Lev Vygotsky’s work has become the foundation of Social Development Theory, and a great deal of recent research and theory in cognitive development has emerged from his idea that children have a zone of proximal development, the area where they will next develop; what is in the zone of proximal development will become the next, actual development in learning at some time in the near future. If we want to teach children, then we must determine where their zone of proximal development is located in order to provide them with the next learning they need.
My MAP tests put my student group in the mathematical fourth grade on average, but my quiz came from a seventh grade textbook, chosen for its “rigor” by our Assistant Superintendent.
The problem with today’s math “quiz” can be seen in the above pictures. Is the quiz extraordinarily difficult? For the average seventh grader, definitely not. I might note that the “mean absolute deviation” or MAD requested in the above picture is not the old familiar mean average, but the mean of the deviations from the mean by the values in the data set. Those MAD problems are more long than hard. I regard this test as entirely doable. My kids need more time, though — time to get ready for this quiz and time to finish the quiz.
Students came in at lunch to try to finish. They stayed a few minutes after lunch. No one got through that test. I want to give them high praise for continuing to tackle the material even if demands for my help kept coming from all sides. Most of them did not toss up their hands. In the real world, though, future teachers probably will not be answering questions like, “How do you do this?” during a test. (Maybe I’m wrong. I never used to do anything like this, but the tests became so unfair at a certain point that I no longer saw a just alternative.) I did not do the problems for them, but I did provide instructions at various critical points.
A coworker plans to throw out some questions. We’re not supposed to do that, but I intend to throw out the end of the test and I intend to curve the cursed thing. Some creative, differential grading is about to come into play.
Try to imagine tackling this beast if you are operating at a third grade level or lower mathematically: If the average puts the kids in the fourth grade, some are lower than that average. Add on on a language barrier, not too badly taxed by this particular exam, and a number of my students were struggling but managing, while others were painfully lost. Those lost students need remedial math, far more remedial math than they can receive while I am frantically trying to teach them all the above material in around six days of class time — the total amount of time that was available for this unit.
All our shackled math classes must travel together, so now I must move on to probability, even if every teaching instinct tells me I have to reteach the material above. If I reteach, though, what chance do we have to be ready for the required probability test? Probability might be a win for us, too. Kids relate to card games and dice. This island of math is more likely to be in my students’ zone of proximate development than most of what we have seen this year.
We could use a win.