The essence of making Number based Mathematics meaningful is to bring the subject to life and allow the learner to think for themselves, giving them the responsibility for their own learning. Teachers today need to facilitate the learning of mathematics, as opposed to “teaching” it and allow each learner to assimilate the concepts in their own way. Michael Ymer is an experienced Mathematics teacher who has been involved in many Victorian and National initiatives in mathematics. He works as a consultant in a wide range of Professional Development programs for schools, teachers and parents. He provides services for teachers in all schools.
Michael is an enthusiastic and entertaining presenter who has a clear and practical approach to the challenges that confront schools in mathematics. Teachers spend a large portion of their numeracy time teaching skills in computation. While learning computation skills is important, this needs to be balanced with the development of thinking skills. Students need to be able to choose and use the appropriate computation skill when confronted with non-routine word / problems
. Although students are natural born mathematicians, teachers have the opportunity to increase their skill and knowledge. We need to ensure that we keep their love for Maths open and enjoyable rather than a confrontation they abhor. Michael Ymer extended a range of ideas that assisted teachers in investigating the stepping stones towards teaching and learning addition, subtraction multiplication and division. He provided us with Classroom management advice, suggested classroom resources, task centres, grouping students and investigative learning for our class.
A Task Centre is a collection of individually housed mathematics problems (or tasks) that require the use of concrete materials (housed with the problem) to solve or make a start to the problem. Some students may not need the materials to solve the problem; but if the materials are not present many students would be prevented from accepting the challenge.
Ymer uses a variety of organisational tools to assist with the smooth functioning of his Mathematics sessions. One such tool is a SmartBoard file which contains a bird’s eye view of what a student’s desk should look like. Students then have a visual guide as well as the verbal instructions to help them become ready to learn, thus catering for those students who are not auditory learners, or those with auditory processing difficulties. All activities are initially explained in a group situation where the teacher will sit with a student and role play how the game is played and even details such as how books are to be ruled up.
Many of Ymer’s ‘warm-up’ activities are seen by the students as games that are enjoyable and therefore not threatening to those who lack confidence. At times students will be working in ‘like-ability’ groups or pairs and then at other times they may be working outside that grouping. ‘Target 100’ is an activity which enables a student who struggles at Mathematics to best a student who is perceived to be a high achiever, thus increasing confidence and enjoyment of Mathematics.
This is done through using a combination of luck and skill. In this activity two students compete to see who can get closest to 100 without busting (going over 100). One student will deal the cards and the other student will add or multiply the cards, depending on the level of the student. This will continue until the student decides to stop as they are unable to go any further without busting and the roles are reversed. The opposing student then sees if they can beat their partner.
All of Ymer’s activities can be adapted to cater to the individuals in any given class. Simple adjustments can be made on a needs basis. ‘Land Grab’ is one such activity. A multiplication activity based on arrays, it encourages students to become aware of the Distributive and Communicative properties of multiplication. It can be used as an introduction to multiplication in a fun and non-threatening manner. Gone are the days of standing students up and putting them on the spot to answer questions that they may forget in the stress of the moment.
To play ‘Land Grab’, using a piece of grid paper and 2 dice, one student rolls for the other. The student doing the grabbing on that round, multiplies, or works out using the grid paper, the amount of ‘land’ they are able to grab.
The student then traces around the array on the grid sheet, writes in the table and his or her name and they swap turns. Both students work on the same page and this continues for a time limit or until the page is full. A tally is then made and the winner is the one who “grabbed” the most land. The distributive property is realised when a student is not able to fit in their array and they must break up they array. For example a roll of 5 x 4 can be split into 3 x 4 and 2 x 4. Altering the dice used or providing a tables reference sheet are further ways a teacher would be able to adjust this to cater to individual needs.
Ymer encourages the use of technology in the classroom. He uses the SmartBoard regularly to set up his lessons and is also an iPhone advocate and regularly incorporates this tool into his Mathematics lessons and professional development sessions. A great storyteller, Ymer enjoys using his family members in the stories he tells to set up activities. This draws the children in and they listen as opposed to tuning out.
Multiple Intelligence theory tells us there is a range of preferred learning styles in any classroom. Tasks need to be are tactile, kinaesthetic, visual and encouraged interpersonal skills. Through these tasks students become more excited about mathematical challenges. A ‘good task’ requires A balance of the following principles:
✓ the task is intrinsically motivating ✓ the task requires hands-on materials to support its solution ✓ the intellectual challenge is likely to result in a first level of success in 15 - 20 minutes ✓ the maths problems can sometimes be the tip of an iceberg; the beginning of a deeper investigation; strategies used, solutions formulated. ✓ the task can be used to illustrate the process of Working Mathematically ✓ the task has three lives:
- as an invitation for two students to work like a mathematician - as a whole class investigation - as a deeper investigation guided by an investigation sheet