What's worked for you in the past?
I use visual models to illustrate the concrete. I also incorporate writing when students write something algebraically or graphically. For example, we write "number tricks" to create and solve equations. So for an equation like -2x +5 = 21 Students would write the steps show the written meaning next to the algebraic expression: Choose a number. (x), Multiply by -2. (-2x). Add 5. (-2x +5) The result is 21. (-2x +5 = 21).Then students can backtrack starting with the last clue and use inverse operations. My result is 21 (-2x +5 = 21) . Subtract 5 (-2x +5 -5 = 21 -5 ). Divide by -2 (-2x /-2 = 16/-2). My chosen number was 8 (x = -8). When it comes to functions, we usually write what the function notation means. For example f(x) = 3x -10. When we input the value for x, multiply it by 3 , and sibtract 10, we will get the output called f(x).
What do your students find the most difficult?
Recursive function notation and what it actually means. They get intimidated with all of the notation, although they are capable of doing the math. Often times we have to orally dictate what the symbols mean. So I make word cards (inout, out put, previous input, given, base case) to hover above the symbols to help in comprehension.
How do you think programming can help with this transition?
I think programming will be an interesting test of how students apply functions to the real world and what questions they will have when the programming language differs from the mathematical reasoning they were taughts regarding functions (like the example at the end of the video).