What should our math curriculum include?

I have started writing curriculum. I am always creating new curriculum every time I tutor. I do two things, gear the content towards the students individual needs but also break down the content into an easy to understand manner. Right now I am writing an Advanced Algebra Curriculum. I chose to write this curriculum because although I have found a really good "Basic" Pre-Algebra Curriculum, I have not found anything that is good for advanced students. The point of this post, however is not to discuss a particular curriculum but the OVERALL mathematics curriculum in our state (and probably other states as well).

When I look at how mathematics is taught from K-12, I am not impressed. Kindergarten math is fairly good although I think we can challenge students more. Still, students need to focus on reading and reading comprehension in Kindergarten so that they are ready to tackle context problems in first grade. I do like the fact that children are taught how to count by 1's, 2's, 5's and 10's in Kindergarten. This ability will serve them well later. I also think that when we are learning these skills, we need to extend it and teach students how to count tallies and how to switch between our skip counting: For example: children should practice: 5, 10, 15, 20 (now skip to ones) 21, 22, 23. This can be illustrated by both tallies and counting numbers on a clock. Why not extend it to other useful things while we are practicing the concept.

First grade - third grade is designed fairly well for the traditional student. We should teach multiplication and division in a better fashion and be more creative in our teaching approaches to the concepts taught.

By fourth grade - students should be ready to start working on adding fractions and decimals and working with percents. At this point, we really need to let the kids that are naturals in math continue forward rather than holding them back to the same curriculum as the traditional student. My son was getting all of his arithmetic skills solidified during the fourth grade and by fifth grade was ready for an advance pre-algebra curriculum.

Many students will need fifth and even sixth grade to continue to focus on the basics but I think we spend too much time on doing the "hodgepodge" approach. We teach a little of this and a little of that including many skills that we have taught before and will teach again. I feel at this level we need to get children to truly master the basics that will be so useful later in Algebra and above. Students need to get solid on working with fractions. So many Algebra students are still so uncomfortable with fractions. Students need to become strong on overall "number sense" - when we say the number 12 - immediately different number should pop into one's head: 1,12,2,6,3, and 4. It should be automatic. We should also immediately think: 12,24,36,48. Experience and playing with numbers (in fun activities rather than boring rote memorization) will accomplish this successfully. This will provide students with far more help in later math than learning perimeter and area year after year after year. Perimeter and area are not hard concepts. They can be taught quickly including comparing and contrasting the two so they are not thought of independently. Students should also constantly revisit older material throughout the year so they retain the information.

Now, we get to the years of middle school math. This is where I feel we waste precious time and also tend to "lose our kids." So much of the same is repeated or they teach 1/2 of algebra in 8th grade that the students know the first half of Algebra when they get to their first Algebra class and think they can breeze right through it only to start to fail (after they have gotten used to their lax ways) once the material changes.

I propose this idea for an overall curriculum: These guidelines focus on arithmetic and algebra prepartion. Each year there should be simple units (that are not too time consuming) that teach: Geometry, Probability, and Measurement.

Kindergarten - Stress skip counting, start working on number families, and spend more time on reading

First grade - Build a strong basis for conceptual problem solving, become solid on addition facts and introduce subtraction facts. Stress the 10's family and "building to 10's" in subtraction. Students should be able to tell time to the minute and count coins. These two concepts are direct links to their skip counting they have been working on in Kindergarten and early first grade.

Second grade - Students should be focusing on regrouping in addition and subtraction through hands on models

Third grade - confirm students have mastered addition and subtraction with regrouping, teach multiplication and division while stress factors! This should all be done with fun hands on learning, not through worksheets!

Fourth grade - Students should now be able to do multi-digit multiplication and division as well as master decimals, students should be introduced to adding fractions conceptulally.

Fifth grade - Students should master working with fractions and percents. As part of this, students should learn LCM's and GCF's as well as factor trees. Students should master basic powers and square roots building their idea of number sense. Students can even start to explore related but "higher level" mathematics. When teaching squareroots - the advanced student can see how to simplify something like the square root of 12 into 2 squareroot 3 or the squareroot of x to the sixth power to x to the third power. These connections we use in algebra should be introduced when appropriate. This is more important than teaching them how to solve x -4 -10 algebraically at this point!

Sixth grade - By this year, advanced students should be ready for Advanced Pre-Algebra, traditional students should be ready for Simple Pre-Algebra, and Slower learners should review previous concepts but also do some simple Pre-Algebra.

Seventh grade - Your advanced student should be taking Algebra 1 (which follows the Advanced Pre-Algebra class taken previously that has completely prepared them for the course). Your traditional student is ready to do Advanced Pre-Algebra this year and your slower learner should have a full curriculum in Basic Pre-Algebra with Algebra Enhancements (teaching some of the easier Algebra concepts at a higher level).

Eighth grade - Your advanced learner is ready to take a high school level geometry class. Strong students can take an Honors Geometry class. Your traditional student will be well-prepared for Algebra 1 after having taken Advanced Pre-Algebra the year before. The slower learner will be ready to dive into the Advanced Pre-Algebra this year.

Ninth grade - All 9th graders taking Algebra 2, should be required to do an Algebra 1 Review (very fast paced, main concepts) before taking their Algebra 2 class. Instead of spending so much time re-doing Algebra 1 in Algebra 2 (like we do now), the advanced student should be able to get through all Algebra 2 concepts including trigonometry.

Tenth grade - Here I feel students would benefit from a class that teaches "Pre-calculus" skills within the Calculus AB curriclum. By the end of the year (and this should be a year long course), students will have gained appropriate knowledge for Pre-Calculus and Calculus AB.

Eleventh grade - The advanced student would proceed into Calculus BC

Twelth grade - The advanced student would take either Probablity and Statisics or College Mathematics. A college Mathmetics course would include basics in probability and statistics as well as introduction to financial mathematics, set theory, and formation of proofs for basic Abstract Algebra. This survey course would hopefully spark the interest for those going on into college to major in Mathematics.

The traditional student and the slower learner would follow the same path (9th grade Geometry, 10th grade Algebra 2) with the tradtional student taking a complete Precalcus class in their junior year. Their senior year could consist of Calculus or Probablity and Statisitcs. The slower learn would spend their freshman year in Algebra 1, their sophomore year in Geometry, their junior and senior years taking Algebra 2 if needed to be spread over 2 years. They might also benefit from a lower level survey class designed to meet their needs.

Overall, I feel we have too many poor math teachers who teach math. I applaud the great ones but when my clients come in and tell me that Ms. So&So says we are not allowed to ask questions in class, I just don't understand it. Math is not always easy but it is not as hard as we make it out to be. We also push too many complicated equations on our students instead of making sure they understand the underlying basic concepts. The main question of the year is, "WHEN am I going to need to use this?" Well, the answer is: Some of this stuff, NEVER (if it really gets that complicated, we will have the computer do it for us!) other stuff - well, yes - if you understand the basic concepts and uses of what you are learning you will apply it to what you do but you won't apply something you don't completely understand.