When it comes to equations with negative number of the letter, surely a strategy that is in line with the approach with positive numbers of the letter when it appears on both sides (ie collect the letters on the side where there are the most - incidentally, students observe that 0a is greater than -a, so it works whether there are letters on both sides of the equation or not). eg with 5 - 2a = 17
add 2a to both sides and subtract 17 from both sides - gives 2a = -12, so a = -6. This also avoids the need towards the end, to divide by a negative. Just a thought!
Craig - That and other similar questions are called epistemic questions based on the idea of epistemic actions. Stellan Ohlsson (1995) contended that for optimal learning, a learning design should be created around certain learning activities that he calls epistemic tasks. These are tasks that are meant to stimulate the learner to describe, explain, predict, argue, critique, explicate and/or define. Learning is expected to be maximised as a result of organising knowledge and engaging students in these learning activities.
When it comes to equations with negative number of the letter, surely a strategy that is in line with the approach with positive numbers of the letter when it appears on both sides (ie collect the letters on the side where there are the most - incidentally, students observe that 0a is greater than -a, so it works whether there are letters on both sides of the equation or not). eg with 5 - 2a = 17
add 2a to both sides and subtract 17 from both sides - gives 2a = -12, so a = -6. This also avoids the need towards the end, to divide by a negative. Just a thought!
Craig - That and other similar questions are called epistemic questions based on the idea of epistemic actions. Stellan Ohlsson (1995) contended that for optimal learning, a learning design should be created around certain learning activities that he calls epistemic tasks. These are tasks that are meant to stimulate the learner to describe, explain, predict, argue, critique, explicate and/or define. Learning is expected to be maximised as a result of organising knowledge and engaging students in these learning activities.
I often use it also to describe three specific types of feedback to students: directive, corrective, and epistemic. https://3starlearningexperiences.wordpress.com/2018/06/05/no-feedback-no-learning/
Love it, thanks Paul! Hope all's well with you