Steve Demme, creator of *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 *Algebra 1*.

Manipulative Blocks, Fraction Overlays, and Algebra and 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 is also a digital app version of the manipulatives that offers a virtual experience with the manipulatives. The app is available for iOS devices.

One of the things I think makes *Math-U-See *so popular is that many parents and teachers find that author Steve Demme’s presentations 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.

*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 review for previously learned concepts.

There are eight books 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*. Placement tests for the different levels are available free at the *Math-U-See* website.

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

Test booklets for each course 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.

Instruction manuals are printed in hardcover books with full-color covers so they can be used a number of times. Complete answer keys with solutions are included for all problems at all levels, an especially helpful feature at 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 DVDs. 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.

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 some other programs.

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 *Algebra 1*, you will also need to purchase the set of Manipulative Blocks or the digital manipulatives app. *Math-U-See's* manipulatives are primarily plastic blocks somewhat similar to Base Ten Blocks and Cuisenaire Rods, color-coded to correspond to each number. (See my review of both.) The 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 that “teach the teacher.” Note that DVDs have subtitles for the hearing impaired. Parents must watch the DVDs to understand the basic concepts that are the foundation of the program. On the DVDs, 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 DVD presentations are critical components of the courses although instruction manuals have briefer lesson presentations of the same material covered on the DVDs. I expect that most parents will have their children watch the DVDs with them, although it was originally intended that parents with students below high school level watch the DVDs 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 problem 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.

Primer 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 Counting and Addition Songs *audio CD. 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, 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 *Math-U-See *website. 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 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

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 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. The addition of the honors exercises largely alleviates concerns I expressed in my review in the first edition of *Top Picks* about the program's ability to challenge advanced students. Students can also move through the texts more rapidly if they master the lessons quickly.

Even at 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.

In *Algebra 1,* Manipulative Blocks and the Algebra and Decimal Inserts are used, but less than in earlier levels.

*Algebra 1* does not cover as much territory as do most other first year algebra courses. For example, complex work with radicals as well as motion problems are taught in *Algebra 2*, although they are included in most other first year courses. Slower students should find the pace very manageable. Honors lessons will challenge brighter students, but you can always speed up by moving students through the courses more quickly.

The rest of the upper level books no longer use manipulatives. However, *Geometry *students need a protractor, a compass, and a straight edge to draw constructions.

*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 *Discovering **Geometry*. For example, *Math-U-See Geometry* deals only with regular polygons when teaching about interior and exterior angles of pentagons, hexagons, etc. There is not as much work with tangents as you find in *Discovering **Geometry*. 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. As with *Algebra 1*, *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), bringing the total of *Math-U-See’s* combined algebra coverage close to that of 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 pre-calculus 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. (Note that this course and *Calculus* are the only *Math-U-See *courses that require a calculator.) This is a straightforward, fairly traditional course.

The *Math-U-See* series culminates with *Calculus. *While *Calculus *teaches the content typical of other calculus courses 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.

The DVD 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 newest editions’ instruction manuals for *Math-U-See *high school level courses now include a teaching component so that students do not have to rely entirely on the DVDs.