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BRAINSAREFUN

SUCCESS WITH

MATH

some straightforward solutions

SUMMARY: What parents and teachers can do to accelerate success with math and math performance.

INTRODUCTION

In response to numerous requests about how to provide failing math students with success, I provide these remarks. They shall not review the entire Brainsarefun Technology. That has been thoroughly documented in other articles listed alphabetically at the More fun with Brainsarefun Index.

TOPICS FOR DISCUSSION

Commonly, the problem with most math instruction is that so many students have experienced so much failure with mathematics that they are no longer able to focus when presented with additional instruction or tutoring. This is doubly true for "most" female students in the fifth grade and above. Up until the fifth grade female students often exhibit significant math skills. In fact, to this point teachers often point to the girls as their best students. Why they suddenly turn around and exhibit so much failure with math is not the subject at hand. Whatever the complex reasons, the fact is, they do. It is preventable.

The first job of all good math instruction is to evaluate the skill levels of the students in order that they can be placed at the appropriate instruction level. Secondly, all (except perhaps the top 20%) need to experience massive success and recognition, fast! They must receive the message that they, too, can succeed with math. To accomplish this massive success we are going to focus on providing students with new experiences; ones at which they haven't already failed. Master these new experiences and the typical child will accelerate as much as one-full-year in the first thirty hours of instruction. Following are some very simple examples. They can be extrapolated into very complex instruction, but the fundamentals remain consistent.

ANSWERS FIRST - Brainsarefun Basic Teaching Technique

Never ask a question to which you have not first given the answer. Make sure, especially at first, that the answers remain visible. This will eliminate all cheating. Know what skills you want the students to learn an drill them to mastery. I begin by having the entire class learn to chorus:

Simple example:
First provide the answer, "The answer is four."
The problem is, "What is two plus two?"
My turn: The answer is four.
My turn: What is two plus two?
Your turn (signal): Four.
Keep your eyes on the class.
Continue the drill until everyone is responding on signal.
Reward students who are chorusing correctly.
Ignore students who aren't.

TABLES

Mastering mathematical tables is an excellent example of how all new skills and information need to be first broken down into their component parts and the parts drilled to mastery. Students who haven't mastered the basic tables and operations are going to have a very difficult time succeeding.

Three of the four fundamental mathematical tables are rarely mentioned. They must all be drilled to mastery. The four fundamental tables are:

1. The Multiplication Table
2. The Division Table
3. The Addition Table
4. The Subtraction Table

Students must recite and write out their tables, with samples in front of them, until they are confident and fluent. Time the writings and chart them. Collect all papers and keep them in portfolios. Even in high school math classes, even in college, students are often not confident about their basic tables.

OPERATIONS

How many times have students "guessed" at he wrong answer and then blamed their failure on misinterpreting the operation, "Oh, it was an addition problem. I thought it was subtraction."

Clearly, randomly and rapidly write signs on the board and have students copy: "+++--/+//-XX-"

After 30 - 60 seconds of writing return to the beginning and have them all chorus their work along with you: "plus plus plus minus minus division plus division division minus times times minus." They must be trained to write and read operations with confidence

Are you confident that all students know that the word "plus" means "addition?"

THE EQUAL SIGN

Everything on the left side of the equal sign must equal everything on the right side of the sign. Show many examples of this being true and untrue.

THE AMAZING MATH MACHINE

The Amazing Math Machine is something that teachers and parents create using a simple spreadsheet program. In its simplest for it looks like:

The instruction sequence remains consistent:

Point to first number. Everyone choruses first number.
Point to sign. Everyone choruses sign.
Point to second number. Everyone choruses second. number.
Point to answer. Everyone choruses answer.

Example: Two plus two equals four.

I have developed many math machines. Some have included money, graphs, percentages, decimals and algebra, but all always show the answer until the child is fluent, confident and accurate.

I have used the machine with everyone crowded around a computer. I have used overhead projection systems. I have written problems out on the board. It doesn't matter, as long as you get everyone chorusing and the right answer is always visible.

The big advantage to the Amazing Math Machine is that it instantly calculates and displays the answer. Plus, it's fun.

FLUENCY AND SPEED

All tables and operations must be drilled to fluency. This is not accomplished by slowing down. Students who can not confidently write the numbers 0 through 9 are going to have a hard time doing math. Have them write, count and graph their speed at writing their numbers until they are fluent and fast. Time them in 10, 20, 30, and 60 second bursts. Simply have them write the entire number sequence, 0 - 9, as many times as they can. Have them count their numbers, write down the score under their writing, go again.

Progress can be easily tracked on a sheet of paper stapled to the front of a manila folder belonging to each child. Children keep track of all their daily work in the manila folder. Five minutes before the end of class papers can be transferred to a three-ring binder/portfolio.

Students earn points by starting on time, staying on task, completing their assignment.

SOLUTION KEYS

Most math teachers, parents and students are familiar with answer keys. But answer keys are not enough. It wasn't until I was 58 years old that I was introduced, by Carol Gambill, to the power of a solution key. Solution keys show the student, step-by-step, line-by-line, what their answers and their papers should look like. Solution keys are not written on the board. They are written out by the teacher, on paper, just as the teacher expects the student's work to look (including correct headings). Solution keys need to be developed for all written work, homework, tests and quizzes.

The first step is to have students copy solution keys, exactly. Teaching students how to focus and copy without error may take two weeks of solid drill, but remember, "Fluency."

Once this level of fluency is mastered, then the problem may be handed out to the students a second time with only the answer. Finally, the problem may be presented without solution or answer. Most students will be confident enough by that time to succeed at creating their own solution keys.

The point is, do not ask questions to which the answers have not been provided. That come later. Right now, it's our job to set children up for success, not failure.

Experiment with providing students with math experiences that are new - designed for success, not failure. Failing students will thank you for it. Frustrated parents will begin believing in their children again.

Good math instruction expands with he following. These sites provides the additional background required for critical thinking and advanced instruction. Review these sites:

Mathematically Correct
Corrective Mathematics
Direct Instruction Mathematics
Brainsarefun Basic Teaching Technique
Brainsarefun Homework Solution (at the heart of all Brainsarefun instruction)

With this common background, further discussions about the effective teaching of math will make great sense.

COPYRIGHT NOTICE: BRAINSAREFUN SUCCESS WITH MATH and THE AMAZING MATH MACHINE © January, 2002 by Rory Donaldson. All rights reserved. In order to help reverse the tide of academic failure and optimize success, individuals may copy brainsarefun solutions for non-commercial use at no charge. Contents may not be sold or repackaged in any manner without the written permission of Rory Donaldson. Since all material is copyrighted, please ensure that this entire copyright notice and contact information continues to be attached to each article you download. Mr. Donaldson appreciates the feedback. Additional solutions may be viewed and downloaded at no charge by logging on to brainsarefun.com. New titles are being added regularly. To view most recently added titles you may click here.

Suggestions and comments encouraged, email: roryd@brainsarefun.com.

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