Math Mania - Part 2

Since the time we started homeschooling six years ago, I have been on the hunt for that "perfect" math curricula.  My mom always said my sister and I were "good with numbers".  I did well in school and got good grades in math.  I know my facts and can easily make change.  The Farmer is great with math and excels at mental math and figuring.  We want these things for our kids.  But when it came time to teach them, it seemed I wasn't able to help them understand math.

I gave them workbooks, flash cards, and speed drills.  We tried numerous math programs including A Beka Arithmetic, Math-U-See, Teaching Textbooks, Saxon, MEP, Math Lessons for a Living Education, and RightStart, but in the end that long term retention is just not there.  You can read more about the evolution of our math journey and a complete overview of MUS here.

As I prep for upcoming curriculum fairs, book sales, and homeschool conferences, once again, I'm assessing our math situation.  Last week, I gave a brief overview of the history of math here.  This week in part 2, I will attempt to give an overview of some approaches to math and how popular math curricula fit those approaches.  

Spiral Math - The spiral approach to mathematics is covering the same topics or mathematical concepts over and over, little by little, adding difficulty at each level or in every grade.  For example, you will cover addition, subtraction, multiplication, division, money, time, measurement, etc., in 1st grade, 2nd grade, 3rd grade, etc.  The idea is that the student will be exposed to the concept many times and thus will eventually master the concept. 

There are many math curriculum that fit the spiral approach.  Some of the more popular are Saxon, A Beka, Horizons, and Making Math Meaningful.  You can view a Saxon 5/4 math table of contents here to see the spiral of concepts.  Notice how every lesson teaches a new concept.  Now compare it to Saxon 6/5 table of contents here to see how the next level repeats the concepts.  Again, teaching a new concept with every lesson. 

Generally more concepts can be covered in a shorter amount of time with the spiral approach.  The down side is that students are exposed to concepts early on that can be too difficult.  Also, when many concepts are introduced at once, without mastery, students become confused and frustrated.

Mastery Math  - The mastery approach to math is when students are taught one topic at a time until they have mastered the concept being studied.  The student is not allowed to move on until that particular concept is mastered.  Advanced students are able to progress quickly.  But slower students are held back based on mastery of that one concept when maybe developmentally they are not ready for that concept.  However, if allowed to go on they may be ready and able to master a different concept.

The most common mastery based math program is Math-U-See. Their scope and sequence is very unlike most math programs in that each level (grade) focuses on one main concept.  Their elementary scope and sequence is as follows:

Alpha - Single digit addition and subtraction
Beta - Multiple digit addition and subtraction
Gamma - Single & multiple digit multiplication
Delta - Single & multiple digit division
Epsilon - Fractions
Zeta - Decimals & percents

Sequential Math -  I view sequential math as a bit of a combination of spiral and mastery.  Sequential math introduces one concept at a time in multiple ways with ample practice.  Then it moves on to the next concept with some built in review of the former concept.  It gives the student some time to catch the concept before moving on unlike the spiral approach, but spends maybe a chapter or two rather than an entire year like the mastery approach. Each new concept is designed to build on the last.

Some math programs I consider sequential are Singapore, Math Mammoth, MCP Mathematics, Alpha Omega, and RightStart.

You can view the MCP Mathematics grade 4 table of contents here.  Then compare it to MCP Mathematics grade 5 here.  When looking at grade 4, notice how they cover similar concepts, but how each chapter builds on the last.  For example, chapter 1 is addition and subtraction; chapter 2 is place value; chapter 3 is addition of whole numbers; and chapter 4 is subtraction of whole numbers, etc.  In essence, the scope and sequence does spiral.  However, it doesn't move as quickly as a more traditional spiral such as Saxon.  The concepts are introduced one chapter at a time rather than each day, one lesson at a time.  There is also built in review, enrichment exercises, and tests to ensure mastery of the concept. I see this approach as the best of both worlds.

Rainbow Resource offers a chart of Math Program Comparisons.  This chart is very helpful in determining several math program approaches as well as things like whether it's manipulative based, grade level specific, and the level of teacher involvement.

So what does it all mean?  In Part 3, I will attempt to pull this knowledge together as I continue to research math curricula for the upcoming school year.  Stay tuned.....