Teaching math in a problem-based manner pays dividends…

So end-of-grade test scores have come back. I’ve spent this year co-planning mathematics lessons with a 3rd grade teacher, Laura, at a school near my university in Charlotte. Laura is a 2nd year teacher and graduated from here (UNC Charlotte) 2 years ago. At the beginning of the year we committed to doing things right– planning a balanced math curriculum that was heavily standards-based and very focused on problem solving.

At the beginning of the year her students ranged from Level II to Level III….all students have to reach Level III by the end of the year in order to move to 3rd grade. 22 of her 23 students passed the first time and all of them showed growth from the pre-test score. The one student who retested passed on the retest…giving her a 100% pass rate!!

For me, the commitment that we made to teach problem solving and use a standards-based approach was not a risk. I was confident in it. But for Laura it was a risk. While we had planned and worked together the year before, teaching nearly the whole year from a standards-based approach was a risk that she was willing to step and take.

During the year we knew the kids were learning. When they were able to solve tasks like the classic 8 + 4 = __ + 5 or multi-step, multi-operational tasks, we had a hunch they were moving in the right direction. They talked about mathematics and reasoned at a high level. Still, we were uncertain how it would carry over into a standardized testing situation. It is refreshing to know that in this case, the commimtent paid off and there was evidence of student learning, not only in students’ communication and reasoning, but also on the state mathematics exam.

NC Schools Adopting Standards-Based Math Curriculum

As this is the year of textbook adoption many schools are transforming their mathematics programs by adopting standards-based mathematics curriculum. Charlotte-Mecklenburg Schools- which has over 100 elementary schools and nearly 3,600 K-5 teachers, has decided to adopt Investigations in Number, Data and Space, a curricula designed around a problem solving approach to learning that teaches the skills through real-world contexts and solving authentic problems. Many districts that are finalizing their decision have Investigations in their top 2 or 3 curricula.

We know from the research that the use of Investigations as a comprehensive curricula results in students who have equivalent computational skills, but Investigations students have superior understanding of problem solving and flexibility of concepts- being able to solve tasks, represent them in multiple ways, and explain the mathematics embedded within the concepts.

The issues that are raised by some with adopting a curricula such as this are primarily two-fold: the need for teachers to receive professional development to use such a curricula effectively, and the need to support teachers in their daily practice.

The teacher manuals are structured in such a way to provide the teachers with all of the supporting material- pacing, sample higher-level questions, possible student responses, guidance on formative assessment in the midst of a lesson and end-of-unit assessments to use to examine students’ understanding of a subject area.

When it gets down to it- teacher change is once again an issue. Just as discussed often times with technology integration, scientific inquiry or problem-based approaches to mathematics– what are the best ways to support teachers’ adoption of these effective research-based practices?

What knowledge do teachers need in order to teach mathematics?

I’ve spent the day up at the University of North Carolina in a meeting discussing and identifying what types of mathematics knowledge teachers need in order to be effective mathematics teachers?

Deborah Ball, the Dean at the University of Michigan, came and spoke about content knowledge that was specific to the teaching of mathematics. She described her current work which describes Mathematical Knowledge for Teaching (MKT), which includes knowledge about:
content common to all people
content specific to mathematics teachers
the intersection of content and students
the intersection of content and resources
curriculum
the mathematical horizon

Specifically, we talked about the number of courses that preservice elementary teachers take related to content. The Conference Board of Mathematical Sciences published a book about Preparing Mathematics Educators which stated that preservice teachers need a minimum of 9 hours about content knowledge related to school mathematics. They advance recommendations about what should be included in these 9 hours.

As all of North Carolina pubic universities revision their teacher education programs these are issues that need to be considered.

In your opinion, what do elementary school preservice teachers need in order to be effective mathematics teachers?

Basic Facts or Problem Solving: Math Wars Revisited

This morning in the rational number course that I am helping with, there was a discussion about how to teach fractions. As in the case of all courses and workshops that I facilitate, the discussion of teaching from a skills-based or a problem solving-based approach resurfaced.

It’s interesting to follow my beliefs- having been raised in a skills-based, memorization approach, but being taught how to teach from a problem-based perspective, I struggle with the idea that there are extremists on both sides are saying all skills and all problem-solving and neglecting the need for a balance. As I continue to work with teachers they tend to jump to one side and not like that balance-area in the middle, which is really what research is showing to be most effective.

Just some food for thought…

Hello from Williamsburg, VA

I’m back in Williamsburg, VA at my alma mater William & Mary helping with the first week of a course on rational number.

We’ll be doing some of the following things:

• solving tasks involving fractions, ratios and percents
• looking at connections between mathematical concepts
• examining how to teach rational number developmentally across grade levels
• analyzing student work samples involving rational numbers topics

I came in late last night, so I haven’t seen much of the area. But, how can one go wrong in a town focused on 17th century America and cobblestone roads.

Have a great Monday,