Thursday, February 22, 2007

Another Response to a DI Proponent

The following is another reply to a highly knowledgeable proponent of the Direct Instruction program in Joanne Jacobs' ongoing discussion 'Teachers Wonder About Direct Instruction'. Mr. DeRosa has systematically countered my arguments for a more balanced view of pedagogy, allowing teachers to adapt and modify approaches for their students. I have made it clear that I see the value of the DI program for many children, but not all. I will continue to advocate for some flexibility in methodology, however, I will not bend on the issue of standardized math content. I'm sure some readers are tiring of this and were hoping to see some more Problems of the Day. Don't worry - they're coming!

More ‘bang for your buck’ is an expression that would definitely ring true for central school administrators and board members who often relate to the ‘business model’ of education and for whom the ‘bottom line’ is maximizing district scores at minimum cost to the taxpayers. From that perspective, adding a column of 15’s may be a ‘waste of time.’ From the perspective of math educators and mathematicians like Liping Ma who has called for a more ‘profound understanding of fundamental mathematics’ the following scenarios may not be:
One child who didn’t recognize 15 x 10 = 150, explained that she added up the 5’s to get 50, then moved her finger to the next column and counted on by 10’s: 60-70-80-90-…-150. Ken, you might argue that’s the result of not learning her skills well enough and you may be right. A different view is that she demonstrated an understanding of place value that many 4th graders do not have. Actually, I will never convince you of that! Another child for some reason, said that he counted by 15’s up to 75 and then doubled it to get 150. What an inefficient method and waste of time, right? Another student demonstrated his understanding of place value and emerging sense of the distributive property by explaining that ten 10’s = 100, ten 5’s = 50, then added the sums. Several students just visualized the standard algorithm in their minds, getting 50 in the one’s column, pictured writing the zero and carrying the five to the next column, counting 5-6-7-8…-15.
About 7 of the 20 students multiplied 15 x 10. Guess that class wasn’t trained properly, right? I do not believe in having these kinds of dialogues every day for 15 minutes! I do believe that when students see other ways of approaching a question, their understanding deepens. Certainly, some children will be confused by being shown alternate methods and these students need to be shown one straightforward approach in the clearest possible manner. But this is not true for all students. Let me share a dialogue I had with one of the SAT students I taught last night. Won has been in this country for about a year and he is clearly an outstanding problem-solver with very strong skills (and he expresses himself in English surprisingly well). After reviewing a challenging problem asking for the least value of y satisfying some inequality involving 2 variables, Won raised his hand and showed us a much simpler method: “Just make x and y equal”, etc… I asked Won if his teachers in Seoul allow students to discuss different ways of solving a problem and he just smiled at me and said, “No, they tell us how to do it.” Guess that supports a more direct model, right? I asked Won how he felt about following the teacher’s method and he replied, “Oh, I usually did it my way anyway and he only checked my final answer, so it was ok.” Is Won merely the exception to the rule and he’ll learn math despite the methodology. Let me guess what you might say!

One of my daughters who is a regular and special education elementary teacher told me that several years ago she taught from a scripted program for reading and spelling for a special population of children. She expressed that these children absolutely learned with this program provided the teacher strictly adhered to it. She felt confined by it but recognized its value. However, she noticed htat some children soon became bored and were able to move at a faster pace but that she couldn’t simply give them more advanced materials to work on their own nor could she move this subgroup to another class. Yes, Ken, this is an implementation problem, but probably not uncommon. Here’s how she put it to me: Dad, for children who come to us one or more years behind, this type of program helps them to catch up and that’s really good. She also said that many children may only be able to learn in this kind of structured environment, but she did not feel that it was appropriate for other children and, in fact, she thought that one of her goals was to prepare her students to move into the ‘mainstream.’ Just one point of view.
No matter how I argue my points, I know you will have a counter-argument because of your intimate knowledge of DI and because you have seen it work. I can’t argue those results. But statistics often don’t tell the whole story and everyone knows how we can prove almost anything we want by by how we present the data and by the assessments we use. I looked at the 5th grade posttest and, while I was impressed with some of the required skills, I saw questions that used some models and terminology that are non-standard and inherent to the program. I also did not see too many questions that got at assessing conceptual understanding or applying the skills in other contexts. I may not have seen enough to form a real judgment however.



Dickey45 said...


That is why we are in a pickle as to how to create standards that lead to assessments. The standards and curriculum are very much a part of each other. If a state (such as Oregon) has very developmental/experiential/discovery based standards, then they will pick curriculum such as Everyday math. If the state has standards that are traditional, then they will use curriculum such as Saxon or Singapore or Connecting Math Concepts by SRA (not to be mistaken with Connected Math).

In my opinion, it's all in the standards, baby.

Dave Marain said...

oh you are so right! now disband all of the committees of experts, start over again with a group of non-extremists who can make a reasoned judgment based on a world-class curriculum. dickey45, i'll bet you could decide what mathematics children need! Some individual has to take charge and end these 'wars' and make a decision. Get on with it and get over it. Who are the real victims in this war?
In the absence of clearly defined goals and in the absence of statements of mastery of a basic fund of knowledge by NCTM, there has been an extreme backlash. This needs to be repaired ASAP by those who see the benefits of both sides and who understand what underlying skills and principles must be stressed at each grade level. Let's form a National Math Teacher Panel. You want to be CEO?

KDeRosa said...

Who are the real victims in this war?

These students.

I'll bet you could decide what mathematics children need

The mathematics they need are the skills to solve college level problems like this.

The math skills needed to solve this problem are the math skills that will be repeatedly called upon for any student wishing to pursue a career in a math/science/engineering field.

The problem requires nothing more than the application of high school level math and the distance formula. There's no time to reteach these skills in college. The student must know them well enough by the end of high school to apply them to solve problems.

It is the responsibility of K-12 schools to get their students to this level. It is as simple as that.

Dave Marain said...

It is my responsibility to deliver the curriculum I was hired to teach. Since there is considerable diagreement about what skills and concepts should be covered in each course this becomes problematic at best. Every year, Rutgers University hosts a "Good Ideas in Teaching Precalculus" workshop in March. Every year, teachers continue to argue about what topics should be included in this curriculum. What's wrong with this picture! Despite your comments, there is still no general consensus that the role of the math teachers is to deliver a technical curriculum to prepare students to solve engineering and physics problems, if I caught your drift. There is still a pure theoretical side to mathematics that has a place in our instruction as well. Some of the greatest discoveries in math came from the theoretical mathematicians who didn't give a **** about whether their theories about abelian groups had any practical value. Turns out they did...
This is not a black and white proble,m but it is one we must grapple with and resolve.