A Superior Court in Seattle has taken the unusual step of ordering the city’s Board of Education to reconsider its adoption of a program known as Discovering Math. Ordinarily I wouldn’t be writing about what happened in a courtroom in Seattle earlier this month, except that this case is the first of its kind involving reform math. And reform math is what we have in Branford.
Judge Julie Spector reviewed all the evidence the BoE had in choosing the math text and found no solid reason for any reasonable board member to consider its adoption. Discovering math, an inquiry-based high school program, is very similar in philosophy to Investigations, which we now use in our three elementary schools.
The judge’s ruling focused on the actual merit of the program, rather than the process by which the math program was adopted. Click here to read it. Parenthetically, I am still waiting for the minutes of the meeting back in 2007 when our program was adopted.
So get your paper and pencil out. Let’s explore Investigations to see how Investigations claims to promote a deeper conceptual understanding of math.
Let’s add 578 and 43. The authors of Investigations represent this as 500 + 70 + 40 +8 + 3, horizontally. Now, I am not complaining about this, as when we do mental math for lack of a calculator or paper and pencil, many of us conceptualize the answer in our head. And, it does show that you understand the “7” in the number represents 70, not 7 or 700. But, the US algorithm is:
578
+43
To use the US algorithm the student is taught to carry extra 10’s in the ones column over to the tens column, etc. To an elementary school student this may be difficult to understand, but with proper repetition through the elementary school years, most students become proficient. The problem with Investigations, in this case, is that it avoids the concept of adding and regrouping and it fails to show that the US algorithm is more efficient. Suppose you are now adding $7,894, 345.00 to $38,547.00. The Investigations method is going to put me over my word limit.
Now, let’s multiply 568 by 32. This means (30 x 500) + (30 x 60) + (30 x 8) + (2 x 500) + (2 x 60) + (2 x 8) with Investigations. The US algorithm is:
568
X32
Students are taught to multiply the “2” by “8”, then “6” and then “5”. Then, they are taught to multiply the “3” by the same numbers. But, the “3” is actually a 30, so no number is put in the one’s column. Students are taught the importance of place value by vertically aligning the multiples in the proper columns. The Investigations method is inefficient and has more chance of error while the US algorithm works every time. Imagine using the Investigations method, but with larger numbers.
Lessons with geometry involve guessing how many boxes fit within a box and other lessons have students draw a power polygon. (There is no such thing as a power polygon) Some problems looking for a difference ask the student to add up rather than subtract. Other assignments ask the students to solve simple problems using many strategies. Lessons work simple ideas to death without ever getting across the most efficient strategy. First graders identify patterns rather than learning math facts. All of this is all disguised as “discovery learning” or inquiry-based.
Let’s look at the reality.
See for yourself by clicking on this You Tube video of a parent. The parent, also a tutor, contrasts her 3rd grade daughter’s homework with Investigations to a 3rd grader at a nearby school. The video demonstrates what it is like for students with Investigations. Suppose the Investigations student moved to the other school. She would not be able to do the math at that school.
The other major concern with Investigations is that it is a spiral-based program. The theory of spiraling is that students get a bit of exposure to a concept and then the program changes gears to an entirely different topic. Students are supposed to then have their “a ha” moment when the program returns to the original concept.
The spiral basis of Investigations is evident as the program jumps from topic to topic. Unrelated concepts such as multiplication and, then, geometry, for example, are introduced within the same school week. However, gaining any command of the task at hand via this schizophrenic approach is absurd. The value of practice is lost and students are left confused with little skill. Furthermore, spiraling makes it difficult for teachers to identify struggling students.
Enough said. Here is what the experts have to say.
The National Math Advisory Panel, a group of mathematicians and educators appointed by the US Department of Education in 2008, published specific guidelines that the members felt must be part and parcel of an elementary school math program in order to provide the strong foundational skills necessary for algebra. Briefly, this group reviewed all of the available research concerning math education and formulated specific guidelines for states to model math curriculum by based on these studies. This panel suggests that the US algorithm is as necessary as conceptual understanding. They also emphasized the need to avoid spiral-based programs because they do not allow for sufficient mastery of topics to occur.
In addition to the NMAP, the National Council of Teachers of Mathematics similarly published its ‘Focal Points’. The NCTM previously had a single belief in inquiry-based programs, but subsequently took a stand together with the NMAP to emphasize the need to provide instruction with the US algorithms in concert with conceptual understanding. Both groups highlight the need for all math programs to provide more detailed instruction on fewer topics and to practice with the US algorithms until fluency and automaticity are gained.
