Support material for Step 2 Tutorial

## Table format for analysing steps you go through in order to complete the challenge

 Steps Knowledge and understandings and processes students are expected to use (from prior knowledge) knowledge and understandings needing to be taught Skills or processes needing to be taught Thinking skills needing to be used or taught Where will they likely get stuck

As your students work through the task they will each be at very different points. This table will help you keep track of students' progress (where they are in the cycle) and to understand individual student needs at different points. It will help you understand where to 'pause' in the process to teach or revise a skill or understanding needed before moving on.

## Example of working through the analysis table from "Sweet Maths Challenge" (more details of this task here)

 Steps expected from students (eventually) Knowledge and understandings and processes students are expected to use (from prior knowledge) knowledge and understandings needing to be taught Skills or processes needing to be taught Thinking skills needing to be used or taught Where will they likely get stuck look at the container - write down all the 2D shapes 2D shape recognition; circles, semicircles, rectangles, squares, etc. write down all the 3D shapes 3D shape recognition; spheres, cuboids, cones, hemispheres, cones, partial cones recognition find/recall the formulae for each shape recall new conical sections formulae find volume of one sweet if it's a regular 3D shape then easy (use formula)    -finding the average diameter of a sphere using various methods; e.g. 1 - volume of a small irregular shape (science curriculum link) by displacement of water find empty space (between sweets) ?? ?? modelling using available materials or on paper? HERE!

# Step 3 guides you in HOW to reflect on the algorithm created in step 2

• Function of Step 3 for learners: change learner’s attitude from being afraid to fail  and pin point their mistake and to go through the algorithm, tools and the process to identify the strong and weak points in them.
• Function of Step 3 guide for teachers:  change the attitude from telling the student the answer to  being a guide in their reflecting on their learning process.

Step 3 is divided into three SUB-STEPS which are described below.

## SUB-STEP 3.1. Look closely at where exactly the algorithm stopped working

 Focus on the overall algorithm. One way to check its effectiveness is to allow another learner to use it and see whether they arrive at the same result i. e. they manage to complete the task or the problem set out in step 1 of the thinking task framework.  I want to know more...

## SUB-STEP 3.2. Find whether the model/s used to build the algorithm appropriate

 The  model/s did not have the desired function. In other words, the models were “random” or “out of context”

## SUB-STEP 3.3  What is the purpose of the entire exercise of moving through the thinking task framework?

in progress

I want to know more

# I want to know more...

## SUB-STEP 3.1. What was the exact point (at which step) did the algorithm fail?

• Function: change the algorithm from being ineffective in completing the task to being effective in completing the task
• Outcome: Point out specific points in the algorithm that were not so useful in completing the task
 This step is to analyse what occurred in the previous steps of the algorithm. It would be helpful to remember at this point that an algorithm could be viewed as a set of instructions that could be used by someone else (i.e. another student at more or less the same stage of learning as the creator of the algorithm)so that he can follow it and come to the same conclusions or outcome.

Possible procedure:

In order to figure out where the algorithm stopped working, attempting to answer some of these questions might be helpful

•   Does the algorithm (built in step 2) work to do the task set out in step 1? Find where it works and why. If it does not work or the task can not be completed using the algorithm, then why it does not.
•  If  the algorithm work in doing the specific task set out in step 1, does it still work if extended to  ALL of the generic problems? Start checking from the actual task to other similar or generic tasks.
•   Reflection here involves testing the algorithm to see whether it works in only some or all of the extended tasks.

## SUB-STEP 3.2. Which model/s were used and why

• Function:change the models used to build the algorithm from being less appropriate in building a good algorithm to being more appropriate and effective in building a good algorithm
•  Outcome:  Increase the efficiency of using thinking models for building algorithms
 There are various models that are available, the ENV, contradiction, multi screen etc. that maybe used as tools in the overall application of the thinking framework. Even other models outside the framework could be used if they are deemed more effective. One of the challenges in building a good algorithm is to use the correct model. Sometimes there might be a need to look for a combination of models i.e. bring in more than one model to build the algorithm. However, in the beginning at least using just one model to build the algorithm will enable you and your students to get a better understanding both of the model/s as well as their applicability. The ENV model is perhaps a good one to begin with, its simple and is applicable in a wide range of problem solving tasks. However it is important to be aware that there are limitations in using this or other models.

Possible procedure:

• Learn something new about the models; look at examples of models used in a few proven effective algorithms amybe in other subject groups
• Looking critically at step 2. Were the models  used correctly? For example you were using the ENV model (a thinking tool) ....now, go back and check, did you focus on:

(1) the correct parameters?

(2) maybe you should have focussed on the values instead?

(3) or even whether you were using it to work out the parameters and values of the same element?!!

Support resources:

## SUB-STEP 3.3 Understand the context in which the thinking task framework has been used

• Function: change the process involved in steps 1 and 2 from out of context to bring it closer to context…..
• Outcome: To have a clear understanding of whether to go back to step 1 or to go back to step 2
 How does it sit in the super system......a quiet reflection definitely on the part of the teacher, eventually on the part of the student as well. At this point you need to review the original aim of why you had set out the task in step 1 as well as algorithm that emerged in step 2 and visualise it in the larger context of the super system. While working on the level of the super system a series of tasks were set out, all meant to achieve the overall aim or context both of curriculum content as well as the thinking skills framework. Aims: an overview

Possible procedure:

• the function of the algorithm is to have steps that help in solving the task in step 1. If this function is fulfilled, you would have said “yes” to the question above
• In that case you are ready (as a learner) for a higher challenge, or if you are the teacher, you are ready to go back to step one and get busy snatching the fish away! You need to devise a more challenging task for your students  make sure this algorithm will fail for the new task, or it will need some more criterion to be added to make it work.
• Both of the above points in the reflection process take you back to the first step. However, it is important to keep in mind that if you have identified flaws in the algorithm, go back and change the algorithm (step 2) or if you identified that the models were used incorrectly, go back to step 2 to change these.

Support resources:

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