More About MathLabs

The concept of MathLabs is intended as a mathematics learning enhancement program for elementary schools. It is hoped that the notion will be understood and implemented in this spirit. It is worthwhile, therefore, to elaborate a little regarding some aspects of this potentially powerful idea. The opinions represented here are strictly those of the website’s author, and they are grounded in his having been so directly and long engaged in what is described.

The IIT SMILE Program (see the page About the Author) began in 1986 and was quite an extensive teacher development program for its time. Within the course of its run (roughly through about 2001) it seemed that teacher development programs were springing up everywhere. Such programs featured or emphasized everything from cooperative (collaborative) methods to inquiry learning and concept map techniques. Likely, anyone involved with one of these programs would admit to a common concern: How could they get the program participants to actually use any of these techniques in their own classes or at their own schools? Indeed, most such programs eventually altered their criteria for formal “completion” (which might then be used for various teacher advancement or salary “credits”, … CPDUs and the like) to involve some sort of evidence of actual implementation.

In truth, teachers don’t like changing what they do, especially when what they do fits in with their own personalities. It could take years of attempting a new pedagogical method before a teacher feels comfortable with it. (And you can rest assured new theories would have transplanted the former methods by then anyway!) The author recalls a seminar about cooperative learning in which the presenters explained that, “This isn’t easy; it took us eight years to get it right.” Well, think about the damage that teachers could do to a curriculum while they attempt to get comfortable with some new methodology. So, in general, teachers are rightly reluctant to adopt new pedagogies. Sadly, this is one reason why many teachers are now having directives imposed upon them: You will use collaborative learning! You will use a particular software program! You will make a website! You will bring students to the board! You will use clickers! You will do this and you will that. But this is very bad for education. Teaching mathematics is primarily about teaching content and concepts. The instructional methods should be determined mostly by the teachers themselves, not imposed upon them from on high.

By contrast, the essence of MathLabs is that (a) they are school-provided activities as opposed to activities that individual teachers provide. Moreover, (b) they are meant to be done entirely apart from the ordinary classroom time and space devoted to the grade level mathematics curriculum. Thus, these activities can only add to the students’ motivation and understanding; they cannot possibly detract from the grade level curriculum. Again (cf., the Home page), it takes neither a three-ring binder nor a seminar to define a MathLab. It takes only these few lines:

A MathLab is a learning activity, typically performed by students working in teams, for which the following three (Q/R/V) aspects occur:

  • Q (Question): a real world question is posed by the teacher,
  • R (Resolution): the resolution of the question involves the use of mathematics,
  • V (Verification): and the result can be verified by empirical means.

That’s all. Anything else, such as lab reports, assignments, assessments, discussions about such things as approximations, rounding, error analysis, ideas for variations or improvements, etc. are entirely up to the teachers and the schools.

This educational enhancement must be driven by both teachers and administrators. Clearly, “school-provided” means teachers-driven (emphasis on the plural). However, the administration must assist. Only the administration can either elongate the school day (five minutes a day would more than exceed the time needed) or sponsor the activities before or after school hours, or on weekends. MathLabs are not meant to be a regular (e.g., weekly or monthly) math curriculum activity. For example, if it is believed that only ten MathLabs have value, then do two in 6th grade, and four in each of grades 7 and 8; or, perhaps two in each of grades 4 through 8. If some sixteen to twenty MathLabs have value, then spread them out over a number of grades, likely not more than four per grade. Think about it: Adding just five minutes to the school day would provide, every 24 school days, a two-hour time slot for a MathLab per grade!

It should be noted that the idea of a “longer school day” has become the latest school reform controversy in such places as Chicago. Not surprisingly, the teachers have countered with two important questions: “How much more money are we going to get?” and “What are we going to do with all this extra time?” Well, MathLabs might help with the latter.

Moreover, only the administration can provide the resources—namely, location and cost—for MathLabs. Clearly, these activities might be performed in hallways, gymnasiums, auditoriums, or in various outside locations, or at remote (field trip) locations. Most importantly, a whole repertoire of materials must be obtained and secured by the administration. A review of the MathLabs listed in this site would reveal the need for such things as plenty of cardboard, string, rope, tape, coins, plastic containers of various shapes and sizes, water, Lego® Bricks, Post-It® Notes, beads of various colors, electronic scales, battery operated cars, meter sticks, various weights, graduated cylinders, etc.

But, primarily it will be the teachers who conceive, design, rehearse, and coordinate the actual student performance of each MathLab. It is believed that, over time, creative teachers worldwide would devise enough quality MathLabs to provide for the schools that wish to embrace such activities.

Two cautionary points are worth mentioning.

1. Never attempt any one of these activities without having fully performed it (i.e., rehearsed it) apart from the students. Murphy’s Law is in effect: If something can go wrong, it will. A teacher might be surprised how easy it is for water, beads, coins, etc. to end up all over folks and floor! Moreover, you do not want to discover, in front of the students, that an activity doesn’t work because you didn’t think of something. Truly, the devil is in the details. Like a trial lawyer who never asks a question without first knowing the answer, you should never perform a MathLab without first knowing exactly what will happen.

2. Try to stay with the threefold Q/R/V (Question/Resolution/Verification) criteria as defined here for a good MathLab. Such activities do not come easily, especially because of that third criterion, the empirical verification. That is why it is so important to share good MathLabs with each other via sites such as this. Unquestionably, should the idea of MathLabs catch on, certain teachers and administrators will want to use the allotted time and space to do other kinds of mathematics learning activities that are hands-on, real-world, collaborative, etc. Yes, some such activities will have great value, but the fear is that the available time and resources might just become an extension of classroom learning which, from the student perspective, often inspires the same old question, “Why do we need this?” The most important purpose of MathLabs is to impress upon the student the belief that we really do (R) use mathematics to (Q) answer real world questions (V) correctly! Try not to stray from that important motivational objective. Again, Q/R/V is not easy to achieve. That is why we need to help each other in the search for quality Q/R/V MathLabs.

Collaborative School Activities for the Teaching and Learning of Mathematics