Children's math anxiety and the effectiveness of timed tests also were hotly debated among members of the parent-teacher task force.
The 28-member group has met regularly since last May to share "best practices" on creating excitement about math, particularly for the large numbers of high-achieving children in local schools.
While "Everyday Mathematics" is the core curriculum for Palo Alto elementary students, supplemental materials are used throughout the district at the discretion of teachers and principals.
Because individual schools and teachers have autonomy over those choices, the task force was created to promote the sharing of ideas across the community.
Parent Avivit Katzir and El Carmelo School Principal Chuck Merrit, the task force's co-chairs, told the board the group had expanded its focus — originally to address the need for greater challenge among high-achieving students — to all students, not just gifted children.
Katzir and Merrit said the group heard presentations on more than 20 "exemplary approaches" used on local campuses, including "Number Talk at Barron Park," "Embedded Math" at Escondido and the online Khan Academy in the Los Altos School District.
They debated the nuances of creating temporary "flexible groupings" of children — based on ongoing pre-assessments — to teach students in smaller groups related to their achievement levels.
Katzir and Merrit were quick to distinguish "flexible groupings" from traditional ideas about laning or tracking. Flexible groupings should be temporary and frequently changing, based on quick assessments before each unit, they said.
"With flexible grouping, a teacher will have three groups within the classroom, and the material presented to each group will be appropriate to the level of the student," Katzir told the board.
The task force also hotly debated the best ways for children to achieve "automaticity" with basic math facts, with some defending timed tests and others arguing that such assessments create math anxiety.
Task force member Jo Boaler, a Barron Park parent who also is a professor of math education at the Stanford University School of Education, said the group felt timed tests should be left up to the teacher's discretion, not required.
Boaler passed out a four-page paper arguing that neuroscience research shows that timed tests can engender math anxiety in young children (see sidebar).
In the end, the task force recommended that educators "review practices that promote automaticity and reduce anxiety around learning basic math facts."
The task force decided to omit an appendix — presumably reflecting the debate in greater detail — from its final report, Merrit said.
"We do have a version of our appendix. It's not lost information, but it was the decision of the task force not to include it in the final report," he told the board.
School board members pressed the co-chairs on what system had been established for the ongoing sharing of ideas.
Merrit's response — that the primary "point of contact" would be math-coaching teachers known as Teachers on Special Assignment (TOSAs) — appeared to disappoint them.
"Are your presentations available for the public to see? It was a great professional development experience for teachers and parents, but are they sharable?" asked board member Barbara Klausner.
"Say I'm a parent volunteer who wants to start a Math Olympiad in a school, and I want to know where out of our 12 elementary schools I might find other people who had experience with this program. To me, this was the point of the task force," Klausner said.
Merrit said he was still in the process of collecting the presentations, which will be uploaded and linked to the school district's website for the Math Task Force.
Board member Melissa Baten Caswell suggested an online "wiki" model for sharing, where teachers could post what's going on in their classrooms.
"The turnover in this district or in any organization makes it really important that we don't allow things to just sit in people's heads," Caswell said.
Klausner said she doesn't want to "lose the focus" on the original motivation of the task force to address the challenge needs of advanced students.
"What we have here are a lot of good ideas, but if someone wanted to focus on that goal, what should they do? How do you decide how to allocate district resources toward that mission? We haven't heard what the next steps are on this task-force report," Klausner said.