Tuesday 13 October 2015

Gamification in Maths Class

Using games to encourage student engagement is a concept I am quite interested in. I personally enjoy games and can see a range of cross over benefits. I love way that games employ Epic Meaning, Content Discovery and Application of Multiple skills to incentivise and engage players, and I am keen to use similar techniques for my students.  

So for final term of the year, when some students can find their focus waning and there is a few weeks with "non assessable" periods, I thought it was the perfect time to try Classcraft.



Classcraft is an attractive, customisable free classroom reward system. Something like classroom dojo, but more mature. Classcraft offers an $8 per month premium edition, with some more bells and whistles and a developing LMS. I am still working through the free edition, to check it works for my students (initial response is very positive).

If you would like 2 months free premium access, just tell them that I sent you,

or you can just use this link: https://game.classcraft.com/signup/i8z5qX4sKi7yYeE7j


Class Set up
Setting up classes is reasonably easy. I had a spreadsheet with my students' names and details, which Classcraft let me import. Then I needed to set up teams (knowing which students should be together, or not). All up it took less than 30 minutes to have all students in the system, with updated details and teams set.

Finally I wanted to adjust the 'abilities/powers' to ensure no rule broke school rules (no food in class, etc) and customise rewards for homework/good behaviour. This took perhaps another 30 minutes to work through the customisation.

Introducing this to students
The students came back from a 2 week holiday looking a little disappointed that the holidays vanished.

I started the lesson by reviewing the program...
probability....
consumer mathematics...
they were not impressed, so I proposed we have a little bit of game.

I presented Classcraft with the below Powerpoint.



You may notice that given this is a Mathematics class I have included a Probability task in week 3 called "Black Magic" to see how students choose between difference choices, and an Interest comparison task, called Coins of the Sphinx.

I told the students that all content and assignment submissions are happening through the existing LMS, however any request for points can be communicated through the Classcraft system.

I am still working through this system, but the initial response from students is very positive:

Comments sent by Students:

"I am really looking forward to this game!"

"I am totes into this roleplay thing thank you for doing this!! bruh it gr8 thank you"


I will put up another post in a couple of months to describe how the class enjoyed it.



Meanwhile here is the Infogram about GamificationGamification
Created by Knewton and Column Five Media

(Classcraft short link: bit.ly/1Qi5X3Y)

Friday 9 October 2015

Linking Unit Circle and Trigonometric Functions

In my opinion Mathematics is most powerful when the same concept can be demonstrated in multiple representations. Luckily most concepts satisfy this but I have found that Trigonometric functions are a particularly great example of this. We can plot the values on a Cartesian Plane with a reoccurring cycle or on a unit circle (rotating as the functions move through cycles). I also see the set of algebraic rules as another representation of the concept.
Students often hold onto the first representation that they understand, however being able to translate their understanding into a variety of representations truly shows deeper understanding.

Using diagrams such as the following to superimpose the trigonometry function on top of the unti circle shows the piston like function of 'piston' like nature of the Sine Function.
But then this begs the question, what about Cosine? Well we could subtract pi/2 radians (or 90 degrees), or I have found showing the Cosine function on the Y axis (I.E. x = COS(y)) students can visually connect connect the Unit Circle and Cosine Function.
Clearly it is important to highlight that we generally see the Cosine Function moving Horizontally (I.E. y = COS(x)) but this can atleast link representations.

 Once the Unit Circle and Function are linked then we can review where there may be multiple answers for a certain Sine, Cosine or Tangent value.


Providing student an interactive aid can assist in this being explored by students. They can move the 'a' value to extend the angle.
Then additionally they adjust other variables in "y=b f(cx)" to change the size of the circle, or adjust the impact of the angle.
I have found after providing basic description of the below interactive students learn best by playing with it, and trying to use it to answer questions with a set range of x, but with multiple solutions. Click below to explore further.



 

Algebraic Super Heroes

Introducing algebraic law can be boring for students... and for the teacher too... well it is a rather dry topic.
Students struggle to see the point to remembering which law Associative or Distributive Law, and how do you even say Commutative (are you sure it isn't Communicative or Communitative?)
And the real point of empowering student with tool to do Algebraic Manipulations, is lost to repetitive matching exercises.

