Strategy: Visual-Aided Mathematical Strategy (Using Computer-based images)

Article: Diezmann C., Lowrie T., Sugars L., Logan T. (2009) Visual side to Numeracy: Student’s Sensemaking with Graphics. APMC 14(1), 17-19

Callow J. (2005) Literacy and the Visual: Broadening our vision

Vacca J. L., Vacca R. T., Gove M. K., Burkey L. C., Lenhart L. A., & McKeon M. A. (2012). Reading & Learning to Read

Description of Strategy:The main concept behind this exercise is to demonstrate the usefulness of a technique often re-used in Mathematics. The presentation comes in the form of a multimedia approach through computer pixelated images. The aim is to have these images supplement the lesson being taught about transposing. The images will be shown one after the other, demonstrating the step-by-step progress of transposing (changing subject of formulae) and how this might be applicable to other subject areas such as chemistry, physics and business subjects.

1. The teacher may start by using these images to provide an explanation of the term transposing. The image also presents the term changing subject of the formula. The following image demonstrates that transposing, is in fact changing the subject of the formula, hence, writing the literal equation stating that transposing = changing the subject of the formula.

2. Following the previous demonstration via images, teachers may continue the explanation. The teacher continues guiding with an oral and literal explanation of shot-by-shot images. As the example in the images indicates, we are exploring how to go about finding the width (w) of a rectangle, given the Area (A) and the length (l) of the figure. This process helps both the teacher and student identify the Do’s and Don’ts of solving equations.

3. The teacher will provide further demonstrations on how to overcome mistakes, pitfalls and miscalculations while trying to place unknowns to the left, and knowns to the right of the equal sign in the equation. The images below represent a follow-up of previous explanations, detailing the care that must be taken in remembering the correct placements of symbols.

Application to a Subject Area: Mathematics, Physics, Chemistry:

As mentioned in the beginning of the strategy description, this is a process repeated in several mathematics based subjects. This principle is used to identify the correct proportion to achieve the same effect due to an increase in one element. This speaks to both physics and chemistry, which is especially and heavily dependent on a student’s ability to correctly transpose elements of an equation.

The teacher should explore the possibilities of when transposing is used in other subjects. This will provide students with enough schemata, to approach physics and chemistry or other subjects dependent on this technique with greater confidence. The students can be given assignments on a 4-week basis, to determine if the practice had a positive effect on their retention skills. Each assignment should increment in difficulty, so as to avoid overwhelming students with voluminous equations.

This system can easily be monitored by assignment submissions, where the emphasis is placed on ensuring every student masters at the very least 80% of each exercise. This score should prove to be satisfactory as you would take into consideration miscalculations resulting from human error. Each week could consist of (a) Transposing with Minus and Plus Signs, (b) Transposing with Divide Signs and Product Signs, (c) Transposing with Squares and Square Roots, then lastly (d) Transposing with (a), (b) and (c) in combination.

The images below represent the importance of demonstrating other ways in which transposing is used in Mathematics. The purpose of finding the Rate when given the Interest in Simple or Compound Interest where both equations are dependent on skillful and correct manipulations of the symbols. Therefore, 100 I = PRT, I = PRT / 100 and A = P (1 + r/ n) ^ n.

Benefits of Visual-Aided Mathematical Strategy (New Literacy Approach):Students should learn and be able to demonstrate the importance of this technique. The aim is to

provide opportunities for students to see when and where these techniques would be useful. This method will help students develop a sense of self-monitoring to determine when they have found the correct answer. The student who is carefully instructed by a teacher to view Mathematics from this perspective will be better able to make sense of abstract concepts.

The hope is that students will be able to see this as more than an exercise in just Mathematics class. The idea is to widen their perspective to other areas where this same method (transposing) is used. This principle can also be helpful in literacy instruction, as they will see why the term Highest Common Factor makes sense. The term common refers to an object present in two places. The term highest refers to the largest number of factors present in the two places, hence, the term Highest Common Factor. The definitions and behaviours will make more sense, as the teacher explores these multiple meanings.

Drawbacks of Visual-Aided Mathematical Strategy (New Literacy Approach):The ultimate drawback is that, some students may need additional practice or other methods to

make the lesson more apparent to them. There might be a need to create your own videos of demonstrating the method, or referring students to Youtube channels showing the same or alternative methods of this technique. The truth is each student is an individual thus each of them will learn in different ways.

In this case, it might be helpful to have these students choose an alternative method of presenting or participating in the class-activity. The students may also be encouraged by the teacher, to participate in a discussion to determine whether or not this technique is absolutely necessary in mathematics. These discussions could provide further insight for students as they explore with the teacher whether or not the findings are either True or False.

Modifications:1. Find other interactive methods whether by animation or otherwise to engage students in

mastering transposing.

2. Develop mathematic game activities than can involve all students to break up the monotony of pure traditional instruction.

3. Encourage students to create their own math-based games to share with the class if possible. The other option would be to share one of your own involving the method being used in class.

Keywords: new literacy, prompt, visual aided method, literacy instruction