The Maseno University first year students of MMA 106 (a service mathematics course) class in the 2012/2013 academic year used their own mobile phones to make teaching videos. Their motivation was the Khan Academy videos which they watched in the math lab to strengthen their understanding of certain concepts covered in class. This is part of an ongoing research on the effect of certain teaching interventions on the students achievement and motivation in mathematics. To watch a few of the videos, click here. Feel free to send your comments and suggestions.
In December, the Philedelphia police department in the United States released a csv database of major crimes (murder, rape, burglary, etc) since 2006. Since then, community software developers have been mapping the data. The community involvement is hoped to spur the future release of large city data sets.
Within the Kenyan context, we can ask: What large sets of statistics can we get access to that are of general interest, and how can we represent that data in a way to get important information across to community members? It is vitally important to report data in a way that keeps people informed about what is happening in their country. A good place to start might be the Kenya National Bureau of Statistics.
Attitude is one's perception about something. There are two types: negative and positive attitude.
Negative attitude drives away the positive energy needed to do something. for instance,many students have a negative attitude towards mathematics.
This leads to poor performance in the subject because of the perception that maths is hard. Teachers and students should work together to fight negative attitude.
This can include the introduction of maths related games such card games,simple mathematical patterns or sequences with hidden rules and getting the students to participate fully.
Teachers should also try and attend to all students including the slow learners and introducing regular quizzes on what has been taught to enable the students to have constant practice.
ITS YET ANOTHER YEAR BEFORE US. MOST OF US ARE HAPPY AND WITH MANY EXPECTATIONS ABOUT VARIOUS THINGS IN LIFE.SOME OF US WANT TO PURSUE VARIOUS INTERESTS IN LIFE AND MAYBE EDUCATION. BUT MY QUESTION IS THAT WHAT ARE YOUR NEW YEARS RESOLUTIONS?
BEFORE A NEW YEAR STARTS,ITS ALWAYS ADVISABLE FOR TO TAKE TIME AND TRY TO THINK ABOUT HOW HE OR SHE WOULD LIKE TO CONDUCT HIMSELF DURING THE NEW YEAR. WE WRITE DOWN WHAT WISH TO ACHIEVE AND THE STRATEGY TO BE USED. THIS ACTS AS OUR FOUNDATION AND REMINDER ON WHAT IS REQUIRED OF US. MY PRAYER IS THAT YOU TRY AND WORK HARD IN ALL THAT YOU INTEND TO DO IN THE YEAR 2013. LET IT BE INDEED A NEW YEAR TO YOU. DO NOT CARRY YOUR PREVIOUS FAILURES BUT TRY AND IMPROVE ON THEM. DO EVERYTHING IN A DIFFFERENT WAY FROM HOW YOU USED TO DO IT BECAUSE THE CHANCES OF SUCCESS ARE HIGHER THAN WHEN YOU STICK TO THE SAME WAY. HAVE A SUCCESSFUL AND PROSPEROUS 2013!!!!!!!!!!!!!!!!
This was a peculiar mini maths camp where we went to a students’ educational camp. We had a full day session, unlike the half-day session we usually have when we visit schools. The organizer, Annette, had raised the tempo for us by promising the campers that by the end of the day, those who hate maths will love it. I am confident that the activities we did excited them about maths and for that I am proud.
The day was split into the morning, mid-morning and afternoon sessions. The former two were two hour sessions and the last one three. We had an unexpected extra half day for just dialoguing with the students about importance and joy of maths.
We had planned to have a game (or puzzle) in each session for an hour, and a computer (ing) session in the remaining hour. During the first computer sessions, the campers were introduced to Geometry and Algebra using Geogebra. The Monty hall game was done in the second session and was useful to introduce the concept of proportion, probability and data. CAST (Computer Assisted Statistics Textbooks) was then used to take them further into statistics. With it they explored the properties of mean and median.
The concept of transforming a “complex” math problem and looking at it in a simpler form was done taught using game 15 and tic-tac-toe. In the remainder of the evening session, we did a math puzzle which employed the concept of odds and evens in order to save captives.
On Sunday morning (second day), we had only planned to say goodbye. The students had a couple of questions and as we responded, it was revealed to them that they will be expected to teach standard 7 pupils standard 1 maths. It was very lovely watching them practice how they would go about introducing the concept of multiplication, using toys and not the blackboard.
