Remarkable Spreadsheets

Yes Spreadsheets really are remarkable. I say that because the project I reviewed could not have been done without the concept of spreadsheets and certainly the advent of spreadsheets for personal computers lends unimaginable power and numerous options to their use. The project was named “Graphing Our Throw Away Materials” and it is directed at 6th grade science classes who are studying conservation by looking at the amount of trash generated on a daily basis. The teacher had her classes do a “Throw Away Journal,” collecting data on the type and number of pieces of various materials that were being thrown away in their own homes. Once data was collected the students entered the data in spreadsheets and did an analysis of it using basic charts and statistical analysis. Finally they attempted to judge the accuracy of their conclusions relative to other classes and outside sources. The “main message was that there is a great deal we throw away.”

This 6th grade science project is a brilliant start on an 8th grade data analysis project in mathematics. The lesson would only need to be adapted in two ways. The first adjustment to be made is the actual measurement data that is being gathered. I would want to collect the data using a volume (cubic ft.) or weight measurement. Weight is probably more practical but in either case you are able to draw a broader set of statistical conclusions. By piece, as done in this project, compares equally a one pint plastic bottle with a two gallon plastic bleach bottle. Volume takes away much of that relativity (but not all).

The second change is not really a change but takes the project to another level. I would then ask the question, how can the students impact the results? We would then design an action plan for our homes and once implemented, students would go back and collect the data again. Now students can really contemplate the influence individual families can have on the big picture. From the mathematics point of view we now have volume data before and after implementation of an action plan and we can do an analysis using high level statistics such as confidence intervals, correlations, quartiles, trends and from that draw more in-depth conclusions.

Integrating math and science in this way is terrific and I applaud Ms. Wiedenfeld’s efforts. It was a job well done.

Netiquette for Our 8th Grade Classroom

http://docs.google.com/View?id=dp2f2p3_21dm6979cz

Jigsaw Your Mathematics

I have been reading a great deal recently about a collaborative learning technique called Jigsaw Classroom. Although it is not new to the classroom as such, the technique was originally developed in the early 1970’s as a tool whereby teachers in newly integrated schools could bridge the racial gap and transform negative classroom atmospheres stemming from intense competition when using traditional learning techniques. What was different about Jigsaw was the teamwork required in the learning activity that allowed individuals within assigned groups of 5 or 6 students, not to compete with one another, but rather work to research a common assigned theme or subject area with each student becoming an authority on a subtopic within the context of the larger topic and then presenting their findings as a presentation to their Jigsaw group.

The strategy as a whole has seen a great deal of success, but as so many times happens with good stuff that you would like to use effectively, there are challenges that present themselves which at the outset need to be overcome. The first rather obvious challenge for our classroom is the number of computer terminals available. We have only five computers and making use of Jigsaw Classroom will require us to develop a strategy that can successfully deal with that limitation. Secondly, there is an inherent challenge of adapting the concept of Jigsaw Classroom to the learning of mathematical topics and principles. Jigsaw Classroom has most often been used in subject areas other than mathematics.

In addressing the issue of computer resource limitations a potential solution would be to assign the use of all terminals to each of the subtopic groups for a designated period, allowing each student to contribute to the research gathering activity. A key advantage of this strategy would be the subtopic group’s ability to synergize individual research efforts and collaborate on establishing the significant aspects of their subtopic and options for effective presentation to their Jigsaw groups. Unfortunately this strategy is less advantageous if the time frame for all groups to complete the project is of insufficient length to allow for adequate research time for each subtopic group. In that case it may be necessary for one individual from each subtopic group to be assigned the online search responsibilities using a single terminal, while the remainder of the subtopic group reads and prepares analysis of the research. This would allow for each Jigsaw subtopic group to access a single terminal for research purposes.

As for implementing this technique within a math classroom, a little searching of my own rendered a number of tried and tested methods for applying the Jigsaw Classroom technique in mathematics. This included topics such as polynomial factoring, special segments of triangles and numeration systems. The methodology used in these examples to incorporate this collaborative technique could easily be applied to such topics as integer and number theory, fractional computations, statistical analysis and a variety of other mathematical learning avenues.

Next step, Jigsaw Your mathematics …