# The Mathematics Teacher Training Scholarships -  Scholars and Alumni event 20th January 2018, Birmingham

Not only was it an opportunity to network, it also provided skills and strategies to teach two really difficult topics in Mathematics: Statistics and Geometry.

The session on Statistics covered Probability which had plagued me with questions for over 20 years since I first got taught it myself. Questions such as “Why should I multiply probabilities of combined events instead of adding them?” “Does the word combined not mean add?”  “After multiplying probabilities to get outcomes for each branch of the probability tree, why should I add the probabilities of the different possible outcomes when I’ve just been multiplying them?” Why when two events are mutually exclusive should we add their probabilities?” Shouldn’t we be subtracting like the word exclusive suggests?”

Jenny Gage, co-author of the book ‘Teaching Probability’ gave some amazing strategies for teaching Probability based on research. Her suggested approach is to teach Probability first as a Frequency Tree until students have a thorough understanding of the concept. The idea is to run an experiment on something familiar to the students, such as submission of homework, using a spinner rather than dice, coins or cards which are alien or offensive to many cultures. Spinners could also be manipulated to give a greater possibility of outcomes than dice, coins or cards. We were given a practical demonstration of this approach.  Working in groups, we ran ‘The dog ate my homework’ experiment using two spinners. The first spinner results would indicate whether the student was lying or telling the truth about his homework. The second spinner would indicate whether the truthful student was accused or not accused of lying by the teacher. All students found lying from the first spinner results would be automatically accused. Each group was to collect physical data for 24 students using Maths manipulatives. Brown indicated that a student was truthful, orange indicated that a student was lying, green indicated a student was not accused and white indicated that a student had been accused. Physical data collected was put onto a two way table. The results could then be transferred to a Venn diagram or a Frequency Tree and used to stimulate discussions of whether the experimental outcomes matched the expected outcomes. Completing the Frequency Tree provided answers to my 20 year old questions on Probability.

I highly recommend the Mathematics Teacher Training Scholarships events as an invaluable source of strategies and resources in the teaching of Mathematics.

By Chinyere Mbanefo