principles in Action NCTM

Productive and Unproductive Beliefs

Notebook

In your notebook, describe how you will embrace productive teaching and learning beliefs to enact a math learning community where CCSS Mathematical Practices, a growth mindset and praise focused tangible evidence are central to students’ math learning and your teaching practices.

As you work through this course, consider how productive beliefs, a growth-mindset and enacting the Mathematical Practices will help you support the math learners in your classroom.

From the Field

No matter what your ability is, effort is what ignites that ability and turns it into accomplishment.”

Carol S Dweck
Mindset: The New Psychology of Success, 2008

 

When students are given fixed messages about their own potential – with ideas that they are smart or not – they develop ‘fixed mindsets’. Such mindsets impact students’ learning greatly and they have been associated with long-term low achievement and avoidance of harder work (Blackwell, Trzesniewski, & Dweck, 2007; Boaler, 2013a; Dweck, 2006b).

In a recent study the students found to be most impacted by fixed messages, were those who were placed into top tracks (Romero, 2013). Ability grouping sends a fixed mindset message to students – that they are smart or not – and fixed mindset thinking is detrimental to students in many aspects of learning (Dweck, 2006) and at all levels of achievement.

One of the groups of students with the most persistent and damaging fixed mindset thinking is high achieving girls, who persistently avoid STEM subjects at high levels (Boaler, 2014; Dweck, 2006a).. …“

Raising Expectations and Achievement. The Impact of Wide Scale Mathematics Reform Giving All Students Access to High Quality Mathematics, Jo Boaler and David Foster

 

How Can Research on the Brain Inform Education? SEDL


Every Kid Needs a Champion –Rita Pierson

Discussion

Reflect back on your experiences in this session. Share one “aha!” and one question related to establishing a community that supports math learning.

Go to the Discussion Forum

Go to the Aha! Forum

Notebook

Complete the Session 1 Notebook page using the indicated prompts. In the final field of your notebook, reflect on the key take-aways from this session for your own learning and record ideas that you will implement to support math learning.

Key Learnings

  • Establishing norms and setting expectations with students for mathematics class (whole group, small group, pair and individual) are important to do right from the beginning of the year
  • Involving students in creating the behavioral norms is a critical piece of establishing a safe learning community
  • Developing the learning community is an ongoing process (Do all learners feel safe and respected? Are all learners involved?)
  • The classroom set-up and math learning community impact students’ ability to learn
  • A growth mindset creates greater confidence and greater persistence
  • Difficulty and challenge and productive struggle means ‘not yet’
  • Praising intelligence makes students vulnerable. Praising process and effort helps students develop Mathematical Practices
  • Math abilities can grow through hard work… the power of ‘yet’ - when math learning creates growth mindset environments steeped in ‘yet’, equality can happen