Tuesday, December 30, 2008

Mammoth Math!

Mammoth Math: The name is very appropriate because not only is this a terrific math program; but Mammoth Math’s associated websites yield resources in “mammoth” sized proportions.

The author of Mammoth Math, Maria Miller, is a former math teacher turned homeschool mom whose goal is to provide high quality, affordable resources to help parents teach mathematics to their students.

She’s certainly succeeded with her websites and her curriculum.

Through 20 years of teaching and tutoring, my own and other students, I’ve developed strong opinions about what works and what doesn’t with math instruction. In my opinion, a good math program for homeschool students should:
  • be structured on incremental instruction and systematic progression,
  • emphasize topic mastery that enables student to move at their own pace
  • use manipulatives and models to clarify concepts,
  • teach mathematical patterns and mental math by discovery
  • offer plenty of review options as needed,
  • introduce algebra concepts with models through the elementary years
  • emphasize math reasoning through varied word problems,
  • present problems without distracting page elements and put just a few on the page
  • be simple for the parent to implement and the student to understand

Mammoth Math achieves each of these objectives and does so at a very affordable price. The Light Blue Series includes complete grade level instruction for grades 1 – 5. Each grade level can downloaded for around $27 through the Kagi Store. CurrClick and TOS have some of the materials.

Each grade level includes two worktexts (A and B), answer keys, tests, a web link to generate extra practice sheets for an infinite amount of practice. These can be purchased individually, but the full set is the best value as it includes Soft-Pak, software based math and language arts supplements for FREE. (I found the language arts Soft-Pak worksheets handy). Hard copy books and the materials on CDs are available from a couple of vendors listed on the website. Downloads are reusable within one family; but they should not be resold. I think that the down-load format offers the best value.

I received the complete Light Blue Series 4th grade curriculum in two downloaded Ebooks of about 170 pages each. Each workbook (A and B) came with a separate downloaded answer book. These downloaded very easily and were simple to save on my computer and open in PDF format. The index was easy to follow and the pages printed clearly. I simply printed off the pages we needed and placed them in a three ring binder for my daughter to go through during the week. Most pages are black and white; however, when there was color on the page I found it better to print them in color.

I like that Mammoth Math teaches one concept at a time and visual models are used to illustrate the concepts. There seem to be just the right number of problems on each page to reinforce the concept, but not so many to overwhelm the student. One feature I especially liked was that the worksheets included a grid over the problems to help students keep their numbers aligned properly. This is a HUGE help with children whose handwriting is a little messy. I also liked the way mental math skills were developed in such a way that the children “discover” the method as they were able to understand it.

In addition, each book contains a List of online resources, games, etc for the students to use.

Mammoth Math's scope and sequence has fewer topics within a grade level; but they are presented to “mastery”. Parents beginning this program should make use of the placement tests available at the Mammoth Math website to help you find the right level for your child. This scope and sequence is very efficient for students who grasp math easily because they can move through the curriculum quickly without sacrificing thoroughness in basic arithmatic computation. Students who struggle more with math can take as much time as needed on a topic, or leave it for while and come back to it later. Students who just don't like math will appreciate the reasonable number of problems they are presented with in each lesson and the variety of practice options available.

Parents employ diagnostic prescriptive teaching with Mammoth Math. Once a student takes the test in the Light Blue Series, if extra practice is needed, the parent provides it through the worksheet generating web link. The parent can closely define the difficulty of the review sheet or they can make up their own (which would be useful for mixed review). Further topical review is also available through a different teaching series I’ll explain tomorrow. Parents also can make review sheets every week to keep skills current.

Since I believe in the use of manipulatives I wondered about their inclusion in Mammoth Math. Here is what Maria wrote to me:

Manipulatives: you won't really find those anymore in the books you get... but I employ a 100-bead abacus in the Place Value 1 book. In the fractions book I encourage the use of manipulatives and the books include cutouts for pie models.

