Interactive Concept Development

I'm reading through the Overview and Implementation Guide for enVisionMath, by Scott Foresman-Addison Wesley (Texas). Because I am used to a traditional, instructivist curriculum, where the teacher guides the student step by step through the lesson, teaching algorithms to help students with knowledge and understanding, I just naturally have some concerns. So, how "new math", how "fuzzy math" is this math textbook?

(My principal stated, as she was giving me the materials, that there were many group activities for developing new concepts and I might want to look over them. Hmmm.)

Several things JUMP out at me.

On about every page so far: "Research says . . ." followed by an explanation of what enVisionMath provides. (There are lots of "Research says . . ." explanations.)

I notice that this seems to be TAKS (our Texas test) driven, and I see that all of the 20 topics are designed to be covered prior to the spring date for students' taking that test.

[One of my prior posts (Expectations Need to be Measurable and Concepts Need Time) referred to an article by William H. Schmidt, where he explains that "top-achieving countries" focus on fewer concepts so that teachers can cover them in depth, rather than the many (up to 20) that our country's math curriculum force teachers to cover.]

And I see that these 20 topics are covered in about 127 lessons (so they can be covered prior to the TAKS), some topics being covered in as few as 4 lessons. So some of the topics are small, bite-sized that hopefully are reinforced throughout the year. I hope there is built-in reinforcement. I'm hoping . . .

Uh-ohhh! Here it is! Interactive Learning

Research Says that students learn best when they have opportunities to interact with teachers and with other students. . . [Research says] Problem-based instruction (before making math concepts explicit) enhances learning because it gets students actively engaged in thinking about a problem and shows students that their thinking is valued.

Teachers are instructed to pose the problem, asking students to work in groups on a problem and share their thinking "before receiving teacher guidance that makes the math explicit".

Before making math concepts explicit ???

And I see lots of writing, writing to list and explain the steps you used, writing to explain what you and your partner decided to do to get the answer and why you chose that method.

Oh my!!!

And while these interactive groups are working, teachers are to be making sure that students are discussing what they are doing and that they are using the proper language and vocabulary in their discussions. How on earth can a teacher be listening to 10 pairs of students at one time to be sure they are using proper math language????

This is why teacher directed instruction is so important. When I teach (prior to the group practice) and when I make concepts explicit (prior to group practice), I can also make sure students practice explicit oral vocabulary (prior to group practice).

More later . . .

Group Discovery ???

One of the marks of "new math" is discovery learning. But it's more than just discovery learning; it's "group discovery learning". Students are expected to come to knowledge of mathematical facts and procedures through "communal discovery".

You've heard it before. Only what your child discovers himself will he really grasp and remember. He must "own it" to be able to "use it and truly know it".

Now, let me see. If we want everyone to make the discovery himself, why would we put them in a group? That is exactly the opposite way you have every person discovery on his own. The whole group discusses and comes to an action, tried and agreed upon by the group. (Of course, someone in the group had to make the suggestion, to begin with, but never mind that.)

Now, remember through all of this, the purpose is for each student to make the discovery for himself -- so he can "own" that knowledge.

If you're in a group, how can all students come to "discovery" -- of a math procedure -- at the exact same moment? Someone in the group will come to the discovery first. Must he or she remain absolutely quiet? Must he hide his procedure? Remember this is a group discovery.

So, if someone else in the group makes the discovery, I guess no one else ever gets to "own" anything! Be First or Lose Your Shot at It.

By the way, the teacher is very quietly staying to the side, offering no guidance. And once the answer is agreed upon, the teacher is not allowed to check to see that the procedures were used correctly. Later, no drill will be given for students to use for practice. And there is no memorization of facts -- the facts can be 'rediscovered" on the spot, whenever they are needed.

In a traditional classroom, a teacher gives students an opportunity for small discoveries throughout the lesson, but he or she carefully directs the lesson and teaches precise methods, so that all students learn the most efficient procedures. Then the students practice and practice the steps under the supervision of the teacher. Following the guided practice is the independent practice, during which kids do more practice. Teachers are available to guide students and reteach if necessary. It is during this practice that some students "discover" and learn. And as the procedures are practiced over the next days and weeks, still other students may finally make the discovery on their own. But that "discovery" is just as real as the "discovery" made earlier by other students. In the meantime, the student has been able to successfully get the proper answer on the work because the teacher had taught just that.

I disagree that there is no discovery in a traditional classroom. There is. I see it every day.

And I don't think that it is possible for all students in a new math room to "discover" every single fact and procedure without input from the teacher.