A more important question, considering the discussion about blending Investigations which is scheduled for February 10th, is whether it is possible or even advisable to blend Investigations with other materials. To figure that out you have to figure out what the differences between the approaches are and then examine those differences to see if they can be blended.
If you ignore all the rhetoric and debate about traditional and reform math and look at the details, you realize that the major differences between the two approaches fall into two broad categories – computational fluency and the introduction of standard processes and formulas.
The Investigations program follows the belief that learning the standard algorithms and math facts too soon inhibits the development of number sense and reasoning. Students in Investigations use what the authors call “transparent” algorithms to solve problems. Formal exposure to the standard algorithms is deferred until later grades and limited to comparing and contrasting the standard algorithms to the “transparent” algorithms taught in Investigations. The standard algorithms for addition and multiplication are studied in Investigations in Grade 4; the standard algorithms for subtraction is studied in grade 5. The standard algorithm for long division is not studied. PWCS has moved the lesson studying the standard algorithm for addition to Grade 3 and subtraction to Grade 4, but the nature and extent of the lessons are still limited to comparing and contrasting the standard algorithms to the “transparent” algorithms taught in Investigations.
Traditional math programs follow the belief that the standard algorithms are a primary computational tool, that learning them to the point of mastery allows students to explore more complex and abstract concepts. As such, traditional math programs teach the standard algorithms when students begin multi-digit addition and subtraction, generally in Grade 2. The standard algorithms are then practiced and reinforced to the point of mastery. Alternate computational strategies are taught, but only after the standard algorithms have been mastered.
How do you blend these two approaches when the philosophies which underlie them are so divergent? How do you adapt Investigations to provide direct instruction on the standard algorithms and ensure that it provides sufficient support and practice that the processes are mastered when the program is designed around the belief that learning those processes too early or to the point of mastery is dangerous?
The primary difference between the two philosophies is whether the standard algorithms are taught, the extent to which they are taught, and when they are taught. When it comes to mathematics, programs are either traditional in that they teach the standard algorithms to the point of master to students beginning in Grade 2, or they are reform in that they teach alternate strategies and defer study of the standard algorithms to later grades.
Changing Investigations so that it teaches the standard algorithms to the point of mastery would require rejecting the “transparent” algorithms Investigations teaches and replacing them with direct instruction on the standard algorithms with materials obtained from other texts. That would undermine the philosophy which underlies Investigations and, in the words of our staff, “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.”
That sentiment has been echoed multiple times by PWCS staff and TERC, the authors of Investigations. In a February 2006 memo to Dr Walts, Pam Gauch, then Superintendent of Student Learning and Accountability, stated ” Research shows that student achievement will be better with the sole use of a traditional program or the sole use of a reform program than if both are used together.”
Our staff, in the document “Why are teachers asked to teach the Investigations program as it is written, rather than letting them choose from it?” , stated, “Research on program implementation cites inadequate fidelity of implementation as a major reason for program failure”.
Those comments seem to effectively close that debate – adapting Investigations by removing lessons and replacing them with lessons and materials obtaining from other texts will jeopardize student learning and increase the probability of program failure.
You may wonder about the commitments we’ve been hearing for the past several months about a blended approach to mathematics. What we’ve been calling a blended approach is nothing more than unadapted Investigations with a few additional lessons thrown in where necessary to meet SOL standards.
In lieu of the evidence of the inadvisability of changing the nature and structure of Investigations lessons, is creating a blended program with Investigations as the primary text something we really want to consider, or, is there another option to create a truly blended instructional program in PWC?
The opt in for traditional math seems to be that other option. The textbook we used previously in PWC is much more flexible and amenable to adapting. We could use that textbook as our primary textbook and supplement it with Investigations. We could keep the Investigations program intact and the traditional program, which would be available to students at their parents request, would be developed to provide that blend of instructional materials we keep hearing about. Yes, the opt in program would be a traditional program because it would teach the standard algorithms and formulas to the point of mastery, but that doesn’t mean it would disregard conceptual understanding.