Math Dream Sequence A

Here is my first shot at a dream sequence for high school math. It's truly a "dream" sequence: flaws, incomplete stories, and all. My point here is not to hit the nail on the head. I just hope to share an idea that math can be sequenced differently with a better result.

Here it goes:

9th grade

All incoming high school students take the same math course integrating Algebra 1 and Geometry. If they were successful in Algebra 1 in middle school, great. They can take an "Honors Geometry" track embedded within regular Geometry and be leaders in the classroom by completing all problem extensions, helping others, etc.

Students in this integrated math course would receive two math credits and would have two math teachers, but there would be no difference between them. Both teachers would be responsible for both subjects and students would see them as equals.

The course would be 90–120 minutes long and would meet every day. Instruction would be 100% project- or problem-based. Students would be divided into periods by the previous year's academic performance to achieve a diverse group in every class. With two teachers and support from special education and counselors, learning would be differentiated for all learning styles and paces.

10th grade

Learners who are successful in math during the 9th grade would move on to take an integrated Physics / Algebra 2 class. This course too would have an Honors track embedded within it. Extensions to problems would be required by these Honors students who would be expected to take a leadership role in the classroom.

This course would have two teachers: both certified in math and science. Again, students would not know who was who - both teachers would take responsibility for teaching both subjects. The class would be 90–120 minutes long and meet every day. Instruction would be 100% project- and problem-based. Learners at all levels would be in the same classroom for this course.

11th grade

By the third year of high school, some students would be prepared (and will need) to take Pre-Calculus. Others may have struggled through their first two years of math and/or have educational plans that do not require them to learn much more advanced mathematics. Having already satisfied 3/4 of the MIchigan's requirements in mathematics, it's at this point that it makes sense for a few divergent paths to emerge in math sequencing.

  1. Students in need of advanced mathematics understanding could take a stand-alone, hour-long, problem-based Pre-Calculus course or a more traditional semester-long Pre-Calculus and Calculus 1 course sequence at the community college.
  2. Students not needing advanced mathematics who are interested in a service career could take an integrated Statistics & Social Science (Sociology/Psychology) course.
  3. Students interested  in more hands-on technical career could earn their math credit through a program at the nearby Career and Technical Education Center.

12th grade

By creating divergent paths during the 11th grade, students' math options would become even more specific to their desired outcomes and ability during their fourth year of high school.

  1. Students following a path of advanced mathematics could continue to take advanced courses at the community college.
  2. Students following a service or health career path could earn credit through industry-specific math courses offered at the community college.
  3. Students attending the Career Center would continue to earn their math credit through the programs offered there.
  4. Students choosing to change paths would be supported to do so according to their ability.

Conclusions

To reiterate the point made in the first paragraph: this plan is not perfect. The cost of doubling up math in the freshmen year is substantial and would have to be offset in some way elsewhere in the school. The cost and quality of off-campus courses would also need to be considered.  

With that said, it gets students where they need to go without compromising classroom culture by splitting the most skilled math students from those who struggle. It creates math teaching teams who can support each other to truly differentiate. It provides ample time for students to complete challenging projects and problems. And, by providing two Michigan math requirements in the first year, it provides students the opportunity to re-take a course if they struggle and fall behind. It starts to get at some of the questions I was writing about last night.

I realize that there are a lot of points and assumptions that I'm making without specifically spelling them out. As a rule, that's probably going to be a theme in my writing. I simply don't have time to pull out every detail. The point is that I hope others will join in the conversation. Things will get spelled out in time. If you have questions, I encourage you to ask. 

Math Switch-a-roo

Lately, I've had trouble getting the sequence of high school math out of my head. For example, in Michigan, where I work and live, most students learn math as follows:

  1. Algebra 1
  2. Geometry
  3. Algebra 2
  4. Pre-Calculus
  5. Calculus

Following this sequence, the only way for a student to get to calculus while in high school is to take Algebra 1 in the 8th grade. Since not every student needs or will be successful in calculus, most students wait to take Algebra 1 until they get to high school.

In my district, a quarter to a third of students take Algebra 1 in the 8th grade. It's safe to say that most of these students are "good at school." What I mean is that they tend to watch their grades and have supportive families. Completing schoolwork comes somewhat naturally to them. Their being good at school is one of the reasons they get scheduled at a pace to complete calculus their senior year.

As a school administrator charged with the task of re-thinking teaching and learning, I have to question whether this practice is wise or necessary. Here are some of my questions:

  1. What effect does being in a math class full of peers who are good at school have on your overall learning experience?
  2. What effect does being in a math class absent any peers who are good at school have on your overall learning experience?
  3. What effect does putting all students who are good at school into one math class have on the rest of your courses or your school culture (especially in small schools)?
  4. What implicit messages are you sending students by separating them by ability in this way?
  5. What data and research exists to support separating students into ability groups in math?
  6. What track record of success can schools who practice this method of scheduling math show to back up their practices?
  7. Who says that algebra should be split up like this? Is this best for learning?
  8. Who says that any math should be separated at all? Should we integrate everything and teach logical chunks of math each year?
  9. Can 8th graders comprehend Algebra 1 deeply enough to change gears to Geometry for a full year before going back to Algebra 2?
  10. Might there be other ways to sequence and structure math to better serve our students' needs.

I don't yet have answers to all of these questions, but I'm seeking them out. What I'm fairly certain of though is that math is sequenced the way it is because of tradition and status quo. We can change things if we have the will.

Last week we decided that all of our incoming 9th graders are going to take geometry. We're breaking the sequence to buy some time to think about algebra, to integrate all learners in all classrooms (from special education to honors students), and to allow my 9th grade teacher to focus on one subject instead of two or three.

Next year, I'm not sure what we'll do. What I'd like to do is teach all algebra in one class with two teachers and twice the time. I doubt I'll have the numbers on my side to make that happen the way I want, but I have a year to think about it, to share my ideas with others, and to come up with a better solution.