Reflection 9 : Area of 5? Is it possible? (26 October 2010)

In this tutorial, we were being “assessed” through a simple activity, Area of Five. Our task was to create quadrilaterals with an area of 5 squares. Is it possible? Yes, it could be done! We were given geoboards, rubber bands and ‘geo-dots’ papers. We manipulated using rubber bands, experimented with and tested out our assumptions. Initially some of us were ‘boxed’ in by our interpretation of quadrilaterals as the usual regular 4-sided figures. When the idea of decomposing a square into 2 triangles is being shared, we begin to see the possibilities of abstractions such as, ‘half of a square’ and ‘take away from the whole’. Probing questions were asked to scaffold the used of subtraction strategy to find other possible ways of making quadrilaterals with area of 5 squares. Soon we began to use the idea of triangles to come up with more ‘sophiscated’ quadrilaterals.

Where is the assessment? As we discussed and experimented with all the different possibilities, we were being assessed. Through our solutions, it could be seen how we process our thinking and whatever prior knowledge we had about quadrilaterals. The strategies that came out naturally from us which were evident in our solutions indicated our knowledge and competence. In order to stretch the learning, scaffolding would then be required to ‘teach’ higher level thinking, thus developing and sharpening students’ meta-cognition. The practice and drill exercise using mental calculation strategies showed how on-going assessment could be used to diagnose and improve students’ learning. Through this and the word problem activities, we could see that mathematics is no longer about computational skills but testing students’ thinking skills as well. Newman’s error analysis procedures gave six reasons as to why a student could not do word problems:

(a)  Reading - a child who could not read a word or symbol

(b)  Comprehension - a child who can read but cannot comprehend the problem

(c)  Knowledge of heuristics/strategies - 

(d)  Transformation - a child who can understand what is read but unable to identify the operation to solve the problem

(e)  Computation difficulty - a child who can identify an appropriate operation but do not know the procedure to carry out the operation accurately

(f)   Use computation for a solution

In the spirit of ‘teach less, learn more’ we need to redefine how workbook exercises are to be ‘dished out’ in class. In other words, we have to provide engaging and meaningful learning experiences so as to help us gauge our students’ understanding, identify their strengths and weaknesses. This allows us to support our students in their learning and help them to become better learners.

How does assessment engaged students then? According to Black and William assessment refers “to all activities, undertaken by teachers and their students in assessing themselves, that provide information to be used as feedback to modify teaching and learning activities.” Through the ‘Area of Five’ we saw how learning could be assessed informally to help students learnt meaningfully. As teachers observed students’ learning behaviours, they would be able to make informed moment-to-moment decisions in the execution of their lessons to maximise learning in the classroom. As they gather and interpret these information, teachers would be able to ask themselves whether their students have learnt or how well they have learnt; whether they have provided input to support students in their learning. In assessment, validity and reliability is an important consideration that teachers need to know. When making assessment, it is important to use as many evaluative measures to ensure that reliability and validity are not compromised.

On-going assessment allows teachers to determine the gaps in students’ learning and bridging those gaps with further instruction or guidance. In the course enabling them to make changes and refinement to their teaching or reinforce concepts taught when they find students are not keeping up with their lessons.  

Assessment is an integral part of the learning process. It should be used diagnostically in relation to the student and is part of teaching! Students are engaged in their learning when they are motivated to learn, demonstrate positive attitudes and show a desire to increase their understanding and mastery of what they learn.