Homeschoolers using math programs that do not teach conceptual understanding frequently benefit from supplements that use manipulatives to explain concepts. This is especially true for the math facts, since they are foundational for learning the rest of math.
Demme Learning, the publisher of the popular, hands-on Math-U-See program, has created two Accelerated Individualized Mastery (AIM) programs to help students working below grade level master the math facts. AIM: Addition and Subtraction is for students ages eight and above, and AIM: Multiplication with a Bridge to Division is for ages ten and up. AIM uses the same teaching methods as does Math-U-See by incorporating manipulatives, activities, and interaction. The AIM programs are not intended to be used as the first introduction to basic computation skills. Rather, they are for students who were previously introduced to either addition and subtraction or multiplication, but who have not yet mastered their math facts.
The goal of both programs is to help students develop both conceptual understanding and the ability to quickly recall math facts. A parent needs to work with students through some or all of each lesson. The amount of assistance needed will vary from student to student, but this is not an independent-study resource.
You should take a break from your complete math program to concentrate on one of the AIM programs, but if that is not possible, either AIM program can be used alongside a complete program. AIM sessions should last no longer than 15 minutes at a time, although you might do more than one session in one day.
Components
Each AIM program includes a resource guide, manipulatives (colored blocks), posters, Fact Check Cards, and access to a package of digital resources that are accessed online. The physical products come in a box that includes a card with a code to be used to get access to the online resources. You will need internet access on a regular basis to utilize the digital resources. (Access does not expire.)
The digital resources include a few brief videos for parents that explain elements of the program, short videos that teach the student the key concept for each lesson, printable pages (e.g., worksheets, games, instructions for activities, and assessments), solutions, and access to a worksheet generator. Both the videos and the activities included within the digital resources are essential parts of the AIM programs. While you do not need to use all the activities, you should use many of them since they are a critical part of the review and practice in the programs, and they should be enjoyable for students.
A set of thirteen 8.5 x 11” posters (printed on cardstock) is included in the box. You are directed to display the pertinent poster for a lesson if there is one.
How It Works
Parents need to prepare in advance. They should begin by watching the videos for parents and teachers; there are six for Addition and Subtraction, and five for Multiplication. These each run from one or two minutes to just over six minutes, so it won’t take long to watch them. (You can save the last video in each sequence for later viewing if you want.) Before starting a lesson, parents need to read through the lesson in the resource guide and check out the activities and resources in the digital resources to determine which to use. They also need to watch the brief instructional video for each lesson, and parents might have students watch with them.
These instructional video segments are very different for the two programs. Those for the Addition and Subtraction program have been excerpted from the complete Math-U-See program. They are briefer than those for Multiplication, and they usually do not provide introductory comments or the context for the concepts being taught. On the other hand, the videos for the Multiplication program were created specifically for the AIM program. They more fully explain the context and concept being taught in each lesson.
Parents will then work with students through each lesson, following the four steps described below. Students might not watch the instructional videos at all if parents choose to present the lesson themselves.
Sessions follow a four-step process:
1.) The parent presents a concept using the blocks to help students develop conceptual understanding. Then the parent writes out problems and shows their solutions.
2.) The student demonstrates understanding by repeating the process themselves following the “Build, Write, Say” method explained in the program. A number of different learning strategies are implemented at this stage, many of which are in the digital resources. For instance, in the Addition and Subtraction program there are 17 activities you might use. Many of them are games that utilize the colored blocks.
3.) Students draw, write, and say the math facts to transition from dependence upon concrete objects to using their visual memory. Drawing replaces the building in step two.
4.) Parents use the Fact Check Cards to assess mastery of the facts. Fact Check Cards are small flashcards showing individual math facts to be mastered. There are three blank stars on each card. Each time students can say the answer in fewer than three seconds (on three separate occasions), you will color in a star. The fact will be considered mastered when all three stars are filled in.
Pre- and Post-Assessments
Before you begin, you should watch the brief video about how to use the assessments, then use the Before-AIM Assessment provided in the digital resources for the first lesson. Both the pre- and post-assessments are given orally. Children do not write answers. The assessments help you verify which facts your child knows as well as the methods by which he or she recalls the facts. After-AIM Assessments for both programs help verify that students can say the answers to math facts within three seconds without having to use blocks or fingers or depend upon complicated mental processes.
Addition and Subtraction
The Addition and Subtraction program should take about six to eight weeks to complete. It is arranged in 22 lessons, and each lesson includes all four steps described above. The box for this program also includes a set of colored pencils, with colors that match the blocks. Learning the colors to associate with the blocks is an important aspect of this program. Students first work with the colored blocks to represent math facts. They shift to drawing pictures of the manipulatives using the appropriate colored pencils. Then they draw only a colored line to represent each manipulative as they write the problem, helping them to gradually shift away from reliance on the blocks. (Updates were added to the online resources in June of 2021 to improve the transitions from topic to topic and provide additional assessments.)
Multiplication with a Bridge to Division
Multiplication with a Bridge to Division has ten lessons on multiplication plus an optional two lessons on division. Division is taught as the inverse of multiplication, and the two division lessons present techniques that are to be used to cover all of the division facts. The time required for this program will vary greatly depending upon whether you teach the division facts.
This set costs slightly more than the Addition and Subtraction set because it has more than twice as many colored blocks so that students can build much larger math facts. Students build math facts with blocks as with the Addition and Subtraction program, shifting from working with blocks to drawing them, then using only the numbers. However, they do not use colored pencils for drawing, relying less on the colors of the blocks than is the case with the Addition and Subtraction program.
Summary
The Accelerated Individualized Mastery programs are likely to be more useful to those not already using Math-U-See since they duplicate the methods and some lesson videos already used in that program. The AIM programs use time-tested methods that have worked for many students, and some students might find those methods so successful that they want to shift into Math-U-See for their complete program.
