Linear velocity day one


Last week the class found that mass varied linearly with respect to volume for a bar of soap. This week the students were asked to sketch what a graph of time versus distance would be for an object moving at a constant velocity starting at time zero, distance zero.


The intent was to informally assess one aspect of quantitative reasoning, of the ability to think mathematically. The students have had twelve plus years of mathematics, can they think in the mathematical language? Instead of "Graph the following coordinates" the question of "What shape will an object moving at an unchanging speed make on a time versus distance graph?" 



More than one student did have a variation of a linear relationship.


Some students were further away from a linear function. 

Curves were a common feature.


There were perhaps five or six linear solutions. There were at least an equal number of blank graphs. The students with blank graphs explained that they did not know what the graph would look like, they could not even guess. 


The traditional mathematics curriculum does not teach students how to think mathematically. Curriculum reform movements such as common core, early algebra, and algebra for all have not produced students who think quantitatively, let alone feel competent in mathematics or enjoy mathematics. The two common sentiments expressed by students is one, "I am not good in mathematics" and two, "I don't like mathematics." A dozen years of math and the result is students who do not like mathematics and do not believe that they can do mathematics. Contrast that to the excitement of kindergarten students in shouting out numbers. No one is born disliking mathematics or thinking that they cannot do mathematics. It takes teachers to accomplish that. 

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