Singapore Math fans now have another choice!
Like the original Singapore Primary Math series, Math in Focus (MIF) is especially strong in developing conceptual understanding. It differs from the original Singapore series in that it is also aligned with the NCTM (National Council of Teachers of Mathematics) standards… the math standards that prevail in the U.S. However, unlike most programs aligned with the NCTM standards, it does not try to teach every concept every year. Instead, it focuses on fewer topics but teaches them thoroughly so they need not be retaught continually.
The program covers kindergarten through eighth grade, and the scope and sequence is advanced as with the original series. A major focus is upon preparing students for success in algebra. Consequently, algebraic thinking and expressions are introduced early and used frequently throughout the series.
Throughout the series, concepts are taught moving through a sequence of concrete to pictorial to abstract. Concrete learning happens through hands-on activities with manipulatives such as counters, coins, number lines, or Base Ten Blocks™. Pictorial learning uses pictures in student books, drawings, or other forms that illustrate the concept with something more than abstract numbers. The abstract stage is the more familiar way most math problems are taught and practiced with numbers and symbols. Manipulatives are used throughout all levels, but they are used much more frequently in younger levels than older. But even at fifth-grade level, manipulatives are still used occasionally, while pictorial illustrations are prevalent in all the lessons—far more than in other upper elementary programs.
While there are Classroom Manipulatives Kits for Math in Focus, each Teacher’s Edition has a chart showing simple alternatives that will work. For example, I’ll chart here some of the first-grade kit components and the suggested alternative:
|attribute blocks||seashells, pasta, buttons|
|coin and bill combination set||real coins plus bills made from construction paper|
|craft sticks||marker set, unused pencils|
|demonstration clock||cardboard clock face with hands attached with brad|
|number cubes||number cards, spinners|
|pan balance||ruler, paper clips, and string|
Virtual Manipulatives CD-ROMs are also available—one CD for grade K-2 and another for grades 3-5. They are a bit expensive for use by a single family, but some might find the investment worthwhile. They are super easy to use. You can select a type of manipulative and move it on the computer screen to demonstrate concepts. They are quite simple to use—enough so that you could let your children manipulate them too. Virtual Manipulatives do not replace all manipulatives in the program, but they could replace most of them. Keep in mind that the object of using manipulatives is to allow the hands-on learning experience that might be critical for some learners, so Virtual Manipulatives should be used judiciously.
Along the same line, calculator usage is taught in the fifth level. It is sometimes suggested as optional within a lesson, but there are lessons dedicated to learning how to use it. In this program, students should be well-grounded in their computation skills by the time they hit calculator use, so it should not interfere with mastery of computation skills.
Lessons at all levels also follow the same progression. A lesson begins with the teaching presentation. Next, the teacher walks students through guided practice. Then students do independent practice.
Both guided and independent practice problems are in the hardcover student books, while the consumable workbooks are designed for only independent work. This means that students will need separate paper or a notebook for their work in their hardcover textbook unless you don’t mind treating it as a consumable book.
Lessons concentrate on a single concept rather than providing continual practice on previously-learned concepts. However, review is provided in a section at the beginning of each chapter titled “Recall Prior Knowledge.” In addition, word problems, practical application problems, and critical thinking activities included throughout the lessons frequently draw on a wide range of mathematical knowledge. The goal of Math in Focus is to teach concepts so thoroughly that frequent review is unnecessary.
The entire presentation in Math in Focus really challenges students to think much more deeply about mathematics than do most other programs. Students can’t just breeze through the lessons. Students who grasp concepts easily will likely do very well with this program. For students who struggle, you might slow the pace and take more time with the concrete and pictorial lessons, and you might also offer extra guided practice.
Math in Focus mirrors the original Singapore Math’s layout with books A and B for each level for Teacher’s Editions, student textbooks, and student workbooks, essentially splitting the course for each level into two parts. Kindergarten is the exception to this layout since it has only workbooks rather than separate texts and workbooks; there are four of these relatively thin kindergarten student workbooks. (Note: Kindergarten level is very classroom oriented. It is very dependent upon presentation from the Teacher’s Edition. Much of the teaching involves group interaction. Some of this can be adapted for a parent working with only one child, but this level is the most problematic for homeschool use.)
A separate assessment book is available for each level but is not essential. One book covers both parts A and B. Student texts have chapter reviews/tests. Student workbooks have cumulative reviews at the end of every few chapters as well as a mid-year and end-of-year review/test. These reviews/tests should be adequate for assessment in most situations, but you can purchase an assessment book if you need more.
The program is designed to be taught from the Teacher's Edition (TE). The TE for each level has lots of useful information in addition to detailed lesson plans. Reduced student pages are shown in the TE so you know which pages to use when. Answers overprinted on the reduced student pages serve as your answer key. The TE is essential for kindergarten, but it is possible to work with only student texts and workbooks for first grade and up as long as you’ve got time to work out problems to check student answers without an answer key. TEs explain how to present each lesson and also suggest additional activities. They point out common errors children tend to make and suggest solutions. In addition, at the back of each TE a section of reproducible Teacher Resource pages is to be used as teaching aids for the pictorial and concrete lessons. You might find it difficult to figure out what these are supposed to be and how to use them without the TE. You will definitely miss out on some elements of the lessons without the TE, but concepts are presented in so many ways, that you might find that you are not even aware that anything is missing. I would recommend to most parents that unless they already have a strong background in teaching math with manipulatives, they should get the TE for at least grades 3 and up. (I’ve already mentioned that the kindergarten TE is indispensable.) In the TEs for K through 2, the teaching part of the lesson has fairly explicit instructions that tell you what to say and do. These instructions become less explicit for third grade and up, but they are very helpful. Even with the TE, some assumptions are made that the teacher has a fairly good grasp of math and mathematical vocabulary. I suspect that parents who struggle with math themselves might sometimes find the TEs past the first few grade levels difficult to understand.
Math in Focus is presented as a more polished product than Singapore Math. Sturdy and extensive Teacher's Editions, hardcover texts, and full-color printing of both TEs and student texts contribute toward making Math in Focus a beautiful looking and thoroughly developed program, although it is more expensive than Singapore Math. I suspect that Math in Focus will quickly become a very popular option among homeschoolers.