Importance of rough-work to solve maths sums
I remember my childhood experience of doing mathematics. My maths teachers created a habit of maintaining rough-work along with the actual working of a maths sum. My classmates and I used to draw a vertical line about one third down the page and wrote the heading prominently: ‘rough-work’. This provided evidence for our thinking process as we used it to solve questions. I remember my teacher was very concerned about the rough-work along with the actual solution of the sum. That style of working, which was rigorously maintained, helped the teacher to address our way of approaching maths problems.
Last Friday my daughter – a grade 4 student - came to me to seek help regarding a maths sum. Rather than telling her straightforward steps to solve the sum, I used a student-centred approach. I asked, “Mimi where you will do rough-work?” In response to this question she didn’t say anything. She was quiet, her body language and facial expression made it seem like I was speaking some alien language. I asked her about the routine she was guided to use by her maths teacher when solving a maths question. She described the process but there was no role of rough-work.
I thought about that - Why didn’t the maths teacher value the use of rough-work along with the solution to the question. It may be because of time; teachers have more work to do and guiding students about rough-work and ‘the right answer’ is problematic for them. It could because of students; they have more to do and maintaining both portions side-by-side is difficult for them. It could be because of school management who are focused on a ‘traditional-style of Mathematics teaching’ or they figure that rough-work makes the exercise book look messy! May be there is no need to doing both types of work?
I pose both questions to you, to my readers (maths teachers or parents):
‘Is it beneficial to maintain rough-work along with the solution of a maths sum?’ and
‘What could be the reasons students are not maintaining rough-work along with solving questions?’
Using ice breakers and team building activities
Team-building activities are a great way for teachers to get to know their colleagues on a more personal level and, this can work in many different ways but here I will talk about our recent experience on the faculty retreat.We started off with an activity of answering different questions according to the candy we had selected. This icebreaker not only got us as all talking to each other, but it also got us to work with each other. It was also quite simple as well: selecting three candies and chocolates each one of a different type can excite any age and gender. The leader posed some questions on a piece of chart which made us talk all about ourselves in different teaching situations
This icebreaking activity can also be extended by issuing one situation for the entire group or allocating a different situation to each team member, or pair, to work on. Depending on the situation chosen, the activity can be a lot fun.
Those candies and chocolates excited all of us; hence I am posting another idea using our favourite candies called M&M’s
The M&M Game
Pass around a bag of M&Ms and have each person take as many as they want. For each colour of M&M have a question they can answer. For instance,
Red: Name a campus resource.
Blue: Mention one thing you would like to change about the school
Video Recording as a Self-Assessment Tool
I have often observed that the term ‘Assessment’ generates fear or anxiety among learners. In order to reduce that fear factor, I use self assessment tools in my teaching sessions.
Self assessment facilitates students to reflect on their learning. It does not require them to grade their performances rather it enables them to identify their strengths and weaknesses.
Among the many other self assessment tools, I consider video recording as the most valuable tool for self assessment.
After recording students’ microteaches and presentations, I encourage them to follow these steps:
I use the following questions to help the learners to take notes while observing their performance:
i. Were your instructions clear and simple?
ii. Did you rephrase your instructions if students were at a loss?
iii. Did you encourage the students to participate/ answer?
iv. Did you try to involve the whole class?
v. What modes of interaction were used?
vi. Can you specify the proportion of teacher talk vs. student talk?
vii. How effective was the use of technology or A/V aids in your lesson?
viii. Did you notice any errors in your speech?
ix. Did you implement the objectives you had planned?
x. What questions would you like to add to this list?
How did I Lose My First Ten Chess Games?
