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Creating Mathematical Magic In The Classroom

Changes in Mathematics Instruction

- a shift in curriculum toward a deeper study of

mathematical ideas and concepts and their uses in

todays world - a shift in learning toward more active student

involvement with mathematics - a shift in teaching toward classrooms as

stimulating learning environments in which all

students are given the opportunity to reach their

mathematical potential and - a shift in assessment practices toward student

evaluation that is based in many sources of

evidence.

Building a Teaching Bridge from Reading to Math

Reading

Math

Effective Reading Instruction

- Reading is more than pronouncing words..
- We want student to develop good decoding skills.
- We include comprehension from the very start.
- We ask child to make predictions about what might

come next in story. - We use a variety of teaching strategies-shared

reading, guided reading, independent reading, and

read alouds. - We want student to read fluently.
- We want our students to love reading.

Effective Math Instruction

- Therefore, math instruction should consist of

more than simply calculating numbers - We want student to develop good strategies for

solving problems. - We include conceptual understanding from the very

start. - We ask child to use mental math to estimate

before calculating problems. - We use a variety of teaching strategies-whole

group instruction, flexible group instruction,

and small group instruction. - We want students to be mathematically fluent.
- We want our students to love math.

- ...instruction can emphasize conceptual

understanding without sacrificing skill

proficiency - ...understanding does not detract from skill

proficiency and may even enhance it.

Hiebert (2000)

NCTM Principles and Standards

Investigations In Number, Data and Space

- NCTM Standards Based Resource
- Students are striving to
- Justify their reasoning
- Communicate mathematically
- Represent their thinking
- Make connections to other content areas and

the world around them

Investigations

- Offers students meaningful mathematical problems
- Emphasizes depth in mathematical thinking rather

than superficial exposure to a series of

fragmented topics - Communicates mathematics content and pedagogy to

teachers - Substantially expands the pool of mathematically

literate students

Calendar Math

- Analyze data
- Identify patterns including multiples and factors
- Explore whole numbers and parts of a whole

(fractions, decimals and percents) - Use mental math to estimate reasonable answers
- Share strategies for arriving at an answer

In the classroom, students are

- working in a variety of groupings
- considering own reasoning and the reasoning of

others - communicating orally and through
- pictures, numbers and words
- working on a small number of problems during a

class session, sometimes on a single problem for

several sessions - using more than one strategy to double check
- using cubes, blocks, measuring tools, technology,

and variety of other materials to solve problems.

Goals of Instruction

- To develop confident and competent lifelong

learners who embrace mathematical challenges. - To assist children in acquiring strategies to

build new learning skills and to grow as

mathematicians. - To aid children in making meaningful mathematical

connections to their world.

Mathematical Proficiency

- Conceptual Understanding A web of connections.
- Procedural Fluency Using basic skills such as

facts, procedures, and formulas quickly and

accurately. - Strategic Mathematical Thinking Formulating,

representing, and solving problems and

reflecting, explaining, and justifying their

solutions. - Productive Disposition Viewing mathematics as

understandable and worthwhile.

Adding it Up, 2001

Emphasis on Understanding

- Typical of Japanese Math Instruction
- Teachers pose a complex thought-provoking

problem. - Students struggle with the problem.
- Various students present ideas or solutions to

the class. - Class discusses the various solution methods.
- The teacher summarizes the class conclusions.
- Students practice similar problems.
- Source Third International Mathematics and

Science Study unpublished tabulations.

Videotape Classroom - Study, UCLA, 1996.

Emphasis on Skill Acquisition

- Typical of U.S. Math Instruction
- Teacher instructs student in a concept or

skill. - Teacher solves example problems with the class.
- Students practice on their own while the teacher

assists individual students. - Source Third International Mathematics and

Science Study unpublished tabulations.

Videotape Classroom Study, UCLA, 1996.

Traditional Problems

- What is the cost of 5 cans of beans if each can

costs 0.79? - What is the cost of 16 boxes of cereal if each

box costs 2.69? - How much change will Sally get if she pays for 8

pounds of chicken that costs 1.89 per pound with

a 20 bill?

