There are times when I wonder, 'what have we been doing for the last two weeks?' My year tens are at this stage right now. We've been going through linear algebra for two weeks and it's clearly beyond a good dose of my students.
There are a number of issues:
a) They have weak self esteem and give up before trying
b) They have a low work ethic
c) Their algebra skills are weak-non existent (transposing to find c in y=mx+c is heartbreaking)
d) Their operations are weak (explaining gradient in terms of rise/run leads to all sorts of issues)
e) Their understanding of negative numbers is suspect
So I have two choices, teach them the topic and hope that the students get something from it to help them on their next iteration of learning or try and fill the gaps that 9 teachers before me have tried to fill with limited success.
Current thinking would say cater to individual differences and backtrack. I'm not sure that this is the right thing to do. By teaching the topic it gives the students an opportunity to 'get the gist' of what is being achieved (associate linear algebra with lines and equations, learn about gradient and slope, be able to find the y intercept and the like) and then hope that when they do 1B or 2A next year they can use this knowledge to properly participate in class.
I don't know.
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