The next mini maths camp will be on 29th at the same venue. This time around, the camp will run till 6.30 pm not 5.00 pm. I am already looking forward to it.
For the CBM conference, I used a slide and the following were the planned message for each slide. The slide can be accessed here (click to view).
- I’d like to thank the organisers for the opportunity share some initiatives we have taken in Kenya. I’d also like to acknowledge Rockefeller and the Statistical Services Centre, University of Reading for the collaboration which brought me to the UK and has enabled me to attend this event.
- My talk today is about the Maseno maths camp
- I work at Maseno University; it is a public Kenyan university whose claims fame is that it is, to the best of my knowledge, the only university in the world where the equator passes through the main campus.
- The Kenyan curriculum is based on calculation. The Maths camp aims to excite students in Mathematics which is not calculation based.
- The maths camp encourages students to solve puzzles and explore mathematical concepts.
- The first Camp was a small scale success with immense positive feedback and one major complaint. There was too much free time the day should be longer!!
- The second camp was bigger, the day was longer and the feedback was still very positive with the main complaint being about the accommodation.
- There are a number of key themes that have been used in the Maths camps… list them
- In Kenya, playing card games has been looked at as a negative influence on kids. A big part of the camp was dedicated to playing games, and demonstrating their usefulness in teaching children how to understand and follow rules as well as trying to come up with good strategies.
- Everyone was given packs of cards to take away with them.
- Statistics is my area and I believe strongly that we have to get students at all levels to be able to work with data.
- Focus on descriptive and exploratory statistics. Many of the students had never touched a computer before but they picked it up within a few hours on the computer.
- Gapminder had very good data presentations that students quickly understood. The caption compares health (y) and wealth (X). Kenya and S. Korea have their trajectories from 1963 to 2009. This is used to get students and staff thinking about what development could really mean and relates to Kenya’s vision 2030…
- Tinkerplots was used to get students to explore their own data, which was collected as they arrived and halfway through the week, and then given back to them to explore.
- CAST which stands for computer ass… includes exercises, an adapted version for New Zealand schools and has been shown to be effective to help teach statistics in Kenya. A colleague is currently creating a version related to the Kenyan syllabus.
- The image shows them learning how to estimate mean and median in random dataset which may or may not be skew. This exercise reinforces the fact that computers can help improve mental estimation.
- The Geometry sessions served multiple purposes. They provided an opportunity for students to be creative while also providing the opportunity to stretch students beyond their comfort zone. Spherical geometry was discussed in 2011 and projective geometry in 2012.
- Even with the limited computing skills, remember that many students had never used a computer before; the aim was to get students to be able to create simple animations for themselves.
- With GeoGebra, this was achievable and there was even a small competition to create animated house logos.
- Programming is important; if you can write code to do something then you have understood it.
- Computer literacy was too low to assume that students would be able to write computer code but the concepts behind how a computer work and the basics of programming can be taught through practical activities and puzzles.
- Participants acted as human robots and followed instructions from this limited syntax to move objects from one place to another.
- This was to get them understand the nature of computers and how to follow a logic flow when programming.
- Modelling natural phenomena was also used to expand the notion of mathematics. One example of this was the model of swarms, such as schools of fish or flocks of birds.
- Students were told about the simple rules which govern the behaviour
- Only be aware of your neighbours
- Move in the same direction
- Aim to keep a constant distance apart
- Run away from predators
- (Say before you show) Students were asked to follow these rules in the field.
- Students were challenged to understand an open problem in research mathematics. This topic started by discussing how problems can be simplified when posed as other problems.
- We introduced a game called 15; two participants chose a number between 1 and 9 without replacement, one at a time. The winner is the one who chose any three numbers that added to 15 first.
- The numbers can be thought of as being in this pattern in a square
- Which transforms the game to the game of noughts and crosses / tic-tac-toe. This principal of transformation was then used to reframe a question in research mathematics.
- Unconventional number systems and modular arithmetic were introduced as a step towards being able to work with codes.
- Throughout the week code breaking came up in sessions and puzzles and at the end of the week students wrote their own codes to encrypt some of the clues for the treasure hunt and then tried to crack each other’s codes.
- You need to thank all the people who were involved in running the Maths camp, it is entirely run by volunteers with the international volunteers even paying for their own airfares!