Place Value 2 uses a pictorial form of the familiar base ten blocks, but alongside the book one can of course use the physical manipulative as well. Some kids benefit from that. Then, in many of the early addition and subtraction books I also use a simplified pictorial form of the base ten blocks - it's liek a dot for 1, stick for 10, and a square shape for 100. So carrying and borrowing are shown with the help of the pictorial models, and the teacher could also show it in identical manner with physical manipulatives.

Manipulatives do help students to understand concepts, initially, on a concrete level. But I don't advocate a prolonged manipulative use, because kids also need to learn to make generalizations, and learn to reason mathematically. However, I use pictures or pictorial models a lot.

So, if a child has grasped the basic ideas of place value (hundreds, tens, ones, carrying, borrowing) and used manipulatives with those, then it shouldn't be difficult to grasp those same things with bigger numbers - or with decimals - using a pictorial model only.

You can read more here about my views on manipulatives:

http://homeschoolmath.blogspot.com/search/label/manipulatives

I agree with what she says here. I have found that manipulatives are most effective in introducing a concept and essential in the younger grades; but most students who grasp the process do not want to be tied to blocks, tiles etc. The visual models used on the work pages are extremely helpful in illustrating the concept to the student. So much so that, most of the pages are self-teaching! My daughter was able to understand the new concept as it was presented on the page and I felt my role was only to discuss this new concept with her to be sure she understood and had not skimmed over the explanation.

Mammoth Math doesn’t have a lot of bells and whistles in its basic form; but it gives parents the tools to do a very thorough job of teaching math to their children. Because she saw many homeschool parents struggle with math teaching, developing a parent friendly curriculum is the goal that Maria had when she set out to write her curriculum:

The aim of my books is first and foremost to explain math in very simple terms, yet rigorously, concentrating on understanding of concepts. I use picture exercises a lot because they are sort of equivalent to playing with manipulatives and help children understand how math works. After those, come more abstract exercises.

I have been especially interested in improving elementary math teaching. Many parents and teachers think that elementary math is easy to teach and that "anybody can do it". This often results in just giving children rules to memorize without explanations, proofs, and "whys and wherefores" of the facts. Children do not learn to think, but instead just wait for the rule to "arrive on a platter" and then use that for the problems in the textbook on that page.

The bells and whistles of the program are found Maria’s three web resource areas. The web resources she's collected provide many of the activities you would normally find in a bulky and pricey teachers "guide".

The first of these is the Mammoth Math website which features two free newsletters. These newsletters include articles on teaching techniques, free worksheets and lists of online sources of instruction and review materials. One of the newsletters is an email course in math teaching - a virtual in service workshop for homeschool teachers. Subscribing to the free newsletters gives you access to 280 pages of free worksheets taken from Maria's curriculum. Answers to these worksheets are available for a small purchase price through the website. The worksheets are NOT intended to be a complete curriculum, but they are a wonderful resource for any parent using any curriculum.

Maria’s Blog includes teaching tips, interesting problems and (this is my favorite part!) links to other interesting math blogs, problem generators, contests, tutorials etc. This is like one-stop shopping for high quality math resources on the web without having to sort through the typical search engine results.

The true goldmine for math resources has to be Maria’s main website which includes: worksheet generators, lists of free online games, articles, curriculum reviews, and more. There are also abundant free samples from Maria's math series. These resources are FREE!

Here Maria also compares different math curriculum in a very understandable way and provides access to other teaching and reinforcing online resources. As I said before, this website replaces the “teachers” edition found in other programs. The worksheets are essentially self-teaching because the concepts are explained and demonstrated on each page. There are times when a student needs a little extra work, explanation, or drill in an area. When extra help is needed, the online resources provide many options or enrichment. Want a game to practice with - need a practical application or challenging problem? Check out the web pages Maria has listed.

I give Mammoth Math a “two thumbs up” as a math curriculum for elementary students for its thoroughness and cost effectiveness. She has thoughtfully provided many free resources for those on limited budgets. However, even homeschool parents with limited finances would do well to budget for her elementary program. You'd be sure you were covering all the topics well for less than $30 per year.

Consult the website for ordering options and try some worksheets! Be sure to read carefully the differences between the series. The LIGHT BLUE series is the complete curriculum.

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