Q: I attended a workshop where it was mentioned that formative assessment should be frequent, informal and effective. Though I asked the resource person conducting the training on how this is possible I did not get a satisfactory reply. Can you help?
Ans: It is a misconception that Formative Assessment (FA) has to be always preannounced. FA can take place in the classroom at any time announced or unannounced.
To understand how this works one must view FA as a two-pronged tool. One prong relates to assessing progress in student learning, e.g. a language teacher may want to gather information on progress in student hand-writing after having spent a week on say, perfecting spacing between letters and words . This information can be collected informally, unannounced and perhaps over two or three different observations. The idea behind gathering this information is to record progress in development of a skill, a skill that is not fully ‘formed’ as of yet but will progressively get better (in most cases) with time. A road map may be made for this wherein the teacher decides to assess once again, next term how this formative skill is developing. The second prong of FA is the one that provides feedback to the teacher on the effectiveness of his/her teaching, e.g. a Math teacher may ask students to illustrate through drawing, the multiplication table of 2, up to say 5 times 2. By looking at the drawings, the teacher can make an assessment of whether the concept of multiplication has been understood correctly by the children. If it is observed that the ability to perform this task is largely below par, the teacher then takes this as feedback to him/herself to re-teach or tweak the teaching by using another method, or using another strategy. Here the idea is to obtain information on effectiveness of teaching.
The tasks given in both these can be small five to ten minutes ones. These are not tests, they are not even assessments, these are opportunities given to the teacher and student alike to get better and better. If carefully planned and thought out they can be conducted frequently, informally and are most effective in reaching the desired learning outcome.
Q: How important is it for a student to write steps in solving ‘word problems’ in maths.
Ans: Solving word problems should be central to Mathematics. All processes and procedures and abstract symbols should emanate from the word problem. What this means is that the number fact 2 plus 2 equals 4 comes later only after the concrete experience of seeing two bananas in one plate and two in the other takes place. Once the child has been through the concrete(C) experience, pictorial (P) representations make sense. Lastly comes the abstract(A), yes that’s right 2+2 is abstract! The CPA approach as it is called, is widely used in schools of top performing nations as research based on TIMMS and PISA findings reveals.
Students brought up on the CPA approach to problem solving are supported with other techniques such as bar-modelling. These students are adept at visualising problems and solving them in their head or making simple diagrams. (This does not happen automatically but is a skill that has to be taught). As a result they are better poised to solve not only direct but also two or three step word problems.
As long as a student can describe on paper the thought process through diagrams, illustrations or graphic representation and place the numbers correctly in the diagrams, we as teachers should be pleased. This is the toughest step in solving a word problem for the child. This then should be followed by the correct ‘answer’ which is the easier part. This is the point where we should be elated.
On being queried they should be able to articulate their thinking. This is what the NCF means when it talks of mathematisation of the child’s thinking.
One has seen countless cases of Math teachers forcing their students to write ‘statements’ in Maths. Students are forced to structure their statements with words pre-provided by the teacher namely, cost of, amount of, and number of. This forecloses any attempt the child may want to make at cracking the problem on his/her own.
The result is that students struggle with the English of the problem and sadly are not allowed to ‘do the Math’.
To answer your question then in short: Statements in perfect English are not essential but some steps that reveal clearly the process of thinking are good to go. And of course the correct answer, the one that answers the question asked.
Q: What is the ideal length of a class period – 30 minutes, 35 minutes, 40 minutes or more?
Ans: Tough one! I invite readers to respond to this. Do write in with your views giving reasons to support the view.Sarita Mathur
Sarita Mathur is a free-lance education consultant offering services to schools, both rural and urban, in India and abroad.
An alumnus of St. Stephen’s College, Sarita has a degree in Mathematics, Education and a postgraduate degree in Operations Research. The Mathematics background and her well-honed sense of systems and processes had her institutionalise several long lasting and important changes as Principal of The Shri Ram School placing it firmly on the map as a progressive and leading school of India. Sarita has served as a consultant on the International curriculum of the CBSE and also serves as advisor/consultant to several curriculum companies, schools and start-up ventures.