Maths Matrix Differentiated Mastery

--Originally published at Flipping My Primary Classroom

Do you want to be more available in the classroom?

Do you want to have more time to help individuals or groups of students with their specific needs?

Good. So do I . Read on...
Every single time that I present the at Educational Technology conferences I am asked for further details as to how this Flipped Classroom Maths Matrix Mastery Program works. The audience always wants more.

It's a bit of a case of... 'The presenter was OK. A little boring at times...but this Mastery System he had! Wow. I want it!'

So - here it is.

What I'm sharing with you is a mastery system based heavily on differentiation. This is not your classic mastery system whereby students just proceed through content once they have demonstrated they have mastered it. I'm aware of such systems and I think that they are superior to the current traditional model of teaching, but the system I am sharing with you today is more sophisticated, and (I think) better for the learners.

In hindsight, the system's a little obvious. But I guess with Wi-fi, student devices, and Youtube all being sort of new, it took us a while to wake up to it. Let's step through how we get here, below.
Step One

Students are pre-tested. The pre-test is divided up into, let's say 10 questions. Each question represents a specific part of the unit. This is to say, each question on the test represents one of the 10 things that the student has got to learn in this unit. Each of the 10 questions represents one of the key content areas of the unit. For example... here are the first 3 questions:

This unit is all about Fractions. So there are 10 questions which cover all the items we want to learn about fractions for this topic. Please note there are more than the 3 questions I have pictured above. There is about 10! I just included the picture above as a small example.

Step Two
The unit is then marked. This can be marked by teacher, or as a class by the students. I highly recommend that you mark it as a class, with the student, as then they will own the learning. They will then see the mistakes that they have made and be more prepared for the unit to come. Yes. They might cheat. That's a problem. They might make mistakes. Yes. Another problem. But I think you can negotiate this as a teacher. What is far more important than these two problems is the students own the learning. Marking their work, themselves, helps them to achieve this. 

Additionally, it is very quick feedback for the student. It keeps the work relevant. 
Step Three

Now you have a marked pre-test for the entire class. Of course you have got 28 different pre-tests because each student has their own. Here is where it gets slightly sophisticated. Let's say Student A gets questions one through five correct. But they get questions six through ten incorrect. Please see below:

Let's say student B gets questions 1 through 5 incorrect. And they get questions 6 through 10 correct (unlikely, but for simplicity's sake...let's say this happened). Please see below:

Okay so now student A and student B both have their marked tests, and have got different questions right - and different questions wrong. it is time to meet the Maths Matrix. Here it is.
The Maths Matrix is a model devised by myself, Richelle Hatton, Brian Host and Eliza Lindeback during the 2016 school period. It evolved largely from models that Richelle and myself were using through the 2015 period. What it basically is, is a chart or matrix, showing a range of activities that students will be required to complete (though there are some choice areas) in order to achieve a satisfactory mark for this unit.
Let's look how students will use the Maths Matrix.

Student A has gotten questions 1 through 5 correct. They have gotten questions 6 through 10 incorrect. So student a highlights questions 1 through to 5 indicating they have already achieved mastery in that area. This means questions 6 through 10 are left blank. 
Please see below (Please note is only a demonstration for the concept...the actual matrix can be seen below.)
Student A will then proceed to go through the activities and learning videos in question 6. When the student has achieved mastery in question 6, they will then highlight question 6, indicating that they have achieved mastery in this area, and so on.

Student B will do much the same, though of course differently. Because student B got questions 6 through 10 correct they will highlight questions 6 through 10. So it will look like this:
Student B will then begin work at question 1. (I suggest the student work through the questions chronologically when they have got them incorrect.) When student B has successfully completed question 1 they will amend their Maths Matrix so that question 1 is now highlighted. 
Looking closely at the (actual) Maths Matrix below you can see that it is divided into a number of sections. Let's have a closer look at those sections now! :)

The first column is the title of the topic area. 
The second column is a learning video that I have created, and that I require that they watch in order to gain instruction about that specific topic area. This column might include a learning video that I have procured (not mine) from a third party - sometimes a professional website. This second video gives students some extra choice to determine how they would like to learn the content, from me, or somebody else. Students have made it very clear to me that they prefer multiple videos as an option for their learning, because it gives them a different perspective on the same topic area. Students are just like us. They appreciate one or two options. This is not essential. But I think it is good practice. 

The third column are the actual activities that students have got to complete with a successful pass mark in order to satisfactorily complete this topic area (this column is labelled essential). Where possible I keep these activities online for ease of student and teacher access. You will note that this column is labelled 'Essential'. This column is based on the Bloom's taxonomy area of 'Knowledge and Understanding'. It is unavoidable that you must master this specific content in order to demonstrate mastery about this particular topic area. 
The fourth column is labelled 'Application' - again this is derived from Bloom's Taxonomy (Still cool after all these years.)

In this column is a choice of learning materials for the student to engage in order to apply their  learning. This is an application section!
Once the student has completed the entire row successfully it can then be ticked (or highlighted) off.

Time for the next row!
If a student complete all of the rows, great! It is time for extension work. The last column you will see is an 'Extension' column. This should include some project-based learning activities or some higher Blooms 'order of thinking' style activities. 

This image, which you saw at the top of the page, might make things a clearer, and make a little more sense now:

Yes - this involves some considered set up.

Yes - you cannot just walk up to class and do this is in one minute. But… the advantages to this model are enormous.
1. Extreme differentiation from the outset for the students. 
They are not learning material that they already know as they engage in a basic pre-test in order to prove their knowledge (or lack thereof) immediately. Then they advance upon an educational path specific to them, pertaining to the results of the pre-test. The obvious benefit of this is that they are only learning material that they do not know. This is showing a tremendous respect for students time – and your time as well. They appreciate this. I know they do, because I've asked them.
2. This setup in your classroom now allows you to roam more freely.
You are generally not at the front lecturing - unless you want to be. And admittedly, sometimes some groups of students will want this. But...(if this is the case) it won't be everyone. It will be a smaller group. This is because all the learning material you require is really already on-line for the students to access. 
3. This model I'm outlining is a Flipped Classroom Differentiated Mastery model.
Because it is a flipped classroom, all the standard advantages of the flipped classroom apply. Briefly, this means that students can pause and rewind videos. They can learn at their own pace. They can discuss the learning without interrupting the lecturer. They can continue the learning at home. They can show their parents. By watching the videos, Mum and Dad can finally understand what the teacher is on about. The list is endless....
I'm proud of this model. It is the result of a few years of cumulative work of an entire team. I think it's got more application than just mathematics. Let's see what the future holds! :)

Matt Burns
Flipped Classroom International Faculty


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