#### Letter from the Math Chair at BHS

2000

Mathematics is the subject everyone loves to make fun of. It is accepted to not like or understand Math - just listen to music, watch popular tv shows, commercials, or listen to dozens of parents say "I can't help my son/daughter with his/her homework, I'm just not good at Math." Although almost every adult I know can't remember any Math s/he learned in school and shudders at the thought of the quadratic formula, those very same adults want Mathematics to continue to be taught the "old-fashioned" way. The way that only a very few understood in the first place!! Yes, it obviously worked for me (a product of traditional Math at BHS in the 80's) but it didn't work for the vast majority of students.

The BHS Mathematics Department is concerned with students understanding and internalizing Mathematics in a way which allows them to apply the Math to new situations. We are not interested in students regurgitating the formulae in cookbook problems which they don't understand.

The U.S. Department of Education's Office of Educational Research and Improvement appointed a panel of 15 mathematicians, scientists, educators, and policy makers to look at new math programs. They recently nominated 10 programs as promising and 5 of those as "exemplary." Among the 5 are IMP (Interactive Mathematics Project) and CPM (College Preparatory Mathematics). These programs are both currently in use at BHS and around the country. We use the CPM for Algebra I and Geometry ONLY. All three Berkeley middle schools use the CPM Algebra.

Both programs use more of a guided instruction method. Teachers do not just expect kids to "figure it out" but they do want the students to attempt problems in groups and discover patterns and learn from that discovery. The teacher reviews progress through warmups, does sample problems and gives brief "lectures", walks around the room assisting groups on their discoveries, etc. Students are encouraged to work in teams and to ask group members for help. This doesn't mean the teacher won't help. It means the teacher and students time is more productive when the teacher is helping a group or team of four students who are working together. Many studies have shown that we learn the best when we explain it to someone else. Students can often explain something BETTER because they speak that same language (teenagerese). This is NOT meant to replace the teacher, it is a supplement.

The decisions about WHAT is taught in Math is made by the State Mathematics Framework, which the district (School Board) has adopted. HOW it is taught is decided by the BHS Mathematics department, although textbooks must be approved by the School Board. We have yet to find the perfect textbook for any course. Even the Math Analysis textbook which I spent hundreds of hours selecting using student and teacher input (for my Master's thesis), isn't loved by all. Each course (Algebra, Geometry, etc.) has meetings at least once a chapter so that teachers can discuss strategies, pacing, etc.

A summary of the programs at BHS: IMP is a non-traditionalcurriculum which is more problem-based. Units revolve around learning the Math necessary to solve a particular problem. Students take IMP1a,b - IMP 2a,b - IMP3a,b - IMP 4a,b. They may take A.P. Statistics after IMP 3b or 4b, or A.P. Calculus AB or BC after IMP 4b. The more traditional layout is Algebra 1a,b - Geometry a,b or Honors Geometry a,b - Algebra IIa,b or Honors Algebra IIa,b - Math Analyis a,b - A.P. Calculus AB or BC. Students may also elect to take A.P. Statistics after Algebra IIb, Honors Alg IIb, or Math Analysis b. Algebra Ia,b and Geometry a,b are taught using CPM textbooks, which are discovery based but are not exclusively so. Students cannot switch from IMP to "traditional" or vice-versa because the curricula do not match up. Students who do not pass Algebra 1b, Geometry b, or Algebra IIb in the spring may take them over in BHS summer school (provided we have enough students sign up for a full section). Both IMP and traditionally ordered courses are accepted by UC and CSU systems as college prep classes. SAT results are similar.

No curriculum is going to work for every child. The teachers at BHS work together extensively, making suggestions for methods of presentation, altering the assignments this way and that, all in order to have successful students. We are constantly improving and reassessing what we do. With the new High School exit exam and Algebra for all in eighth grade, it is crucial that we have a curriculum which helps as many students as possible. This is our goal.

-Laura Leventer, BHS Mathematics Department Chairperson

#### Responses to the Math Chair

re: Math bashing?

I'm a parent who likes math. I am an engineer, so I have a math background. I remember a lot of math I learned in school the "old-fashioned way". I bet most of us can remember what 5 times 6 is because we had to memorize it. I am not complaining about math instruction out of a dislike for math. I am complaining because my children cannot learn math using CPM. Since there is no other alternative, they are not learning math. Engineering will probably not be an option for them, because they will not have the math background for it.

re: kids learn better from each other

I asked my kid "how's it going with CPM so far this year?" (he hated it last year). He replied "It's a lot better this year because two of the kids in my group have tutors, so they can explain the hard stuff."

I too am very comfortable with math. I did well in math in school, and remember it and enjoy using it. I do research. I learned math the traditional way. The "aha" moments were good, but there was a lot of practice and drill, and we got to the point where we could rapidly solve a variety of math problems, and gained an ability to quickly change our line of attack if one approach was not working. This requires speed in thinking, and some of the gain in the speed came from -- guess what -- drill!! One of our kids attends BHS. Her advice: don't take CPM if you can avoid it. It leaves important holes in your understanding of math.

I'm the parent who wrote about CPM math at Northgate High and I could not agree more with the engineer who wrote that she or he remembers the math learned the "old-fashioned way" in high school. So do I, and moreover as an architect I use algebra, geometry and trig regularly. If I don't remember just how to do a particular kind of math problem, I need only refresh my memory with a reference book and I'm off and running. Despite the previous thoughtful post by the math teacher, the fact is that CPM math doesn't work. Sooner or later the education system that experiments on our kids, to their detriment, is going to have to bow to this fact.

Hi, I just wanted to join the group that would like CPM math to be replaced. My son is an above average student except in CPM Math. Last year he didn't do very well in Algebra. This year, he was getting some help from the Geometry teacher and some help at the tutoring center, but I guess not enough, so we finally decided to get a great tutor, so things are getting much better.

My high school junior (St. Mary's High) went all through public schools in Berkeley through eighth grade. He experienced one poor year of Algebra with a brand new teacher in 8th grade, and we found a super, young, bright high school senior (BHS) to tutor him privately the last third of the 8th grade year. It brought his understanding and his grade up, and then he took Algebra 1 (again) his freshman year and sailed through with an excellent woman teacher at St. Mary's. I feel that there is no shame in taking the class twice and getting a really solid grounding. He did really well in Geometry (sophomore yr--with the same teacher as Algebra 1) and now is secure with Algebra 2 (current junior year). I endorse today's writer who recommends that parents find that young (or old!) tutor who can connect well, on a weekly basis, with your student. This does not need to be a super expensive professional adult tutor. Often the school counselors have names (at King, the after school Homework room coordinator provided several high school student names and we went with the first that said he had the time, $10/hour). they played ping pong when done with an hour or so of tutoring.