This week we have been involved as a class in a Using and Aplying Mathematics unit, to consolidate our use of vocabulary relating to the properties of 2d shape. At the same time I wanted to embed and develop key skills from the ICT curriculum through the use of a Branching data base. The tool I chose to use for this series of tasks comes from Softease Studio, and is called Branch.
The sessions began however, not with Branch, but with a drag and drop sorting tool I had made using Smart Notebook. Other whiteboard users could make something similar, and an image of the tool is presented to the left for reference. The key to making and using Branching Data bases, binary trees or "dichotomous keys" is an ability to generate, ask and use "null" questions to divide a set of objects into two sets initially, gradually refining questions to distill the set until the branches at the end of the tree have only one object. This involves asking questions that have "yes or no" answers. This is process I have found easiest to develop using the observable features and properties of sets or collections of familiar objects. We often use Carrol Diagrams and Venn diagrams to do this, and the whiteboard tool I used as an introductory frame to support student and teacher discussion around this process before engaging with Branch itself, was designed to act as a link between these tools.
Since our task had a mathematical focus, we began with the shapes to the left of the book engaging the children in paired discussions around questions such as
- What can you see?
- What is Special about this shape?
- How is this shape different to or the same as this shape?
"It has four sides and four corners, all of the corners are right angles."
A great set of reponses describing the properties of a rectangle, however in our set we had two rectangles, a square and an oblong. Developing this we began to use the sorting tree model above dragging the two rectangles to the top of the simple tree, and asking the students to propose questions that focussed how they were different. Is it a rectangle ? Or does it have right angles? don't work since both shapes have right angles and by defintition are both rectangles. Are all the sides the same length? Provides a yes or no answer and allows the two shape to be separated.
We used the notebook to practice this idea together, comparing a number of shapes from our collection and then, testing our questions to see if they worked. The children were then introduced to branch and starting with only two shapes each time initially were were encouraged to make a series of trees practicing and rehearsing their questions together.
During follow up sessions the idea of working with 4 shapes was introduced and the children challenged to devise questions that would begin by dividing their shapes into two equal sets. This sounds easier than it is. Eg I have a square, an oblong a triangle and a pentagon. A good starting question might be does the shape have right angles? Does the shape have 4 sides? And because of our previous activity the children suggested these? From here the next question was also fairly straightforward for them based on the practice sessions of small trees the day before. However what happens if we drag a circle, a triangle, a square and a pentagon into the tree? Is it curved? Does it have three sides? Although having yes or no answers don't work in relation to the challenge question set at the beginning of the session. What is needed is to ask a question such as does the shape have "more" or "less" than x numbber of sides/corners/angles? The students were then encouraged to use Branch to explore these ideas, Before during our final session requiring the children to begin with 8 given shapes to design a game for their friends to play and test out.
The children really enjoyed this series of tasks, which challenged their thinking and enabled them through paired discussion to use and apply vocabulary developed in previous classroom based sessions to a decision making process. The UK Primary Mathematics Framework says students in the course of their work should
- Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information
- Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and diagrams
- Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion
- Relate 2-D shapes and 3-D solids to drawings of them; describe, visualise, classify, draw and make the shapes.