The American Math Dilemma

High and middle schools of the US do not encourage enough critical thinking among our students. 


Everything is being done with guidance of a teacher going through steps of a procedure - and this is where the problem is. 


For example, in Math: Teachers provide step-by-step instructions how to solve an equation, how to divide, how to... This does not teach students how to think about math individually. It teaches them to follow the procedure, and maybe get the answer right - but it does not teach how it works, and it does not teach how to think beyond that point. 


Our education system cannot produce great mathematicians, because too many people are taught to follow procedures and instructions.

Native American Sweat Lodge = Imagery for Negative and Positive Integers

Imagine a traditional Native American sweat lodge:

In order to heat these up, stones were placed in fire until very hot, then brought into the lodge:

Those would be your positive integers.

Now, let's jazz this imagery up.

Say we could bring in blocks of ice.

Those could be thought of as negative numbers.

So, when you want to raise the temperature of the sweat lodge by one degree, place in a hot stone +(+1)

When you want to lower the temperature, you can either take this stone our -(+1)

Or you can put an ice block in +(-1)

Get the point?

There are lots of variations you could play with in this imagery.

Try it yourself and let me know.

Ideas bounced around with regards to algebra readiness in Middle School

• AFTER SCHOOL or before school algebra class taught for an additional fee (NOT BEING DONE @ my school)

• Bring in local university students or math-smart volunteers to provide additional resources at key times of the day. (CURRENTLY WE HAVE TWO PEOPLE coming in @ my school)

• Employ an organized teacher who can teach both classes at the same time in the same room, with 2 sets of lesson plans (for accelerated and for grade level). One group works on assignments/projects while other group receives instruction. Then switch. (We continue to consider individual differences in our program and differentiate instruction when possible)

• Consider utilizing administrators to co-teach during select times of the day (WE have done THIS @ my school)

• Proclaim the virtues of small schools, be upfront on what you offer (small schools are not for everyone), change the culture of unreasonable expectations, and develop the teacher to be adept at differentiating in class, thus better meeting the needs of all (WHETHER PERCEIVED AS SUCH, I BELIEVE THIS IS HAPPENING @ my school, ALWAYS WITH ROOM FOR IMPROVEMENT. THE MESSAGING TO PARENTS NEEDS TO BE AS CRYSTAL CLEAR AS POSSIBLE)

• Elect a single day each week and call it "E" Day in math. E stands for either Extension or Extra Help. Send your additional resources into the classroom that day. That way you can have three different teachers work with each small group, either extending or remediating the kids as needed. (WE WERE DOING THIS @ my school VIA MATH LAB, PARTICULARLY THE 1ST YEAR OF IMPLEMENTATION, NOT CURRENTLY DOING SO)

• Differentiate in Grade 7, two levels - Pre-Algebra or Algebra I . By Grade 8, students either study Algebra I or Geometry. (VERY POOR IDEA THAT GOES AGAINST MANY SOUND PROFESSIONAL PRINCIPLES)

• Divide your math class into three groups: high, low and middle, and the math teacher work separately with each group during each class, doing leveled work in each group. While she or he works with one group, the other two groups can be working at problems at their desks. (SOMETHING LIKE This HAPPENs WITH THE APPROPRIATE SUPPORT, IN PARTICULAR, NEED HELP WITH STRUGGLING STUDENTS IN ORDER TO KEEP PACING APPROPRIATE FOR OTHERS. As a general principal, I would hope this is happening in many schools.)

• Split up the students for math, according to their ERB scores and report card grades. Math teacher takes the accelerated class (about 10 students) and the science teacher takes the grade level class (about 10 students). other 2 middle school classes are having English and history (occasionally Spanish) (TERRIBLE IDEA, IMHO, VERY PUBLIC SCHOOL, TEST ORIENTED APPROACH TO INSTRUCTIONAL PROGRAM

• Bring in another teacher with a prep time during math and have that person teach grade level math, freeing up the math teacher to work with the accelerated kids (SEEMS LIKE THE OTHER DIFFERENTIATING IDEAS TO ME)

• Cluster students in multi-aged ability groups for the given subject (math, in this case). 56 students in 4 sections=14 students. Play it off PE, Art, Music or Spanish. (OK, LET'S ADD EVEN MORE COMPLEXITY TO OUR SCHEDULE :-)

• Assess students and appropriately cluster as early as 4th grade. Teach math at same time 4th – 8th grade (TERRIBLE IDEA, IHMO)

• All 6th take pre-Algebra. End of year take CSU Algebra readiness test (MDTP). Remediate if necessary during the summer. Give same test in Sept. to now 7th graders. Those ready receive Alg 1 in 7th. Those not receive a two-year Alg. 1 class. Students in one-year program take Geometry readiness test (MDTP). If not ready, take second part of Alg 1 with their peers. (I LIKE THE READINESS TEST IDEA AND REMEDIATION, BUT NOT THE ALGEBRA IN 7TH GRADE. IT WAS ALREADY PUSHED DOWN TO 8TH FROM 9TH A FEW YEARS BACK. ALGEBRA SHOULD NOT BE CONSIDERED THE END ALL IN A MATH PROGRAM. THIS ALL FLIES AGAINST THE NCTM STANDARDS AND PUTS WAY TOO MUCH EMPHASIS ON A SOLE COURSE.)

Math Class

Recommendation:  that remediation for students in grades K-5 should focus on the properties of whole numbers, like counting, addition, and subtraction. Older students, up to 8th grade, should learn rational numbers in depth, including the meanings of ratios, decimals, and percentages, the panel recommends.

Another recommendation is that all students who need extra math assistance should work on fluent retrieval of basic arithmetic facts, like simple addition and multiplication. Higher-level mathematics often assumes that students can quickly recall facts like “3 times 9” or “11 minus 7,” when such operations may be difficult for those lagging behind their peers, the panel found.