Academic Learning Solutions uses a variety of well-designed Math Curriculums for tutoring struggling learners. This enables tutoring to be based on individual needs. Unlike reading, for math there is not 30-40 years of scientific research regarding effective math instruction. Nor have there been any centers which focus on rating whether the math programs and hundreds of "workbooks" teach math effectively, particularly for struggling learners.
However, we do know that what type of programs work for struggling students -- those based on explicit direct instruction where the teacher teaches the concepts versus "exploratory" instruction. We also know that struggling students need concepts to be incremental, explicit, sequential and cumulative.
Sequential: A sequence of instruction must be evident, and each skill is based on the previous concepts taught. Each skill is taught only after mastery of the previous skills.
Incremental: Teaching in smaller increments than what typical workbooks and textbooks provide. Each increment of a skill must be learned before moving on. For instance, a struggling student is typically unable to be taught how to do long division in a single sitting. It often takes hours of modeling, doing problems with a child, and teaching the skill in increments rather than a full problem.
Cumulative: Frequent and daily review of skills is essential. The "unit" approach is not typically designed for the frequency of review of concepts that struggling students need. Such program design might have a "unit" where it teaches measurement -- inches, feet, yards, etc. But during the unit, there is no review of long division, so students who need repetitive instruction then forget the long division skills, and hence, struggle throughout the year on half-concepts and recall of concepts.
A qualified math tutor should take a full diagnostic assessment of your child's math. If he is struggling in one area, it could be due to lack of mastery in another area. For instance, struggles in long division might exist if a child has not adequately learned place value or multiplication. Math is a sequential skill. Mastery of the lower skills is essential to comprehending upper level math. ALL math skills need to be assessed, not just the area that the child is struggling in. If your student is struggling in algebra, a full diagnostic evaluation of middle-school level math skills is recommended to detect underlying skill deficits that prevent learning.
Workbooks from educational supply places and department stores are not designed to help a struggling student. Workbooks typically also do not teach concepts, or follow a logical sequence of order. They also tend to combine various concepts with a random order versus sequential step-by-step learning. Often, they end up confusing the student further, rather than actually helping. Workbooks mainly provide practice in concepts that the student has already procedurally learned. Practice is good, but only if the concept, steps, and procedures are known.
Hands-on items: A variety of hands-on "manipulatives" when concepts are first introduced, or when concepts add a new level. Math blocks such as Cuisennaire rods, base ten blocks, and Unifix cubes are essential for their learning, and they often need these items longer than classroom teachers provide. One of the biggest hurdles which often requires extensive manipulative instruction for elementary children is the concept of place value. Children who work addition problems from right to left, have usually not grasped the concepts of place value. They do not understand why we "carry" or "borrow" because they do not grasp that they are carrying units, but just are told to "carry the 1 to the next column." Other major hurdles are long division and fraction math (adding, subtracting, multiplying and dividing).
Contact Academic Learning Solutions for an assessment of your student's math proficiency from preschool through upper grade math levels. Once your student is assessed, a recommendation of instructional program will be made, and the rationale for that program will be provided to the parents. Programs which might be used for tutoring your student are listed below. Academic Learning Solutions tutors math skills up to pre-algebra. If your student's assessment indicates proficiency to that level, you will be advised to seek assistance from other resources.
Saxon Math -- Saxon provides incremental and sequential instruction and has a proven track record of success. The advantage of Saxon is that it is leveled rather than graded, which enables a student to use their books regardless of their grade, and not feel they are doing a lower grade math book. Often a "fast-track" of Saxon is provided when a student's skill deficiencies are mainly in a few concepts. This enables the student to complete more than one level in a year, making up for lost instruction. When necessary, supplemental instruction to Saxon will be provided to enable comprehension and mastery of concepts. Click here for Saxon Math Research. Teaching Textbooks -- This series provides incremental and sequential instruction. It is extremely similar to Saxon, except it is computer based. It has gained phenomenal growth and popularity with home schoolers. Unlike many computer programs, it does not use "multiple choice" for instruction. Students must work the problem and enter the exact answer to get credit. Parent monitoring is available through password-accessible components. Parents may choose to have a student re-do certain problems for extra practice by deleting the answers. Fast-tracking is also available with this program, and can be fully explained to parents (or other tutors) to enable fast progress. Click here for more information.
Math-U-See -- This is another great program of incremental, explicit, sequential and cumulative math instruction. Math-U-See is also widely chosen also by home school parents who have found it successful for their struggling learners. Although there have not been any formal research studies on this program, it does have a proven track record with struggling students. Click here for one formal statistic.Click here for Math-U-See Information.
Right Start Math -- After attending a presentation on this program, I am impressed. It is a sequential program based on instruction with hands-on manipulatives. There has been some minimal research on the program. It has gained popularity with homeschoolers. It has levels rather than grades, making it easier to place a child who is behind in math, so they can learn the basics of understanding place value -- a significant reason why many children do not understand math. More information: Click here.
Corrective Math -- These ungraded math components instruct the basic operations of
addition, subtraction, multiplication, division, basic fractions, higher
level fractions, decimals, percents, ratios and equations. For a
middle or high schooler who is significantly behind, they provide a
faster track of instruction than CMC. Click here for Corrective Math Info. Click here for Research. Connecting Math Concepts (CMC) -- CMC is based on incremental, direct, explicit, sequential instruction. It is a leveled math program rather than "graded," so students can be placed regardless of their grade. CMC is not designed well for fast-tracking, so is not the better choice for students who are very behind. It is, however, one of the best incremental programs available. Click here for CMC Information. Click here for CMC Research. Others: When needed for extra reinforcement and/or practice of concepts, Academic Learning Solutions chooses from a number of hands-on lessons from a program called Mathematics Their Way/Math a Way of Thinking, as well as a number of individually-chosen worksheets and manipulative lessons used according to your student's direct need. For younger children, these procedures might be used for the main program of instruction. More information: Click here.