Higher Order Thinking Problems

- Hot dogs come in packages of 8 hot dogs for

2.50 - hot dog rolls come in packages of 6 for 0.90 and

12 for 1.50 - hamburgers come in packages of 8 patties for

4.00 and - hamburger buns come in packages of 8 for 1.00

and 12 for 1.65. - You expect that 24 students and 6 adults will

come to the picnic you are planning. You also

expect that most-but not all-students will have a

hot dog and most of the adults will have a

hamburger. Decide how many packages of each you

should buy, find the cost of the food, explain

why you made your decisions, and show how you

arrived at the cost.

Questioning Students...

- Can you explain how you solved the problem?
- Why did you do it that way?
- How did you prepare for the assignment, the test,

the activity? - Do you like mathematics?
- Do you like multiplication?

Self Assessment

- How did you do with this assignment?
- What does someone need to know to be able to do

this work? - What was easy for you in this assignment?
- What was difficult for you in this assignment?

Throughout The School Year

- Your child will be solving problems that take

considerable time, thought, and discussion. - Children are expected to think about the problems

in their own ways, and to be able to talk and

write about their solutions.

How You Can Help Your Child

- Play games with your child including higher level

thinking games such as - chess
- checkers
- puzzles/brain teasers
- simple card games
- While playing talk about the strategies used to

solve problems and make winning moves. - Children enjoy these kinds of activities while

enhancing mathematical thinking.

Do Mathematics Together!

- Everyday situations
- Count, count, count!
- Classify (toys, silverware, laundry)
- Find 2 and 3 dimensional objects
- Set the table (positional language)
- Count and make change

Family Ideas

- Use sharing to reinforce division and fraction

skills - Incorporate measuring into daily activities
- Baking, gardening, crafting
- Use rulers, measuring cups, scales
- Numbers are everywhere! Look for them on

mailboxes, route signs, in newspapers

Link Mathematics with Daily Life

- Everyday people face situations that involve

mathematics. - Deciding which route to take to a destination
- Estimating the cost of groceries
- Developing a schedule
- Determining the percent off at a great sale

Learn About Math Related Careers

- Math is the foundation for a wide variety of

interesting careers. - Many jobs our children in the primary grades will

experience have not even been invented yet! - It is imperative that our students be able to

think and apply their knowledge to a variety of

situations.

Support Homework!

- Be aware of what is happening in the classroom

and have ongoing dialogue - Play the games which support the math program.

They are essential! - Support student learning by review homework

assignments and basic facts - Dont do homework for your child.

Be Positive About Math!

- Acknowledge the fact that math can be

challenging. - Persistence and hard work are keys to success.
- Struggling at times in math is normal and is

actually necessary to and valuable in

understanding mathematics.

Attitude Increases Ability

- A positive attitude is the essence of productive

learning. - A childs level of confidence determines his/her

ability to obtain and retain new learning. - In social circles you never hear -I really do

not comprehend what I read. - Accept mathematical challenges!

We need to do something

- According to a survey conducted on behalf of a

leading Fortune 500 Company. - 84 of students surveyed would rather do one of

the following than their math homework clean

their room, eat their vegetables, go to the

dentist or take out the garbage - Only 1/3 of students surveyed reported liking

math a great deal. - 43 of students reported having a difficult time

understanding the mathematics they are taught in

school. - By eighth grade, as many as 45 are turned off to

math, describing it as BORING!

Have High Expectations

- All students are capable of doing challenging

mathematics. - All students are expected to know basic facts and

be able to apply them correctly in a variety of

situations. - All students are expected to communicate

mathematically.

Purpose of Games in Investigations

- Games are a central part of the mathematics in

the unit, not just enrichment. - Games develop familiarity with the number system,

such as 10s, 100s, and 1000s and provide engaging

opportunities for practicing computation. - Playing games encourages strategic mathematical

thinking and demands that students find an

optimal way (rather than just any way) of solving

a problem. - Games are played often throughout a unit and

throughout the year to develop fluency with

numbers. It is expected that students will play

games many times. - Games provide a school to home link. Parents

learn about the mathematical thinking their

children are doing by playing games with them at

home.