As Algebra becomes increasingly complicated understand in higher year levels what can (and can not) be done becomes more important.
Visual aids are very helpful (Mathisfun.com has some good visuals here) but to introduce more visual thinking and introduce some Art into Maths (STEAM instead of STEM), I challenged the students to develop some superheroes with the powers of relevant Algebraic Laws.


The students were given a piece of paper and some pencils, and as we described Algebraic Laws, they were to draw a super hero who demonstrated the law in some way. They had a lot of freedom to use creativity. A few students decided they wanted Sports Stars and others created Super Vehicles while some were happy just sticking with various super heroes.


We started with Commutative Law. We discussed the law, reviewed some visual representation. Some students quickly had ideas, others waited for my example, which swung across the screen... it was Commutative Chimp, from the example many students started creating.



I gave the students a few minutes to get started... long enough to get an idea down, but not to finish the 'pretty' drawings. 

 All students had to pause, and then I presented Distributive Law... this time I saw more students with interesting ideas starting before I finished the visual explanation. I would usually stop them, but they were very keen and clearly running with idea so I just ensured that any other students could hear the instructions.
My second example came bounding across the screen; Distributive Dog.



This time I gave the students slightly less time. All the class had come up with interesting ideas and were very keen to show them off. I didn't want too much sharing (not yet!) so I continued on to our third and final law.. Associative Law.

Again description, then visual representation and finally a sneaky Agent Associative example.


The students were very keen to create attractive and accurate posters to describe their Super Heroes (or similar characters).

I set a timer for 8 minutes for students to see the time counting down and to manage completing their creations.
When the time ran out, I got students into groups of 3 (or less). Each group allocated a member to be A, B & C. 


I explained that we were doing a sharing Gallery (like an Art Gallery). We got all the students to BluTack their posters, with one Wall for A, one for B and another for C.
As a class, we all started at "Wall A", we reviewed the posters and could discuss with the artists. Were there any Super Powers that were incorrect? 
Did we really understand the Laws?

Really the Gallery was for checking understanding, but students were proud of what they created and we keen to share.
At the end of the sharing students were permitted to take their posters home (and many put them in their revision folder for future reference.)

In some ways it may have been better to give all of the laws upfront and let students free with them, but giving one at a time ensured focus and allowed each additional law to be a type of iteration for improvement.
I feel this was a good lesson to give students a creative outlet in Mathematics and differentiate learning for some students could repeat the teacher's examples while other could create truly new and innovative characters.



Sunday 4 October 2015

Angle Chase Quiz

After having spent some time with students learning about relationship between angles, parallel lines and internal angle of shapes, the questions all seem to start looking the same. However when I came across a series of Angle Chases on Cut-The-Knot.org (http://www.cut-the-knot.org/WhatIs/WhatIsAngleChasing.shtml) I found it quite engaging, and *spoiler* so did the kids.

One of the particularly interesting angle chases is embedded below.


I took the fourth diagram and loaded it into an online quiz (using Socrative). The Socrative quiz includes images for the students to work along with as well as give students immediate feedback on what the correct answers are (I think I got them correct). You are welcome to use the quiz by logging into Socrative.com and import the quiz SOC-16913178.

The Angle Chase allows students to build on what they have discovered through the exercise (building on the "Epic Meaning" of the activity) and presents the questions in a manner different to the way textbooks generally structure these type of questions.

From a teacher's point of view keeping a track of student's results is vital. Socrative automatically tracks the student's attempts. This allowed me to export the results and check where the students are up to (with names removed below is the report). 


The class results showed that up to angle "h" most students performed well, and then students had mix results. Angle "j" and "r" both achieved less than 30% of correct answers so as a class we discussed these angles, allowing the high performing students to explain their thought process and teach the students which did not correctly solve those angles.

Running of the angle chase took around 20mins, after which some students had completed all angles, and others were beginning to lose focus. At the end of the activity many students asked for more, so I allowed them to work through the other diagrams in Angle Chase diagram.