Yesterday, I attended the Solving the “Algebra for All” Problem conference by Edward A. Silver, Ed.D., Professor at the University of Michigan. Here are some highlights of the conference, just in case you missed it.
Schools are being asked to offer Algebra earlier (in 8th grade) and for all students. Something that I didn’t know is that Algebra used to be taught in college. Also, eighth grade algebra was taught just to gifted students.
The National Mathematics Advisory Panel (NMAP) was established by President Bush in 2006.
One of the results of the NMAP discussed by Dr. Silver was:
– All school districts should ensure that all prepared students have access to an authentic algebra course, and
– Should prepare more students than at present to enroll in such a course by Grade 8.
Students are reaching Algebra without being prepared for it. Therefore, they’re set up for failure.
Being prepared, based on the NMAP report, is to have:
- Fluency with Whole Numbers.
- Fluency with Fractions.
- Fluency with Particular Aspects of Geometry and Measurement.
Check the Benchmarks by Grade for the Critical Foundations on page 20 of the NMAP Report (page 47 on the pdf).
An authentic algebra course is “a course that addresses algebra consistently with the Major Topics of School Algebra” per the NMAP Report.
Check the Major Topics of School Algebra on Table 1 on page 16 of the report (page 43 of the pdf).
We already have algebra for all but not by ninth grade.
What are the driving forces behind all this?
– Global competitiveness
– Equity arguments
– Demand for higher standards
Students in the US are constantly behind students in other countries in mathematics achievement tests. Check out our previous blog post about the latest results. As a country, we are running the risk of not having enough of a technical workforce in the future.
Dr. Silver mentioned that kids get confused as to what’s an equation although they know
they know the concept of equality. He said that we need to tell them that we’re taking and old idea and adding a wrinkle to it. We need to teach them the different kinds of equations. They have an idea that the “=” sign means to do something, to compile.
8 + 7 = __
8 + 7 = __ + 3
8 + 7 + __ = 9 + 6
They may think __ is always 15.
Equality as Balance (Relational)
Use a visual balance to show them equality between different variables/unknowns.
Important Role of Equalizing in Algebra
– If a quantity can be expressed in more than one way, then these different expressions are equivalent.
– Is there a quantity that you can express in two different ways?
– What quantity can be expressed in terms of others?
How many squares are on the border of a N by N grid (picture at the beginning)?
4(N-2) + 4
2N + 2(N-2)
N2 – N-22
All are equivalent
Writing equations is not trivial. It is fundamental.
In the Q&A session it was discussed how we need to help students form arithmetic to algebra which is an abstract world that may not be easy for all to transition to.
I think that as teachers, we need to try to put ourselves in the students shoes and figure out their thought process to be able to solve their confusion and help them learn. This may be a difficult task for us, when algebra was probably easy for us, but it’s not impossible.
Don’t forget to check out the NMAP Report and to tell us what you think about all this.