- We would like to acknowledge that this would not be possible without the software we have been using, almost all of which is free to distribute. The few commercial packages we have used were licenced freely for the camp by the developers. We would also like to thank Wolfram research for the donation of playing cards and the US embassy for sponsoring a large number of participants.
- I will leave you with a couple of the student journal entries. They were asked to write something every day and their entry was then photographed and made available online. These are not representative entries. Thanks you for listening
On Nov 1st and 2nd 2012, I had this wonderful chance to attend this forum where people from different background, yet applied mathematics in their fields were present. These were people with medium and high level mathematics skills. The presentations and discussions centered on revolutionizing the way maths is being given to students.
It was fascinating to see the different apps that were there to aide maths education. The session after lunch on the first day had three presenters who showed some games and how they can be used to train children with logic and maths skills. Certainly there are currently many initiatives that are taking place to incorporate the use of computers to for maths and education in general.
The participants were in agreement that computers are important for teaching maths. The technicalities involved were however not trivial. For instance, one presenter showed an innovative grading system for UK but was also quick to mention that with the current procedures, this grading would be used in 2020. I think the best thing to take out of this is that as people develop on ideas of CBM, it is important to note that it is not an immediate thing but a process.
Maths camp and CBM
The Maseno maths camp presentation was slotted in the section on “Experience: Using computers in classroom”. As the title would suggest, the presentation was about the different activities that we indulged students in during the event, and showing how this would relate to CBM.
The audience received the ideas well. The few I talked to said that it was a good initiative to excite students about maths.
What I felt I learned
There was a presentation on programming where the presenter later on mentioned that there was need to introduce programming to girls in early age. This is since they get involved in more things as they get older and hence do not create enough time to learn the programming. Though this is not the same, I felt that cementing positive attitude towards maths for girls should also be done early on.
People are genuinely interested in seeing that the students learn maths. However, many would not like maths as a subject to be completely drained down as computers take over. Many people defended the abstract component of maths for different reasons, while there were some who felt it was not needed.
So what for maths camp?
The interest has been generated; one teacher was interested in coming for the next maths camp. There are some useful resources that we can investigate more and see how to incorporate them in our activities (mathigon.org).
Maseno University offers a number of diploma and degree programs via e-learning. Usually, there is a mandatory orientation process for all new students.
Unlike in Kenya, Uk has a higher population very well versed with internet and therefore the orientation as we have been running it in Maseno would not be ideal for students from here. I am currently working with a very bright person, re-inventing an orientation that will:
- Sieve the students who need orientation from those who don't
- Require minimum facilitation time
In the Maseno orientation, facilitators were useful for grading and we are here trying to remove all manual grading. We have opted for quizzes yet at the same time ensure that students finish all the tasks involved.
Students will get to open topics by themselves and only send a message to a facilitator once done requesting for enrollment into the main course.
We have planned to use a number of one and a half minute video tutorials and we have just made a first one - teaching students how to open topics. In the process, we came to find that Camtasia can be used to set up quizzes in the middle of a video. I think that having a quiz at the centre of it can get students to learn the concepts we want them to get even in the middle of a video. And finally, we noticed that with the quizzes, one can be able to add them in Moodle where they can be graded automatically as an activity...
I hope to attempt this soon.
This week, we continued discussing infinite sets of numbers, bijections, and modular arithmetic (alongside Pythagorean triples).
Here are some challenge problems to consider!
- Are there natural numbers such that ? If so, find them, if not, explain why.
- Are there such that and exactly two of a,b,c are divisible by n? If so, find an example, if not, provide an argument why.
- Again let be a Pythagorean triple. Show that if is not divisible by , then neither are or .
- How many surjections are there from to ? How about surjections from to ?
I had this task to explain to someone who understood maths, but was not a statistician what is "sums of squares". I was free to use graphs to aide him. So I begun.
The figure above gives a good approximation of how I explained. I drew a two dimensional plane with observations where the horizontal component was made to depend on the horizontal component. I even used the lines to show that it was actually a summation of the squares of deviation from the expected value.
The other guy apparently could not make out well what the expected value is, and was not comfortable with my using the regression model with a line of best fit to explain it.
A friend was standing nearby. I will soon reply with how he responded since it was not me. A challenge to you upcoming statistician like me, how would you have explained it without using the jargon that someone heard of over 10 years ago while in school?
The response will explain more on my title which is not captured here in this post.
Thanks for following.