Balanced Math

Math Philosophy “Teachers are the key to improving mathematics educations…Regardless of the curriculum or the assessment process in a school district, the person in charge of adapting materials for a particular classroom and student is the teacher. It is through teachers’ efforts that students have opportunities to learn mathematics.” Glenda Lappan NCTM

- Computation, problem solving, and number sense are the essential three legs on which mathematics instruction rests.

- “Students who understand mathematics can think and reason mathematically and use what they learned to solve problems, both in and out of school. Teachers who teach for understanding must find ways to engage students actively in their mathematics learning.” Marilyn Burns

- It’s all about concepts, NOT algorithms. Students need to develop an in-depth understanding of concepts to the point where they are able to use what they’ve learned in school in the world outside of school. Developing these in-depth understandings creates and strengthens the connections in the brain. Teachers need to provide concrete, hands-on ways for students to learn math concepts, and then establish ongoing activities that strengthen and extend their understanding. Patricia Wolfe (an authority on translating brain research into classroom practice)

- Math is about what goes on in students’ heads. Teachers must choose activities so that the right things go on in their heads. We must examine student work to see what is going on in their heads. This acquisition of student feedback enables the teacher to adjust and differentiate instruction as needed.

- For students to be successful in math, teachers must know: math content, how children learn, and effective teaching strategies.

- In teaching strategies, teachers must move from concrete, to pictorial, to abstract.

- Mathematics instruction has traditionally focused on students’ proficiency with paper- and-pencil calculations. Yet in all the real-life needs for math, problems do not present themselves ready for calculation. Deciding what to do is the first important step before doing any calculation. It doesn’t make sense to teach arithmetic skills in isolation from situations for which those skills are needed.

- Teachers must give students experiences and opportunities to develop problem-solving skills. It should include problems that require broader thinking than traditional word problems demand. In real-life problems, you-re rarely given all the information you need in one tidy package; you often have to collect the data from a variety of source. Students should call upon the resources they have developed in other situations – knowledge, previous experience, intuition. They need to analyze, predict, make decisions, and evaluate. School should be the place where students can safely develop and practice problem-solving skills. Educational Leadership, “A Vision for Mathematics”, Feb 2004

Examine Student Work We had 39 numbers on the chart yesterday. And we added 12 more today. How many numbers are on the chart now?

How would you share two pizzas among three people? Show and explain your work. Examine Student Work

What is 20 / 4? 1. What does each part of the equation mean? 2. How would you explain 20 /4 to someone who doesn’t know about division?

Balanced Math Manipulatives Literature SMART Board Lessons Web sites Math Corner Kagan Structures

Manipulatives Base Ten Blocks Pattern Blocks Cuisenaire Rods GeoLegs and Miras Color Tiles Dice and Spinners

Base Ten Blocks

What’s Next? 1. Ask children to describe what a pattern is. 2. Show children this arrangement of blocks and explain that it shows a repeating pattern. 3. Invite volunteers to tell which blocks they think would come next. 4. Ask children to continue to the 15th block. 5. Once the children have firmly established the pattern, ask them to figure out what the 23rd block would be. 6. Predict what the 50th block will be. Pattern Blocks

Cuisenaire Rods Cuisenaire Rod Monster

GeoLegs and Miras

Color Tiles

Dice and Spinners

Literature

SMART Board Lessons

Defining and Measuring Angles

Factors and Multiples

Making Change

Shirts and Pants

Web Sites

Complete the Pattern Attribute Trains Base Blocks Subtraction Platonic Solids

Math Corner

Kagan Structures