Because there has been so much discussion about a traditional math track in PWC schools, we thought it might be useful to take a step back and discuss just what traditional math is – especially in lieu of the misconceptions and misrepresentations being batted about.

Let’s start with some of the misconceptions about traditional math programs that we’ve been hearing.

Michael Batissta, who helped develop Investigations: *“For most students, school mathematics is an endless sequence of memorizing and forgetting facts and procedures that make little sense to them”*.

PWCS Staff and school board members: *“Traditional Math is nothing more than rote memorization and drill and kill with no context or meaning”*.

Sherry Fraser, co-director of IMP a high school math curriculum: *“Do you remember how boring and mindless it {Math} was?”*.

PWCS Staff and school board members: *“Students were bored in traditional math”*.

**So, what is Traditional Math?**

That seems to be a rather subjective question with hundreds of different definitions. I suggest reading Barry Garelick’s “*Exploration of Traditional Math.*“ for a more detailed discussion of traditional math and the origins of the reform movement.

From a philosophical standpoint, traditional mathematics follows the belief that learning basic math facts and standard processes to the point of automaticity frees the mind to explore more abstract concepts.

You can liken the philosophy underlying traditional math to that which underlines teaching children how to write. With writing, at first you don’t know what the letters look like or how to form them. So you study which letters are which and learn how to form them and how to combine them to make words. Eventually, you’re able to recall letters and words automatically and your focus switches from how do I write that to what am I writing.

Traditional math programs tend to follow that approach. In traditional math programs students learn what numbers and shapes are and how they work together. But they don’t just stop there. Teachers instruct their students on facts and processes and students practice those facts and processes and then work to apply them to real world situations. Eventually those facts and processes are learned to the point where they can be executed automatically so that student focus switches from wondering how to solve 921 – 378 to contemplating more abstract concepts like understanding the laws of sine and cosine and how they apply in the real world.

In general, any program which teaches the standard algorithms as a primary computational tool to the point of mastery is defined as traditional. Far from being just “rote memorization” and “drill and kill”, traditional programs encourage students to develop an understanding of what numbers are and provide them with the ability to perform mathematical operations numbers in an efficient, effective manner.

**So, what’s the big deal – why is there so much debate? **

Elementary mathematics, for the most part, deals with the concrete. It focuses on what numbers and shapes are and how they work together. It’s where those wonderful computational tools on our hands are of utmost importance. On that both traditional and reform programs agree.

It’s how best to achieve that, how students move from counting on their fingers and toes to estimating the quotient to division problem, and whether learning the standard algorithms is appropriate at all, which is the cause of so much debate. It is the adherence to and belief in the superiority of one approach over another which has lead to so much misinformation.

The National Math Advisory Panel, in it’s 2008 report, stated that the endless debate is a waste of time. Among other recommendations, the Panel stated that, *“students should understand key concepts, achieve automaticity as appropriate (e.g. with addition and related subtraction facts), develop flexible, accurate, and automatic execution of the standard algorithms, and use these competencies to solve problems.”*

I wish that had solved the problem.

**So what does that means for us in PWC? **

The approved curriculum for students in K – 5 in PWC is Investigations in Number, Data, and Space. Investigations provides a highly structured, tightly integrated series of lessons which provide students with a “coherent progression of carefully-sequenced learning experiences”, according to PWCS staff in the report, “Why are teachers being asked to teacher Investigations as it is written, rather than encouraging them to choose from it?”. According to the report, “*When the sessions in Investigations are treated as separate activities to be selected or rejected, this careful continuity is lost, and student learning is jeopardized*.”

Because adapting Investigations to provide a blend of instructional materials would jeopardize student learning thereby making a program which blends traditional instructional materials into Investigations highly inadvisable, an alternate instructional program, based on a traditional text which is more flexible to adaptation has been proposed.

Prior to implementing Investigations, PWC used Scott Foresman Addison Wesley (SFAW) VA Mathematics in elementary schools. Recognizing the need to integrate reform and traditional materials together under a cohesive framework to provide the balanced, blended lessons the NMP recommends, the authors of SFAW have mapped the lessons in SFAW to lessons in Investigations. The hope is that this road map will guide teachers in selecting alternate material to adapt and enhance the traditional SFAW lessons with the more concept focused lessons found in Investigations.

You might think, why can’t we just use that road map to make Investigations the blended program we’ve been told it is instead of doing an alternate program? The report linked above provides the answer. Investigations is a tightly integrated series of learning experience which build on one another. Adapting that sequencing of learning experiences and the content of those learning experiences, like the road map recommends, would change the nature of those lessons and compromise the integrity of the Investigations program.

February 10, 2009 at 9:41 pm

I believe the statement; “The approved curriculum for students in K – 5 in PWC is Investigations in Number, Data, and Space” is incorrect. Investigations is the approved textbook, not the approved curriculum. The approved curriculum follows the Virginia Standards of Learning which can be found on the PWCS website. This is a common misunderstanding.

February 11, 2009 at 8:21 am

The standards every child educated in the public school system in the state is expected to achieve are specified in the Standards of Learning. The curriculum is the instructional material, methods, and approach used by local school districts to achieve those objectives. In PWC, the instructional material, methods, and approach used to achieve the Standards of Learning comes from Investigations. Therefore, Investigations is our curriculum.

March 13, 2011 at 9:18 am

Very Informational…. Nice work.