Professor Bill Quirk, a highly respected professor of mathematics who has methodically analyzed the 2008 version of Investigations, notes that there is no emphasis on the US algorithms that the NMAP suggests, nor is there nearly the amount of practice with basic arithmetic to develop the fluency and automaticity necessary to succeed with algebra and other higher level math.
The NMAP, NCTM and Professor Quirk, in essence, clearly state that it is necessary for students to be able to use US algorithms for adding, subtracting, multiplication and division with whole numbers and fractions and to do so with fluency. They suggest that math programs need to develop a conceptual understanding in concert with using these highly efficient strategies. The reason is not to brag, but because these skills are mandatory for students studying algebra and other higher level math. Programs such as Investigations fail miserably at accomplishing these tasks.
So, how did Branford wind up with this program?
That is the question. Much has been learned about the process of the adoption of Investigations and its inefficient roll out at each of the three elementary schools. Investigations appeared on the desks of the K‑2 teachers during the fall of 2007. Dr.Mary Peraro, in charge of elementary school curriculum, gave the directive to order the program. Investigations was never piloted. The opinion of the teachers and principals with the strongest math expertise within the system was not sought. And, there was very little public input on the adoption of Investigations as the sole elementary mathematics curriculum.
Teachers were given very minimal training before they were asked to teach it. In fact, the second graders of 2007 had teachers who had no experience and minimal training with Investigations. The superintendent’s office plans to expand the program through 5th grade.
From the outset, many parents, mainly at Mary Tisko Elementary School, were disturbed by the inquiry-based structure of the program. Several spoke with leading mathematicians around the country who advised the parents of the flaws with the program. One mathematician, Professor Wilfried Schmid of Harvard University, stated that our children will be two years behind in mathematics if we continued with Investigations. Several parents complained to central office and the BOE IN 2007, but Investigations continued.
A series of Math Nights were performed in 2008 by math educators with a bias toward inquiry-based programs. Parents were told that our students will better understand math because of Investigations. Reasonable arguments against Investigations by some parents were continuously dismissed. Math Nights continue. Parents and students enjoy them because they emphasize fun. Fun needs to be emphasized, but does this constitute enough reason to perpetuate the myth that the program is allowing for a proper math education?
Now, at the eleventh hour, Dr. Kathleen Halligan, the school superintendent and Dr.Peraro admit there are gaps with the program. Both superintendents state supplementing the program can be done as needed. However, this is no easy task for the third and fourth grade teachers who have nearly two years of math to make up. This catch up game is a day late and a dollar short. Some students may never catch up.
We also knew from the outset that Investigations was a failure as a stand alone program. New Canaan has had Investigations for 12 years and now highly supplements the program. We also know that 50% of the districts with Investigations listed on the publisher’s website have subsequently dropped Investigations. In fact, the US Department of Education noted that first grade math achievement was significantly lower in schools randomly assigned to Investigations or Scott Foresman-Addison Wesley than two other math programs. Click here to read about it.
As a parent of two children, one of whom experiences Investigations on a daily basis, I believe it makes no sense to ignore the plethora or research and testimony out there that argues against Investigations and other inquiry-based math programs.
It is important that Branford understands just what happened in Seattle. We don’t have a judge looking at our math program, but we have enough evidence to know that Investigations does not have merit.
There exists no evidence that this program teaches students the fundamentals of math. Experts including mathematicians and math educators have set guidelines that are critical for elementary students to master. Investigations fails to meet these reasonable expectations. Yet, I have been repeatedly told by the central office and our principals that Investigations is the program our district adopted and it is here for the count.
Perhaps it is time for the BOE to “do the math” and revisit its decision to adopt Investigations. I believe it is irresponsible to “wait and see” with our students any further.
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As a Branford resident with a long interest in our school system, I have been following this column with interest, having just helped CT's SDE to make its Phase I Race to the Top application. The State of Connecticut has agreed to adopt common core national standards in math and English/language arts K-12 by August 2010. The Branford Board of Education and superintendent are signatories to that application. Perhaps it would be helpful to have someone from SDE come down and talk about the new national math standards before further action is taken. You can contact Dr. Mark McQuillan, Commissioner of Education, at -- [email protected]. Best. JMGruendel