Math-U-See combines hands-on methodology with incremental instruction and continual review in this manipulative-based program. It excels in its hands-on presentation of math concepts that enables students to understand how math works. It is one of the rare multi-sensory math programs that continues to use manipulatives up through pre-algbegra.

Manipulative Blocks, Fraction Overlays, and Algebra/Decimal Inserts are used at different levels to teach concepts, primarily using the “rectangle building” principle. This basic idea, consistently used throughout the program—even through algebra—is one of the best ways to demonstrate math concepts. There are also digital versions of the manipulatives that offer a virtual experience with the manipulatives. These digital manipulatives are available in an app as well as in the Demme Learning Digital Toolbox. The app is available for compatible tablets from the Apple app store, Google Play, and Amazon.

Math-U-See uses a “skill-mastery” approach, requiring students to demonstrate mastery of each topic before moving on. The program also builds in systematic reviewof previously learned concepts. The program covers all necessary math concepts, but it does not try to correlate the teaching of concepts at the same grade level or in the same order as other programs.

There are eight courses for elementary grades titled Primer, Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Pre-Algebra. The Greek letter designations were chosen particularly to emphasize the order of learning rather than grade level designation. Students should move on to the next level once they’ve mastered the content of a book. These first eight books are followed by Algebra 1, Geometry, Algebra 2, PreCalculus with Trigonometry, and Calculus. A free placement tool to help determine your student's level is available on the Math-U-See website.

Student workbooks and test booklets are softcover books, and the pages are perforated so they can easily be removed, written upon, hole-punched, and placed in binders. Enrichment exercises have been incorporated into the student workbooks for Primer through Pre-Calculus (with the exception of Algebra 1: Principles of Secondary Mathematics). These optional, additional problems stretch students to higher levels of understanding and application of math concepts covered within the lessons.

Test booklets for every level except Primer have tests to be used at the end of each lesson plus four unit tests and a final exam. Neither student workbook pages nor tests are reproducible; you need to purchase books for each student. Student workbooks and test booklets are the only consumable items in each course.

The printed instruction manuals have complete answer keys with solutions for all problems at all levels—an especially helpful feature at the upper levels.

All books are printed in black and white. This is not a particular problem in the first four levels if students are working with the colorful manipulatives, learning the skip-count songs, and possibly watching the lesson videos. In these levels, enrichment pages also offer engaging activities for those students who enjoy dot-to-dots, color-by-number, and other supplemental activities. These multi-sensory experiences make up for the bland workbook. However, as upper levels use manipulatives less and less, the plainness of the workbooks is a point to consider with some students.

For each level, you need both the student pack and the instruction pack. The student pack for each level includes a student workbook and a test booklet for each level except Primer*.*

For Primer through Pre-Algebra, you will also need to purchase the manipulatives used in each level. The Math-U-See Integer Block Manipulative Set is primarily plastic blocks that are color-coded to correspond to each number, somewhat similar to Base Ten Blocks and Cuisenaire Rods. The Math-U-See blocks snap together like LEGOs^{®}. Fraction Overlays are added at the Epsilon level, and Algebra/Decimal Inserts are added at the Zeta level. That means the same sets of manipulatives are each used over at least a few years.

The instruction pack for each level includes an instruction manual plus one or more DVDs with lesson-by-lesson videos that “teach the teacher.” Digital packs include online versions of the lesson videos, instruction manuals, full solutions, and access to digital manipulatives. Note that the lesson videos have subtitles for the hearing impaired. Parents must watch the lesson videos to understand the basic concepts that are the foundation of the program. In the lesson videos, Steve Demme works through each level lesson-by-lesson, demonstrating and instructing. Demme's presentation is enthusiastic and engaging as he clearly explains what he is doing and why. He throws in lots of math tricks, the kind that make me scratch my head and ask myself why they never taught us that in school.

The video presentations are critical components of the courses although instruction manuals have briefer lesson presentations of the same material covered on the videos. I expect that most parents will have their children watch the lesson videos with them, although it was originally intended that parents with students below high-school level watch the lesson videos and then do their own presentations to their children.

After the initial viewing or lesson presentation, parents and children work through lessons together for as many days as it takes for children to master the concepts. Once students have grasped a concept, they practice and do lesson-practice pages on their own with occasional assistance. Typically, children should be spending about a week per lesson, but you need to take as long as necessary for your child to learn each lesson.

The Primer level will generally be the starting place for most kindergartners. The Primer level begins with essential number concepts and continues up through adding to make 10, telling time, and an introduction to subtraction. Children use manipulatives more than in upper levels of the program (and far more than in most kindergarten math programs).

There is no test booklet for the Primer level. At the early levels, you will also want to use the Skip Count CD and Book set. Both a “Bible” version and a “Science and Literature” version are included on the CD.

