Last week in MBUSD, over 500 people from around Los Angeles came to MBMS to participate in an all-day workshop featuring Dr. Jo Boaler, a world renowned professor of mathematics at the Stanford Graduate School of Education. We cohosted the conference with UCLA. All MBUSD secondary math teachers attended, and many of our elementary teachers participated as well. The thoughts of the day provide an excellent framework for the work we are doing in mathematics curriculum and instruction in MBUSD.
A major focus of teaching and learning in MBUSD has been around moving away from lecture as a primary teaching tool, and moving towards students being active in their learning. Teachers are transitioning their role from the “sage on the stage” to that of the “guide on the side,” working to coach, inspire, and support our students. This has been true in our implementation of Writers’ Workshop and Readers’ Workshop. This is also the essence of the Common Core Standards and the new Next Generation Science Standards that are coming out. We are committed to aligning research in best practice to all of our classrooms. We want less memorization from our students, and more skills such as analysis, problem-solving, writing, presenting, and creating.
Every one of Dr. Boaler’s ideas has been researched and observed. Here are some of the messages that she stresses:
- Everyone can be successful at math, from elementary to high school.
- We urgently need to shift teachers’, parents’, and students’ ideas about who can achieve in mathematics.
- Parents who tell their children, “When I was in school, I wasn’t good in math either,” are doing way more harm than good!
- The lowest achieving students are memorizers. The highest achieving students think of big ideas and connections. America has more memorizers than most countries in the world.
- Formulas are great, but if you can’t explain or visualize them, you may not really understand the math behind them.
- Brains grow when they are worked. People can become more (or less) intelligent based on increased (or decreased) use of the brain.
- Rapidity does NOT have a precise relationship to intelligence.
In MBUSD, we are transforming our mathematics program through two major changes:
- Implementing shifts in mathematics curriculum and instruction, and
- Math courses and pathways. Let’s focus first on how we are teaching math.
CHANGES IN HOW WE WILL BE TEACHING MATHEMATICS
Here is how I learned math in high school.
- Memorize your basic math facts.
- Memorize key formulas.
- Practice them on the homework.
- Use them to do well on the test.
Using those skills today, I am still able to approximate square roots to the nearest hundredth, recite the quadratic formula, integrate simple equations, and compute areas of many traditional and obscure figures. But I would never say that I truly understood math. In fact, after learning so much about math teaching and learning in the last three years, I understand math better now than I did as an almost math major in college (that’s another story).
I’m not going to go over all of the 8 Standards for Mathematical Practice (SMP), but let me discuss a few, which will show how different math teaching and learning are from just a few years ago.
SMP #1: Make Sense of Problems and Persevere in Solving Them
In my day, we did problems 1-39 odd. Today, we are moving towards classrooms where an entire class period may focus on one highly complex, multi-step problem. Students have to understand so much to do this, and at first, it is intimidating. In my day, collaboration was called cheating. Today, collaboration is a great way to solve problems together. Students will make mistakes. Instead of just being wrong, students now learn from their mistakes, and go back to work on solving the problem. Oh by the way, in a good problem, there are multiple ways of getting to the correct answer. We celebrate different ways of getting it right.
SMP #3: Construct viable arguments and critique the reasoning of others
In my day, math was a pretty isolated and independent activity. You listened to the teacher, then you did you work. You learned later if your work was right or wrong. Today, we want our students to be looking at each other’s ideas and work, and actually talk about it. We want our students to use math vocabulary, review different solutions, and converse about what seems right, what is a good solution, and what does not work. Just as students discuss a short story or a historical event, they should be talking about math problems.
SMP #6: Attend to precision.
I have had a few people tell me they don’t like the new math standards because there is no right answer. Ummm, no, that’s not true. There is a right answer. There may be no wrong way of arriving at that answer, and we encourage multiple ways. But precision in math is still important: precision in the answer, in the terms you use, and in how you check your work.
CHANGES IN MATHEMATICS PATHWAYS
There are several goals in the new state math standards:
- Fewer standards that are taught in more depth
- All math pathways are geared to make students college ready
With that in mind, we have created two math pathways for our students, both designed to help our students to be prepared for college application and admission. Beginning next year, students in grades K – 6 will all take the same grade level math courses. This is nothing new for grades K-5, but it is new for grade 6. There will be GATE clusters in some of our Math 1 courses (6th Grade Math), but all students will be taught using the same standards. These new math pathways will be phased in over the next three years, beginning with next year’s 6th grade class at MBMS.
Then, in the 2017-18 year, beginning in grade 7, there will be two pathways. Both pathways can lead to students taking AP Calculus, AP Statistics, or other math classes well above the Algebra 2 requirement for college admission.
- Students in the regular pathway will take Math 2 in 7thgrade, Math 3 in 8th grade, Algebra 1 in 9th grade, Geometry in 10th grade, and Algebra 2 or a higher option in 11th and 12th grades. Students can reach AP Calculus AB (1st semester college calculus) in this pathway.
- Students in the accelerated pathway can take Math 2 and 3 in 7th grade (1 course, with two years of content), Algebra 1 in 8th grade, and can end up taking Calculus BC (2nd semester college calculus) as a senior.
The biggest change here is that, beginning with next year’s 6th grade class, Algebra 1 is the highest course our students will take in middle school. Our math teachers and math researchers such as Jo Boaler believe that we have rushed this in the past. Algebra 1 is designated as a 9th grade course by the California Department of Education (CDE). The CDE also cautions against accelerating students in math prior to 10th grade. However, our analysis of MBUSD student performance data indicates that we have had many students take Algebra 1 in 8th grade and go onto further math success, but less than two percent have similar success when taking Geometry in 8th grade. This recent research and analysis of student learning make us believe that both Math 3 and Algebra 1 are excellent destinations for our 8th graders. Nearly all of the comparable high performing districts have made this same change.
Our biggest challenge remaining is to further reduce the breadth of material in our middle school and high school math classes. In my mind, these classes still have way too many standards to teach, therefore we rush through them, and when we rush, it is impossible to use high quality teaching techniques. I am pushing to have our math teachers teach just 8 to 10 big ideas during a math year, and go into significant depth on those topics.
So we have made many changes, all designed to help our students deeply understand mathematics through a balanced approach to math learning that stresses procedural fluency, application, and conceptual learning. We have course changes happening next year which should further help that goal. And we are working on changing our courses in high school, so our teachers are more able to truly teach math concepts, and not have to rush through them.
I am grateful for our teachers who have worked so hard to improve their teaching every day. It’s what our students deserve, and I am appreciative of their efforts. I thank Dr. Brett Geithman and Dr. Chad Mabery for leading so many parent workshops in math. I thank all of the parents who have given us so much input in this process. And I thank the Board for adopting courses and pathways that I believe are best for students.