This was the first show for Teaching Mathematics and what a lot of fun!
I interviewed Robyn Clark Rajab about teaching algebraic functions to Grade 10s. We spoke a lot about how to teach learners to plot and analyse the functions. I personally had a mind shift when we spoke about the effects ‘a’ and ‘q’ have on each function.
Robyn’s 3 pressure points for this section were:
- The learners need to identify, by the equation, or the graph WHICH type of function they are dealing with. I have seen far too many learners confusing an exponential function with a hyperbolic function. If this happens, the learner will run into problems from the start.
- The second pressure point relates to the first one in that the learners need to know what the values of “a” and “q” do to each function.
- The third pressure points relates to “q”. In some graphs, this can be used to indicate the y-intercept, and in some graphs, it is used to indicate the asymptote. Some learners will automatically use “q” for the intercept, as many teachers teach this as a short-cut in linear functions and quadratic functions.
Robyn’s 5 point teaching strategy for this section was:
- Firstly give the learners the parent function in each case, and then get the learners to plot the function, point-by-point.This gives the learners a procedural understanding of how the graph/table behaves. This is important because learners will be able to see what kind of shape each equation makes when plotting it onto the Cartesian Plane
- When the learners know what each parent function looks like, it will be good to go into the characteristics of each function by varying each characteristic. I would recommend starting with the “q” value. This would show vertical shift in each graph.
- I would then recommend varying the “a” value in each function. This will enable learners to see the effect of “a” on each function. Remember that the graph will do different things depending on the magnitude and the sign of “a”. For example, in linear functions, the variation of “a” shows the steepness on the graph. The sign of “a” can also show whether the linear graph is going “uphill” or “downhill”
- Once the learner has a conception of the shape of the graph, and the effects of “a” and “q” on the graphs, they will be ready to work with different types of problems on functions. The teacher will also be able to remind learners about some things which have been learned previously, such as the substitution of a coordinate into the correct place in an equation.
- The teacher can then go on to problems which require a more holistic conception of the graph, such as reflections about the x and y axes.
In the show, I showed three Mindset Learn Xtra lessons that can be used in teaching this section These can be found here:
Links that may help you in teaching this section:
Everything Maths Grade 10 textbook chapter on Functions: https://everythingmaths.co.za/grade-10/05-functions
This website explains the concept of a function: http://www.mathisfun.com/sets/function.html
Another easy to understand way of explaining functions: http://www.wmueller.com/precalculus/functions/1.html
More insight on mapping diagrams: http://www.sparknotes.com/math/algebra2/functions/section1.rhtml
A useful site to explore tables and graphs: http://arb.nzcer.org.nz/supportmaterials/tables.php
A fun, exciting way to learn about functions: http://www.mathwarehouse.com/algebra/relation/math-function.php
An explanation and exploration of linear functions: http://www.algebra-class.com/linear-functions.html
Quadratic functions explained and explored in a note: http://library.thinkquest.org/20991/alg2/quad2.html
A note on the parent quadratic function: http://math.about.com/od/function1/ss/Parent-Functions_3.htm
A video on functional notation:http://www.brightstorm.com/math/algebra/graphs-and-functions/function-notation/
A slide show on the parent graph of the exponential function: http://www.slideshare.net/VLB10525/parent-functions-presentation
A note on the parent function of an exponential function: http://www.purplemath.com/modules/expofcns.htm
A video on the exponential function: http://www.onlinemathlearning.com/graphing-exponential-functions.html
A slide show that facilitates a translation activity with a linear function: http://www.slideshare.net/ctorres2/translations-of-linear-functions-5534236
Step by step lesson on how to transform linear functions: http://www.mathops.com/free/a1lf001.php
Step by step instructions on plotting linear equations: http://www.purplemath.com/modules/graphlin.htm
Step by step instructions on plotting quadratic functions: http://www.purplemath.com/modules/grphquad.htm
Step by step instructions on plotting exponential functions: http://www.purplemath.com/modules/graphexp2.htm
An online graphing tool: http://www.mathsisfun.com/data/function-grapher.php
A video clip on interpreting graphs and function notation: http://www.youtube.com/watch?v=lc0Bm4tX4ZU
Until next time, have fun teaching!