Alpha level focuses most heavily on place value, addition, and subtraction. Beta level teaches regrouping for both addition and subtraction. Gamma primarily covers multiplication while Delta moves on to division. Fractions are the main topic in Epsilon, while Zeta tackles decimals and percent.

Of course, other topics are included alongside these primary themes—topics such as money, measurement, geometry, time telling, graphs, estimation, prime and composite numbers, Roman numerals, and solving for unknowns. While manipulative use remains essential for understanding new concepts, the amount of time spent using the manipulatives decreases in Epsilon and Zeta.

Pre-Algebra topics are similar to those in other such courses: positive and negative numbers, exponents, roots and radicals, the order of operation, geometry, ratio and proportions, and other such topics. One unusual topic for this level is irrational numbers.

There are plenty of practice problems in the latest editions of Math-U-See, but students who need more practice have free access to a computation drill program on the Demme Learning Digital Toolbox. Parents need to choose which math concepts students will practice, then students use the program on their own. You can also use the website’s worksheet generator on the Digital Toolbox to generate and print additional pages of practice problems for courses up through Pre-Algebra. Problems are randomly selected so you can produce a number of different worksheets for the same lesson, even though some problems might show up on more than one worksheet.

### High School Courses

This review covers Geometry, Algebra 2, PreCalculus with Trigonometry, and Calculus. Algebra 1: Principles of Secondary Mathematics (published in 2022) differs in design from the rest of the series. You can read my review of Algebra 1 here. The original Algebra 1 course will remain available for some time, but I recommend the new course for most students.

As you move into the high school level books, students are able to work more independently. The instruction manual for each level is written to the student. Students need to watch the DVD presentation and then read through the instruction manual before tackling the workbook. Workbooks include extra instruction for unusual problems, especially for some of the honors or enrichment problems, but they do not serve as complete course books on their own.

The honors exercises provide more challenging work with critical thinking, word problems, and practical applications, plus test prep practice and preparation for the math required in advanced science courses. Students can also move through the texts more rapidly if they master the lessons quickly.

Even at the high school level, Demme presents concepts simply and clearly, avoiding dense-sounding mathematical abstractions common to so many high school textbooks. The high school courses feature many word problems and applications that make the lessons more interesting. The instruction manuals include complete answers with step-by-step solutions for all the exercises and tests, plus a glossary and an index.

While some students might be able to work through the courses independently, many will need parental or tutorial assistance. Math-U-See offers online co-op classes for those who might want to take a course with other students under the supervision of an experienced teacher.

Geometry students need a protractor, a compass, and a straight edge to draw constructions, but manipulatives are not used for the high school courses..

Math-U-See Geometry is fairly traditional in presentation and coverage, although it is an easier course than most. While it covers the standard topics, it does not go as far in depth as most other high school geometry courses. For example, it deals only with regular polygons when teaching about interior and exterior angles of pentagons, hexagons, etc., and there is little work with tangents. However, Math-U-See Geometry introduces geometric proofs in lesson 24 and uses them through the end of the course. It also introduces trigonometry and transformations in the last three lessons. Algebra is reviewed frequently within the lessons. Math-U-See Geometry should be manageable for average to slow students, and you can challenge advanced students with honors exercises or move them ahead more quickly into Algebra 2.

Algebra 2 moves on to new material rather quickly (as compared to many other second-year algebra courses), and coverage of topics is close to that of many other publishers. It introduces matrices and determinants in the honors section of the last lesson but does not get into functions at all. Students should be able to move on to either precalculus or trigonometry courses after completing Algebra 2.

Math-U-See’s PreCalculus with Trigonometry course dedicates a significant amount of space to trigonometry as one might expect from the title. Vectors, functions, logarithms, and a few other advanced math topics are also covered. PreCalculus students need a protractor, ruler, and a scientific calculator. This is a straightforward, fairly traditional course.

Calculus teaches the content typical of other calculus courses, and it also includes chapters titled “Physics Applications” and “Economics Applications” that help students grasp how useful calculus can be. Calculus does not include an honors component since the course already includes content that will challenge advanced students. (Note that Algebra 1, PreCalculus and Calculus are the only Math-U-See courses that require a calculator.)

The video instructional component makes a huge difference, especially for these last two courses, since Demme does a great job of explaining and illustrating concepts. However, I very much appreciate the fact that the instruction manuals for Math-U-See high-school courses include a teaching component so that students do not have to rely entirely on the DVDs.

### Summary

One of the things I think makes Math-U-See so popular is that many parents and teachers find that author Steve Demme’s presentation of math concepts helps them to finally comprehend much that they were taught in math but never understood. Parents and teachers with a new or renewed enthusiasm for math then do a much better job teaching their own children.