In this article I discuss some general principles in helping students that are behind in math:

1. Test and assess
2. Line up the concepts or areas of study
3. Plan
4. Should you go on with new concepts or not?
5. Suggestion for review worktexts

How to Help a Student Who is Behind in Math?

1. Test and assess

If you have been the teacher, you probably have an idea of the student's weak areas, but knowing for sure is much better than guesswork. By testing you will be sure to catch ALL the areas that are weak. This is important since mathematics builds upon earlier concepts.

You can download ready-made assessment tests from a variety of sources:

• Online math assessment tests from Texas
• California Standards Test — Released Test Questions
  Old mathematics standardized tests for grades 2-11 from California Department of Education.
• Math Mammoth placement tests (for grades 1-6)
• See a longer list of math assessment resources online.

Remember that you're not necessarily using these tests to find out what grade level your child is in (though you can), but also to pinpoint the exact areas that he/she needs help with. So you need to look at the test results closely, question by question or topic by topic. Look at the various topic areas.

You can also have your student take tests for several grade levels, if needful, or only do the problems for certain topics. Stress to the student or child that the test is for evaluation purposes, not for giving grades.

2. Line up the concepts or areas of study

Once you know the areas or topics where the student has gaps, make a list of them.

If there are only a few topics, then it is fairly easy to "fill in the gaps": just use any material (such as Math Mammoth Blue Series topical books) to address those areas.

But what if the student is more seriously behind? What if he/she is in 7th grade but still struggling with 3rd grade topics, such as multiplication tables?

Then you need still have some options. Many of my customers have actually gone back to 1st or 2nd grade math with such students (using Math Mammoth complete curriculum), then studying through every grade level in order to build a good foundation once and for all. Typically, an older child can cover MANY grade levels of early math in one year. They wouldn't need to do every problem in the curriculum; they can "skim through" the lessons, concentrating on those areas they have more difficulties in.

Another possibility is to make up a more complicated plan of study, including the review areas and possibly incorporating the student's current curriculum.

I want to point out that if you are planning to have the student review or restudy many math topics, the sequence of those topics/concepts DOES matter. Certain concepts "flow together". For example, multiplication tables are important to master before studying basic division, factoring, or most fraction operations.

Here are some examples:

addition → multiplication concept

multiplication tables → division facts → divisibility → equivalent fractions, adding unlike fractions, simplifying fractions

place value → multi-digit addition, subtraction, multiplication, and long division

adding and subtracting like fractions, place value → concept of a decimal

multiplying fractions → multiplying decimals

concept of decimal, of fraction, and of ratio → percent

concept of fraction and of ratio → probability

Geometry, measuring, clock, money, and graphs are topics that are usually easy to incorporate into the current course of study.

This scope & sequence chart may also help you.

3. Plan

Like I mentioned, one possibility is to just go back many grade levels and start over, and have the student work his/her way through the various grade levels. I actually think this option is a good one for many students who are seriously behind. Many of my customers have had success with this approach, using the complete curriculum I sell on this site.

If you choose to only fill in the gaps (the weak areas), you may be able to incorporate the study of those just before certain topics in his/her regular math curriculum. For example, if the curriculum has a chapter on division, you could do a review on division before embarking on that chapter. This would work best if the student does not have gaps from many grade levels earlier; in other words, the areas he/she is lacking are from the previous grade level.

For example, if you have a fourth grader that needs some work with third grade topics, your plan could look like this:

* Chapter 1 from the curriculum [Whole Numbers]
* Review of multiplication tables
* Chapter 2 from the curriculum [Multiplication]
* Chapter 3 from the curriculum [Division]
* Review of earlier geometry concepts
* Chapter 4 from the curriculum [Geometry]
* Chapter 5 from the curriculum [Measuring]
* Review of fractions
* Chapter 6 from the curriculum [Fractions]
* Chapter 7 from the curriculum [Decimals]

Another example. Let's say you have a fifth grader that is more seriously behind. The plan could look like this:

* Review of multiplication concept and tables
* Review of division concept and facts
* teaching of multi-digit multiplication
* teaching of long division
* Review of fraction concepts

* Chapter 1 from the curriculum [Whole Numbers]
* Chapter 2 from the curriculum [Multiplication]
* Chapter 3 from the curriculum [Division]
* Review of earlier geometry concepts
* Chapter 4 from the curriculum [Geometry]
* Chapter 5 from the curriculum [Measuring]
* Chapter 6 from the curriculum [Fractions]
* Chapter 7 from the curriculum [Decimals]

Here's yet another scenario for such a fifth grader:

* Review of multiplication concept and tables
* Review of division concept and facts
* Chapter 1 from the curriculum [Whole Numbers]
* teaching of multi-digit multiplication
* Chapter 2 from the curriculum [Multiplication]
* teaching of long division
* Chapter 3 from the curriculum [Division]
* Review of earlier geometry concepts
* Chapter 4 from the curriculum [Geometry]
* Chapter 5 from the curriculum [Measuring]
* Review of fraction concepts
* Chapter 6 from the curriculum [Fractions]
* Chapter 7 from the curriculum [Decimals]

As you can see, your plan of study can vary, and you may have to change it as you go along. The important thing is that you've tested and assessed the student, and you have some kind of "game plan", so you can feel IN CONTROL.

4. Should you go on with new concepts or not?

This is not a "yay or nay" question. With some kids, it's advisable to bring forth some new concepts or new areas of mathematics as well. That can keep them motivated and not feel so behind. Obviously you cannot start a study of long division if your student is lagging behind in multiplication or division, but you may be able to "sprinkle" in some place value, geometry, time, money, or measuring. GEOMETRY is an especially good area to use as "new" material while going over old concepts, because it typically does not require many calculations, and students tend to like it.

In some cases, however, you may have to go back quite far and spend a significant amount of time only relearning old stuff. Typically, it is "new stuff" for the student though. So just use your judgment, go on with your plans, and readjust them as you go.

5. Suggestion for review worktexts

I have written books—worktexts actually—that are an excellent means of reviewing or relearning forgotten topics. A worktext means that the book contains both explanations and problems in the same book (work and text). In other words, there is no separate textbook and workbook but just one book that combines both.

Math Mammoth Blue Series worktexts deal with a few topics in each book, explaining the concepts and providing varied practice, often with visual models.

The topics covered in this series of books range from 1st grade addition to 6th grade topics, and everything in between: place value, addition & subtraction facts, multiplication tables, multidigit multiplication, long division, measuring, clock, money, geometry, fractions, decimals, proportions, percent, integers and more. See a full list of topics & books with grade level suggestions.

These books are sold in electronic form for very affordable prices ($2 - $7). Lots of free samples are available; take a look by downloading these two zip files:
MathMammoth_Free_Samples_Blue_Series_grades_1-3.zip
MathMammoth_Free_Samples_Blue_Series_grades_4-6.zip

See also

How to Teach Math to a Struggling Student - suggestions by Denise from Let's Play Math!