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Lou Connelly (Terri's group) Design narrative: Active Learning in a Mathematics classroom
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Lou Connelly
27 March 2014
Title Lou Connelly ( Terri's group):Active Learning in a mathematics classroom: Using percentages to increase quantities: ( March 2014 )
Narrator
Mathematics teacher to a group of 28 year 9( 1314yrs)who were aiming to complete the GCSE Higher exam in year 10.
Situation
1118 comprehensive school ( 1200pupils) situated in a market town.The mathematics and science departments is housed in a two storey block built around 1960. This classroom is located on the 2^{nd} floor. It has large windows on 2 sides . The windows have blinds. The main door to the the classroom is reached at the end of a long narrow corridor and there is another door at the back of the room that leads to next mathematics room.The interactive whiteboard is positioned in the middle of the wall at the front of the class with a whiteboard to the left . There are 3 tables, arranged to seat 6 on each, from left to right across the front of the class and then 6 tables,seating 2 each, positioned around the back of the room.
Following on from a pilot study conducted in the light of Professor Adrian Smith's report ( 2004) into Post 14 standards of mathematics teaching (Making Mathematics Count ) the department wanted to try out some of the approaches that encourage a more active way of learning , to learn to think mathematically rather than just learning rules ,through the use of group work, discussion and open questions.It was decided to focus on Year 9 for a series of lessons and then feedback findings to departmental meetings.
This group of learners know how to calculate a percentage of a quantity.They also believe that that an increase of 50% followed by a decrease of 50 % will take you back to the original value. The challenge is to confront such misconceptions and aim to build new conceptual links between percentages , fractions and decimals.
Task: Using percentages to increase quantities:
To enable learners to:

Make links between percentages, decimals and fractions

Represent percentage increase and decrease as multiplication

Recognise the inverse relationship between increases and decreases
Actions
1)Prepare classroom for pratical session beforehand with materials (cards ,( photocopied) minwhiteboards A3 poster paper,scissors ,glue ( enough sets for groups of 2/3 )
2)Starter question on IWB Individual work to expose existing thinking. To use miniwhiteboards to show responsesMAIN:Each group of learners were given a 4 card set A Money and a card set B Percentage and to match up the correct percentage increase or decrease between each pair of money cards . Discussion and probing questions to allow them to correct mistakes if they can. Then introduce cards set CWords and cards set DDecimals to provide them with different ways of interpreting the situation. Finally give out cards set Efractions and place them in position .PLENARY: Each group to present their findings in the form of a poster. Two groups were allowed to use the IWB as all cards were on it .Blank cards available to those who wanted to make their own cards. Review the problem question set at the start.
Obstacles:
Lack of time so we decided to extend this session into 2 one hour sessions.
Group sizes and class size I had 6 groups of 3 and 6 groups of 2 ( 12 groups) all working at different rates but some groups helped other groups.
Size of the classroom too small there was not enough room for me to able to move easily between the groups so I positioned myself at the end of the middle table of 6 and asked individuals to come over to me and that worked well for a few of the groups the noise levels did disturb the class next door.
IWB it was a sunny afternoon and the light comes through the blinds ( not very effective when its sunny ) so it was difficult to see the board clearly especially if you are based on the back row towards the left hand side.
Results
4 of the groups managed to use all the cards in their poster but we did not have enough time to discuss them all. There was more success with matching the fractions to their multipliers which I expected. Most groups found the decimal match difficult.
Reflections
The importance of asking the right questions which are pitched at appropriate levels.
Would the outcomes of this session have been different if it had taken place first lesson of the day?
Additional adults to help with practical sessions.
Resources: Standards Unit:Improving learning in Mathematics
Extra content
Comment 1 by Jeni Parker
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Jeni Parker
3:48pm 12 April 2015 Permalink
Hi Lou,
I really like this, especially your description of the classroom for anyone outside of school teaching, I think I would have been guilty of implicit assumptions that people would know about these issues.
Great to see pupils being taught to think mathematically as someone who was 'only taught the rules'.
Jeni