Mind for Mathematics, A: Meaningful Teaching and Learning in Elementary Classrooms-useful classroom tactics and examples for K-6 math

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What does it take to be a good mathematics teacher who actively engages students and addresses learning differences? Gain a mental picture of an effective mathematics learning environment and why it must be founded on growth mindset principles. This easy-to-read text breaks down the complex components of mathematics teaching and divides them into practical strategies. Combining mathematics research, useful tactics, and examples from K–6 classrooms, the book includes reflection questions, action tasks, and activities to inspire and engage mathematical minds.

Benefits:

  • LEARN HOW TO USE DIFFERENT TYPES OF ASSESSMENTS to advance student learning and inform mathematics instruction.
  • OBSERVE SPECIFIC CLASSROOM EXAMPLES and vignettes that illustrate the mathematical concepts covered in each chapter.
  • LEARN THE CHARACTERISTICS OF HIGH-QUALITY, RIGOROUS TASKS that engage students in learning mathematics.
  • GET ADVICE ON BALANCING TEACHING RESPONSIBILITIES and making sound plans for teaching mathematics, including communicating with students’ families.
  • INFLUENCE STUDENTS TO WORK HARD, grapple with challenging problems, and ultimately value mathematics.

Contents:

About the Author

Introduction

  1. Creating the Mathematical Environment
  2. Engaging Mathematical Minds
  3. Reaching Different Mathematical Minds
  4. Challenging Student Mathematicians
  5. Monitoring Mathematical Assessment
  6. Balancing It All

References and Resources

Index

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Chapter 1

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CHAPTER 1

CREATING THE

MATHEMATICAL

ENVIRONMENT

Learning never exhausts the mind.

—Leonardo da Vinci

Imagine it with me: the ideal mathematics classroom where students are eager to learn and groan when the mathematics period ends. Students are involved in and own their learning. They explore and take risks. As the teacher presents a challenging problem, students’ eyes light up, and the class has a healthy buzz as students discuss the meaning of the problem and various ways to start it. Some students begin to ask questions, but not of the teacher—of each other. Some students begin sketching representations, while others try to jump into equations.

Still others grab manipulatives to model the problem. The teacher visits various groups of students so they can ask questions to guide their thinking, while not giving too much away. The teacher knows that giving too much information will dilute the students’ learning process, and they do not want to know the answer ahead of time. Students in this classroom enjoy wrestling with complex, realworld problems and only ask for hints or next-step guidance when they cannot see how to progress.

 

Chapter 2

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CHAPTER 2

ENGAGING

MATHEMATICAL

MINDS

It’s fine to work on any problem, so long as it generates interesting mathematics along the way—even if you don’t solve it at the end of the day.

—Andrew Wiles

During his first week on the job, my school’s new assistant principal came to visit my classroom. Sitting on the floor with a group of students, I looked up and noticed him and waved. I thought that if he wanted to talk to me, he would motion to me or say something. He didn’t, so I finished with the group I was working with and moved on to another. The assistant principal slipped out fairly quickly.

At the end of the day, my principal called me into her office. She laughingly told me that her assistant thought she asked him to come see me because I needed to be put on a plan for classroom management, while her intent was for him to see an example of active learning in a mathematics class. However, all he saw were students out of their desks, all over the place, and it was very noisy. From his doorway observation, he could not tell what students were learning, assumed the worst, and left to discuss my management style at a later time. After I had a chance to explain what was happening in my classroom, the assistant principal apologized and came another time to watch groups working effectively and independently, even if they still worked somewhat noisily.

 

Chapter 3

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CHAPTER 3

REACHING

DIFFERENT

MATHEMATICAL

MINDS

In the end, all learners need your energy, your heart, and your mind. They have that in common because they are young humans. How they need you, however, differs. Unless we understand and respond to those differences, we fail many learners.

—Carol Ann Tomlinson

Picture it with me: twenty-eight willing learners, anxious to begin a new year of learning. Well, some are excited anxious, and others are nervous anxious. Some feel confident in their mathematics ability, while others feel confident that they have no mathematics ability. Many students have memorized their number facts, some can find quick answers to number facts using a strategy or two, and some wonder when they were supposed to have learned number facts.

Most students want the teacher to model how to do mathematical problems and then let them try. Others want to try first and only ask for help if they get stuck. Others just want to watch the teacher and never try at all. One group of students wants to work with concrete materials first, a different group of students wants to work with paper and pencil to apply what they have already learned, and yet still another wants to use visual images to make sense of a problem. Some students want to work by themselves, and a few of them will shut down and refuse to participate in a group activity. Others won’t start independently but want only to work with a partner or small group. And this is only the beginning of the

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Chapter 4

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CHAPTER 4

CHALLENGING

STUDENT

MATHEMATICIANS

The deeper we search, the more we find there is to know, and as long as human life exists I believe it will always be so.

—Albert Einstein

I often find myself on an airplane chatting with the person next to me. I have begun to think of creative ways to say what I do without actually saying what I do.

My heart hurts and my head aches with all the stories of adults who hate mathematics, were never very good at mathematics, and mostly can’t understand why we teach mathematics now in such crazy ways! I want to ask why we should teach mathematics in the same old ways when these adults are living proof that they didn’t work well. I try to explain why we teach mathematics differently today, but too often, their eyes start glazing over, and the mathematics coma begins to set in.

Many adults tell me that mathematics has just never made sense to them, and if they could have stopped with arithmetic, they would have been okay. Fractions and algebra were just too challenging and confusing. Too often, I see and hear the same things from students. Mathematics just doesn’t make sense. I find this heartbreaking. However, we all have experienced joy when our students’ eyes light up because they have obviously made a connection and they truly get it.

 

Chapter 5

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CHAPTER 5

MONITORING

MATHEMATICAL

ASSESSMENT

Effective teaching not only involves imparting information and understandings to students . . . but also involves assessing and evaluating students’ understanding of the information, so that the next teaching act can be matched to the present understanding of the students.

—John Hattie and Helen Timperley

I remember vividly my first year of teaching and especially the first semester. I couldn’t wait to grade my mathematics tests. (No, I’m not kidding.) I was sure that my students had learned everything very well and not one of my students would get below a B. I eagerly took my first set of tests home to grade, and, well,

I was shocked. The grades ranged all over the place, and I couldn’t figure out why.

I knew by the next test their grades would meet my optimistic expectations! But no, they did not. I thought I was a good teacher; I thought my students enjoyed class, and most did homework and tried hard. So why didn’t they have better test scores? You see, as a first-year teacher, I did not understand assessment.

 

Chapter 6

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CHAPTER 6

BALANCING

IT ALL

The major work of the world is not done by geniuses. It is done by ordinary people, with balance in their lives, who have learned to work in an extraordinary manner.

—Gordon B. Hinckley

Many days, as teachers, we feel overwhelmed—we have so much to do, balancing professional demands inside and outside the classroom and demands in our personal lives. Did a little voice in your head just say, “A personal life? What’s that?”

Besides designing mathematics lessons that will develop the mathematical minds in our care, we have other professional areas to focus on, such as communication with parents. The fact that it might feel overwhelming shows how much we care for our students. If we did not care about becoming the very best teachers we can be, none of this would weigh heavily on us. I offer a few thoughts in this closing chapter on how to keep balance in our classrooms as much as possible.

Students and Families

I will admit that when I first began teaching, I was afraid of my students’ parents. What if they did not like how I taught? I was afraid to call parents in negative situations. What I did not realize as a first-year teacher was that my students’ parents and I were on the same side. We both wanted their children to succeed more than anything else.

 

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