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In this article I discuss some general principles in helping students that are behind in math.
If you have been teaching the student who is struggling, you probably have an idea of the gaps in his/her knowledge, 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 because mathematics builds upon earlier concepts.
You can download readymade assessment tests from a variety of sources:
Remember that you're not necessarily using these tests to find out what grade level your child is in (though you can), but most importantly 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.
Administer tests from neighboring grade levels if needful, or ask the student only to do problems on certain topics in the lower level tests to find out exactly what he/she does not understand. Stress to him/her that the test is for evaluation purposes, not for giving grades.
Once you know the areas or topics where the student struggled, 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.
However, 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 still have options. Many of my customers have actually gone back to 1st or 2nd grade math with such students (using Math Mammoth complete curriculum), going through every grade level in order to build a good foundation. Typically, an older child can cover MANY grade levels of elementary math in one year. Such a child doesn't need to do every problem but can "skim through" the lessons, concentrating on the difficult areas.
Another possibility is to make up a more detailed plan of study that includes all the topics that need restudied.
I want to point out that if you are planning to have the student review many topics in math, the sequence of those topics DOES matter. Certain concepts "flow together." For example, the multiplication tables are important to master before studying basic division, factoring, or most fraction operations.
Here are some examples of such sequences where one concept is best studied before another:
addition → multiplication conceptGeometry, measuring, clock, money, and graphs are topics that are usually easy to incorporate into the current course of study.
multiplication tables → division facts → divisibility → equivalent fractions, adding unlike fractions, simplifying fractions
place value → multidigit 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
This scope & sequence chart may also help you.
Like I mentioned, one possibility is to simply go back and have the student work through the various grade levels systematically, starting typically in grade 1, 2 or 3. I feel that this is actually a good option for many students who are seriously behind. Many of my customers have had success with this approach, using Math Mammoth complete curriculum .
If you choose to only fill in the gaps (the weak areas), you may be able to incorporate the study of those just before the same topics in the student's regular math curriculum. For example, if the curriculum has a chapter on division, you could do a review of division topics from earlier grades before embarking on that chapter. This works best if the gaps in the student's understanding do not go back many grade levels.
Example. Your fourth grader needs some work with third grade topics. Your plan could look like this:* Chapter 1 from the curriculum [Whole Numbers]
* Review of multiplication tables from grade 3
* Chapter 2 from the curriculum [Multiplication]
* Chapter 3 from the curriculum [Division]
* Review of geometry concepts from grades 23
* Chapter 4 from the curriculum [Geometry]
* Chapter 5 from the curriculum [Measuring]
* Review of fractions from grade 3
* Chapter 6 from the curriculum [Fractions]
* Chapter 7 from the curriculum [Decimals]
Example. Let's say your fifth grader is more seriously behind. The plan could look like this:* Review of multiplication concept and tables
* Review of division concept and facts
* Reteach multidigit multiplication
* Reteach 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]
* Reteach multidigit multiplication
* Chapter 2 from the curriculum [Multiplication]
* Reteach 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 assess the student's knowledge and make some kind of "game plan," so you can feel IN CONTROL.
This is not a "yay or nay" question. With some children, it's advisable to present some new concepts or areas of mathematics while reviewing earlier topics. That can keep them motivated and not feel so behind. Obviously you cannot start a study of long division if your student lags behind in multiplication or division, but you may be able to "sprinkle in" some place value, geometry, time, money, or measuring topics. 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, you may have to go back quite far and spend a significant amount of time just relearning old topics. However, typically in those cases, the old topics are actually "new" for the student so they don't necessarily feel boring to him/her. Just use your judgment. Start with your plans but readjust them as necessary.
Math Mammoth Blue Series worktexts that are an excellent means of reviewing or relearning forgotten topics. (A worktext means that the book contains both explanations (the "text") and problems (the "work) in the same book.)
They deal with a few topics in each book, explaining the concepts and providing varied practice, often with visual models.
The topics covered in the Blue Series range from 1st grade addition to 6th and 7th 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 here, with gradelevel suggestions for each book.
How to Teach Math to a Struggling Student  suggestions by Denise from Let's Play Math!
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