Sunday, June 1, 2008

One Look at What Works


Here is what The Bear Creek School, a private school in Redmond, uses for math through Middle School. Saxon 1 through Saxon 7/6 and thenthey go to MacDougall Littel. They test kids for readiness for theLarson series Pre-algebra using a test provided by ML. If the kids do not pass, they take what is called "bridge math" using the ML Math Course 2 (isbn 978-0-618-61070- 9). The next step is the Larson series of ML Pre-algebra (978-0-618-25003- 5), Algebra 1 (978-0-618-59402-3), Geometry (978-0-618-59540- 2), Algebra 2 (978-0-618-59541- 9).

ML lists the Algebra 1 and up books on the "High School" tab of theirwebsite but the middle math track student at Bear Creek will take "Bridge Math" in 6th grade, Pre-algebra in 7th, Algebra 1 in 8th etc. Most other students will be 1 year behind or 1 year ahead of this plan. In looking at the texts, I was surprised how big the jump was from Saxon 7/6 to ML Pre-algebra and can see why most students need the ML Math Course 2 book prior to ML Larson Pre-algebra.

One note about Bear Creek (it is a Pre-K through grade 12 school), the majority of the students enter in K. They do a K readiness test but no IQ testing. There is a wide range of abilities in the classrooms. I do not think public educators should discount what is done at this school as impossible in public. There is no magic here, just high expectations and student support to help them meet the expectations. Very little time is wasted on fluff and they have 1 hour of math everyday first thing in the morning-this is rarely violated, less than 5 times through the whole year.

Public school kids deserve this kind of education too! Look at Stella Schola, a choice middle in LWSD (admission by lottery). The head teacher of that school, Brigitte Tennis, runs a program that seems to me to be a reasonable approximation to Bear Creek in many ways. She does not teach to the WASL at all. The only problem is there is room for only 1 out of 4 students who enter the lottery. Her test scores are so high that she is able to fly under the radar of the administration and do great things with her students. Educators should be paying attention to public programs such as Stella. So should the Gates Foundation.

Colleen Wurden


Anonymous said...

If one were to learn about designing textbooks, Saxon (Incremental Approach) would be the book I would choose for learning what not to do.

This is not to say that Saxon does not work - it does? But the question is why and how?

For one, it is nothing at all like Singapore. But rather Saxon is written in the style of a basal reader. Basal readers use an approach where:
1. words are used as a whole.
2. the words are used over and over in each succeeding lesson.
3. New words are added regularly.
So what's interesting about kids coming out of Saxon classrooms is the variation of math abilities - its not predictable.

In other words, its dependent on a lot of other factors - teacher ability being one. But lets overlook content and focus on classroom instruction.

So then one has to look at what teachers do differently and of course one of the things that teachers do is supplement curriculum and in this case they are enriching the instruction (filling in the gaps). So why didn't Saxon think of that when he wrote his book? New teachers supplement less than experienced teachers, which again begs the question, what do we do for staff development - I can guarantee they're not learning how to teach Saxon (ludicrous speed).

The second thing that is clear when you read Saxon problems is the problems sets gradually increase in difficulty. This reminds people of the tradition (ML) 2-page spread. So its pretty easy for kids (and teachers) to just forget about doing the last few problems which offer the most in terms of experiencing learning that will last. Singapore is different and I've often heard 'spiraling' used for both curriculums, but both groups 'spiral' differently - you are comparing apples and oranges.

Much of Saxon can be done in one's head. So the math problems you see being done by Muirlands students at Olympiads are really circus tricks and its dependent on the teacher and parents - not the textbook. This is not a bad thing, but it helps explain why you have 10th graders at La Jolla enrolled in linear algebra at UCSD?

Lets take proportional reasoning as an example and the way it is taught by Saxon. The instruction of low ability groups is different than the instruction for high ability groups. Its dependent on the teacher. Experienced teachers will point out to students which method is most appropriate. Novice teachers will usually teach cross multiplication. All of these methods by the way are considered 'standard' as opposed to the non-standard methods which integrated math philosophers confuse over and over (idiots! they can't even multiply straight)

Saxon is designed from an elementary perspective (developmental) and that is the reason, it leads to tracking in school. Higher tracks get introduced to McDougall earlier. Some schools even adopt easier textbooks for lower tracks (Prentice Hall).

How many teachers are familiar with basic geometry? It is perhaps the most revolting example of a textbook, I've ever seen and students in low tracks won't go beyond this textbook unless they are fortunate to have a good instructor in community college.

With Singapore, everyone is in the same track and 'extra' instruction is for support, not enrichment.

This leads to all sorts of advantages -
1. cost efficiency and resource allocation going to the support track.
2. more students taking higher level math classes.
3. a well-written curriculum that appeals to everyone.
4. more students enrolling in math and science classes, not to mention career paths.
5. data is measurable and easier to collect, since the mainstream curriculum works for the high ability group. We are talking here about what is sufficient for college entrance, not an academic track for future professors.
6. Readability - problems are carefully worded, so that they can be understood by a heterogeneous society. Making the academic leap to ML from Saxon is a leap of faith that students will be able to understand what they are reading in ML. This is why US schools revert to lower ability tracks. Singapore does not do that.

(mass education is a revolutionary concept, not a government enterprise)

Anonymous said...

Something else to think about - the writers of college prep. math also write the Golden State Exam for California - this is an algebra test given to students in the eighth and ninth grade. college prep. math questions are aligned to those test questions. Its irrefutable and unlike the other exemplary textbooks (CT is a software program (CAI) that is hardly satisfactory as a teaching medium) CPM actually looks and thinks more like Singapore, than other curriculum and that's because the authors intended it that way.

Ann Arbor teaches integrated math and she thinks this is as good as it gets!

What standard methods do you advocate for students and teachers?
AA: Calculators are a standard tool in integrated math. Another standard method that students use all the time is trial and error.

How about standard algorithms?
AA: Basics don't interest students and its boring for teachers. We feel its students who must decide for themselves what is the best standard that works for them.

What's you philosophy of learning?
AA: Make it real. Students need to learn how to model reality and the only way to view reality is with statistics. Data points are real, lines are models of reality. That's the zen of math.

What do you expect students to learn when they take your class?
That learning is hard work and lots of effort. There are very few people who grow up to be mathematicians. The acorn doesn't fall from the tree.

Any hopes for the future?
This is the future - get used to it. What works for some people, won't work for everyone.

What's your favorite subject?
AP Statistics

Anonymous said...

The Oak Harbor, WA. school board has postponed adopting Core-plus at this time. They may decide to do a full K-12 adoption for the 2009-2010 school year. Any ideas for curriculum for K-5, 6-8, and 9-12? Let's hear all the best choices! Thanks.


Anonymous said...

We returned in triumph, exulting in the completeness of our vengeance, corn-stalks in hand, ... lets hope this news goes out to other districts.

Anonymous said...

Saxon is a great program, but it only works if it is used as a complete program. Too often, teachers try to cut corners by only assigning odd numbers or half of the problems. This defeats the point of a program like Saxon that is designed to be both incremental and reinforce prior concepts. Bear Creek is guilty of this as well, which may be why a bridge level was necessary.

woodinville daycare said...

the words are used over and over in each succeeding lesson.