African Maths Initiative

Sharing Initiatives in Maths Education

Amagoro Camp - 12-13 December 2013

At this camp, we met boys who had just finished Form 2 and were graduating to Form 3 in 2014. I first asked how many loved maths, eleven out of twenty said they don’t. This was a good eye opener for us.

Thursday 12th

On the Thursday, we had a two hour session where we engaged students in simple games to teach them rules and strategy. The two games we played were game 21 and monty hall.

Game 21

Game 21 is played between two players and has the following rules:

  • Two players say numbers in turn
  • A player can say one, two or three consecutive numbers during his turn
  • The players are not supposed to skip numbers
  • The losing player is the one who says “21”

We posed this question to the students: “Is it possible to always win in this game?”

They voted and we split in the middle between those saying yes and those saying no. Those on “No” said that you don’t know the strategy of a new opponent while those on “Yes” said it is a lot to do with luck. We therefore played the game several times where the winning player would stick till he lost.

We encouraged the students to find a pattern in several students who played and won. After twenty minutes they had notice that the winning player always stopped at ‘16’. We left it as a challenge for them to figure out the rest:

The strategy in this game is to try your best to always stop on multiples of four.

Monty hall problem

The objective of this game was to teach students how we can use data to make evidence based decisions. In the monty hall game, we have only one player who chooses one of three doors which contains a fortune. The player has two choices in this manner:

  • The player gets to select a door first without seeing what is behind the door.
  • The host opens a different door where there is nothing.
  • The player gets a second chance to either stick or switch

In our case we used cards, two whose suits were red and one whose suit was black. The winning card was the black one.

We then asked the students “Is it better to stick or switch”. The students voted 14 (Stuck) 8 (switch). Their argument revolved about luck. We therefore collected data where we got the following:

Strategy Win Lose
Stick 9: proportion = 9/20 11: proportion = 11/20
Switch 6: proportion = 2/3 3: proportion = 1/3

With this information, the students voted 5 (stick) 11 (switch). We then demonstrated to them how by switching one had a 2/3 chance of winning and only 1/3 chance by sticking. We ran a python script for this game where we used one of the two strategies and simulated the game for 100, 1000 and 10000 times. In all cases, switching won close to two-thirds of the time.

Friday 13th

Gapminder

On the Tuesday before we came, the students had been discussing HIV/AIDS in Kenya with the facilitators present. The effect of HIV/AIDS on life expectancy is captured well in Han’s Roslin’s Joy of stats video section of “the history of 200 countries over 200 years in 4 minutes”. We showed them the video and tracked Kenya in Gapminder desktop for discussion. It was great to hear students explain the size of the bubbles and showing how well they were able to follow Roslin’s presentation.

We compared Kenya to China, which had a lower life expectancy and average wealth than Kenya in 1963 but has now improved tremendously. We then included South Korea which was where Kenya is currently in 1960 but has seen tremendous improvement on life expectancy and average wealth. This was used to show application of data and share with them how education can help improve our country as a whole. We reminded them of the Vision 2030 and how its success depended a lot on them too.

GeoGebra

Most students were relatively new to computers. Around three had never touched one and around four more were touching them for the second time. They sat in groups of two’s and three’s and we took them through the GeoGebra window.

We then asked them to plot at least twelve points that were five units away from the origin. It was easy to get the four points on the axes. Some managed to recall Pythagoras theorem and were able to get the remaining four. They then drew a circle by themselves.

The objective of this task was to get them to understand the basic definition of a circle as “a round plane whose circumference is everywhere equidistant from its center”.

After this, we showed them how they use GeoGebra to animate objects. This is done using a slider.

Other online resources

We sat through a section where the students were shown how to browse for important items using google. We shared with them how google uses a lot of mathematical algorithms to search and translate from one language to another.

We also showed them other resourceful websites like: Maseno Maths camp, Maths if fun, Khan Academy and used youtube to get educational videos.

Finally

This was a really fun camp. Though the students started off shy, they quickly picked up and were very interactive. We introduced an award system for those who participated. They were given cards where each earned a sweet on the closing day. I look forward to the next one.

The following people were involved in this event

This is an event of the initiative

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