There are any number of activities we can do in our free time. Different activities require different skills. Personally, I value those activities which require knowledge, abilities and skills…and chess is at the top. My personal experience of losing my first ten chess games will help you understand the complexity of this game:
I lost my first game because I could not distinguish between the shapes of the different pieces. At that time, I suppose I used my visual-spatial intelligence poorly. I lost my second game because I could not understand the rules of the game. The third I lost because I lost concentration. The fourth - I was just looking at my own pieces and I neglected to watch the pieces of my opponent, and I lost my fifth match because I paid more attention to my opponent’s pieces rather than my own. The sixth was lost due to lack of planning. I lost my seventh game because I was playing aggressively and the eighth because I was playing defensively. The ninth game was lost because I was not thinking what my opponent was thinking, and the tenth was lost because my opponent guessed what I was thinking.
Actually, the list does not end here. In every game I play now, I try to improve – to build on my deficiencies. Every game makes me learn. With every game you grow more composed, focused and logical.
Is there any game in the world which requires various intelligences, skills and abilities in the same way? Even if you feel you don’t have time or you are burdened with lots of work, if you are tense, one game of chess will be time well spent.
Let’s Start Reflecting
“Today the class went very well. Students enjoyed the pictures on the power point slides that made the topic interesting for them. Everybody participated very well but Sarah did not participate as usual. Although I asked some very easy questions from her, she was not able to respond. I wanted to talk to her after the class but Group-1 students surrounded me with their queries regarding their project work. I will talk to her personally tomorrow and try to find out what is disturbing her. I really want to help her. I still remember her happy, smiling face a few months back when our class went on a field trip, to a paper making company. There must be some problem with her - maybe at home. I will find out tomorrow…”
Abstract taken from the reflective diary of a science teacher.
Spending five to ten minutes daily on reflecting what went well and what was wrong and how I can improve further is very important. We all should reflect on our everyday life situations and, as teachers, on our teaching practice. These reflections not only inform us about classroom issues but also guide us as what to do next. At the Ali Institute of Education we claim that we transform people into Reflective Practioners.
By Aqsa Kamran
What did you do at the weekend?
Technology presents us with amazing opportunities to re-design the way we teach and learn English. Mobile devices allow me and my learners to interact seamlessly with each other in formal and informal learning contexts. I also have learners from rural areas and they are not as much proficient in English language but somehow they are aware of the usage of mobile technology.
I encourage the students to create a personal visual story about their daily routine. They take a series of snapshots of different moments in their day- e.g., their alarm clock, a toothbrush, a cup of coffee, their walk to the shop….
They describe the actions to me, e.g., I take a shower and get dressed….. Most of the time, it also highlights different aspects of language that require input from my side.
For the next step, I ask them to record themselves speaking English and share it with friends, who can offer feedback. This is a great opportunity to practice pronunciation as well.
Using mobile technology in the classroom has turned the question, “what did you do last weekend?” into a personal story, as students share with other fellows what they did, where they went and how they felt.
Ms. Sumaira Latif
MATH IS IN THE AIR: MAKING OF A GIANT-SIZE CHESS SET
I have a strong belief ‘THERE IS NO MEANINGFUL SURVIVAL WITHOUT MATHEMATICS’. Every maths teachers, every mathematician, is doing, applying and taking help from a very important field of knowledge. If anyone disagrees with this argument, just recall today’s routine and consider when you didn’t use maths!
Every field, occupation, task and activity is incomplete without maths. To reinforce my point I’ll share my recent experience. Ali Institute of Education is arranging a chess tournament between school kids for the first time ever. It is planned that the finals will be played with giant size pieces on a huge chess board, 8 metres square, on the Ali Institute front lawn. The task was to make a huge chess piece to understand the mechanics of producing a stable and long-lasting chess piece. The problem solving process was started with observation. I looked at regular chess pieces with a mathematical eye. They are three-dimensional objects which needed to be converted into a two dimensional drawing, disintegrated into small segments; the measurements were taken for each part, a scale is used and a scaling factor was identified. Proportionality between the actual piece and the large-size piece was maintained by cutting and using circular disks. Contours were made through a series of sequential disks of various sizes. The amount of material and time required to complete the task was estimated. A table containing a list of material, the unit price and the cumulative prices were entered and a request was made to the purchase office.