This is my report on the Arise math program, after I sat in sporadically over about six weeks. This is an integrated high school math, substitute for traditional algebra, geometry, and is one of two choices, along with CPM, offered at the high school my daughter, Jennifer, attends in Vallejo. It has its own web site.
I sat through two units. The first was three weeks and covered three person elections -- the 1980 NY Senate race, with Buckley and two others; Wallace-Humphrey-Nixon and Clinton-Bush-Perot. The purpose of this unit was to learn about matrices. What we discovered, after three weeks of effort, was that if you have three people running for office, it is possible for the successful candidate to win with less than 50 percent of the vote.
After we did that, we compared the popularity of various lunch items, with the same result: the winner had less than 50 percent of the vote.
The students described various ways of arriving at this answer, and prepared and presented a group speech. What they learned about matrices was, apparently, how to make a chart with rows and columns. There was no manipulation of the matrices. My math is 30 years old, but can't you do algebraic and numeric functions with matrices? Isn't that what they are supposed to be learning?
The second unit is encryption. I did observe a nice video that enhanced the presentation of information about encryption. That is, it is a better learning experience if the material is presented in several ways. In this case, there was written material, teacher's discussion and the video. It's just that there was no math in this. The students spent several days decoding and encoding material in the text, and then creating their own codes. Each group then gave a presentation to the class on how their codes worked.
This is supposed to present linear equations. As part of the activity, they used graphing calculators to see how the curve changes as the number in the equation changes. The teacher kept telling them how much more they were learning than students in her Algebra 2 class. Whoopee.
I was totally unable to keep up with this, so that I could provide no feedback to Jennifer as she was doing the work. This has effectively cut me completely out of the homework loop. The teacher does not look at the homework. She says the students get feedback from her as she walks around the room listening to the various teams. And, they get feedback from each other.
Clearly, this is how "collaborative learning" is supposed to work. The students take the problem, in this case decoding a message, work together to solve the problem, and come up with a solution. They never know if that is the correct solution, or, apparently, receive any instruction on how to actually solve for variables in a linear equation.
In my opinion, if you do not get feedback and confirmation that your solution is correct, you never stop floundering. You must have firm, secure knowledge to move to the next level of learning. I base this not just on my high school and college education, but on my experience in teaching expatriate tax to adults. The earlier and more concrete the feedback, the better the tax preparers learned and retained what they learned. If you withheld feedback, they floundered and guessed at the correct method and did not retain enough knowledge to get better at doing their job.
For the record, as many of you suggested, I am now using John Saxon's high school math program to tutor her in math. If we find time to complete that, and her understanding of the concepts presented in Arise improves, I imagine the teacher will give herself the credit.
This teacher has been teaching math for 31 years; CPM for four years, and Arise for two. She starts each class with math drills, no calculators. Given her experience, I cannot understand why she is so enthusiastic.