Thoughts after Two Months of Using Illustrative Mathematics Alongside the Desmos Curriculum

It was time for a change. Our middle school needed a new curriculum that would meet the needs of our students and provide a rich and engaging environment to learn 6-8 Math. After spending months sifting through various curricula, with a little help from edReports, we were able to identify Illustrative Mathematics (IM) as the lead contender. It was not long before we discovered that the Desmos online platform followed the IM scope and sequence very closely and that they had the potential to be an amazing complement to each other. We are now two months into using both platforms and I can honestly say we are not looking back. So, I wanted to write a brief summary of what we are seeing after the first two months of using these curricula.

1) They are amazing together

The two platforms complement each other well, not only in sequence, but in the way that Desmos is designed with IM and OpenUp in mind. You can find complementary lessons for each topic and you can decide which lesson makes the most sense for your students and your own sequence. The material is engaging and the learning is rich.

2) There is a lot of material

Sometimes too much. In the case of IM, there is a lot to cover in a 50-minute lesson, and I often have to cut some of the material to ensure I spend enough time on the main ideas. I know they have to cover enough to meet state standards, but I regularly find that I need to skip certain lessons just to get through a unit in time to move on. Desmos is often closer to being able to get through all the activities in a useful and timely way.

3) They are truly discussion based, in the best way

In the last two months, I have had some of the best conversations I have ever had in my classroom. Students have been engaged and interested as IM and Desmos use prompts such as “which one doesn’t belong”, “what went wrong”, or “which student is correct?”. These are rich conversations that spark curiosity and help my students consider the mathematics from various angles. It is a more creative and interesting way to think about mathematical ideas and it has been amazing to see students engaging with ideas they have never considered. IM pledges that “selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011)” and I believe it. Their prompts are excellent and I am already seeing deeper understanding as a result. As a side note, my students are huge fans of Desmos’s polygraph activity (the mathematical version of ‘Guess Who’) and this has seen some amazing results. They also enjoy the opportunity to create a challenge for a classmate (as long as they can solve their own problem first) and this has them engaged for significant periods of time.

4) The formative assessment you get through Desmos is unbeatable

I generally aim to know what every student is thinking at least 2-3 times during a lesson and Desmos makes this very easy to do. With its custom dashboard, it gives you the power to view all student activity and provide individual feedback to students. You can display student work on the screen and anonymize the screens to avoid embarrassment. You can compare answers with their screenshot function and instantly glance over the whole class’s level of understanding.

The Desmos dashboard makes it very easy to glance at students’ progress

5) IM is free and Desmos is very affordable!

At this point, I don’t understand why every school in the country is not jumping at the chance to use IM. It’s free and completely customizable. I have known some curricula to be prohibitively expensive and the idea that IM is completely free and a rich mathematics curriculum makes it a no-brainer to me (although you do have to pay the publishers if you want the extra workbooks etc). Desmos is also affordable compared to many textbooks and I would highly recommend this if your district has the resources.

In conclusion, barring an altogether different experience in future units, I would wholeheartedly recommend the IM/Desmos combination. With the richness of IM, coupled with the complementary manipulatives and discussions coming from Desmos, I have every hope that our students are going to fly. But, granted this is only two months in, and I could be completely wrong. I somehow doubt it.

Ten Webites I Check Before Starting Every Unit

There are many excellent resource sites out there with inspirational teachers making great resources. However, when it comes down to it, there are only a handful of websites I check on a very regular basis. To make it to this list, I am generally looking for tasks that:

• Are ‘low floor/high ceiling‘ giving access and challenging everyone at their own level
• Have multiple approaches, giving students room for creativity
• Are challenging and hence interesting
• Will give me permission to teach skills
• Make skill practice, more interesting
• Have a story for students to follow

There are many activities out there that fit these descriptions, but there is only so much time in the week. During breaks I have more time to explore but these are the sites that I can check quickly with high yield for your classroom (in no particular order):

1. Mathematics Assessment Project – A website produced from a partnership with the Shell Centre (University of Nottingham, UK) and the University of California at Berkley. Here you will find tasks that will help the common core standards come alive in your classroom. Full of rich activities that encourage discussion and investigation.

2. Standards Unit – This has been around for a while but is still one of the first publications I look at and is close to my picture of what mathematics education should like. A rich, dense set of activities that will give you great ways to work on various skills and topics.

3. YouCubed – A relatively new site that has come out of Prof. Jo Boaler’s (Stanford) efforts to encourage the ‘growth mindset’ in the classroom. I am interested in anything that comes from the idea that anyone can be good at math.

4. Open Middle – I came across this site relatively recently and am sad that I didn’t find out about it sooner. it’s tag-line is: ‘Challenging Math Problems Worth Solving’ and tips the proverbial hat to the school of thought that says that you don’t need to have tenuous links to real world problems in order to get buy-in from students. It appeals to the problem solver in all of us.

5. Emergent Math – With its routes in Problem Based Learning (PBL), emergent math is useful not only for those who want to tear up the textbook and start again with an integrated curriculum, but also for people who just want great projects that they can slot into their established curriculum. Lots of links to sites not mentioned here so worth a look.

6. Mr. Barton Maths – Lots of great resources and activities that will make your classroom a more interesting place. Enough said.

7. Tarsia – Sometimes students just need to practice. There I just said it. But using Tarsia you can avoid ‘death by worksheet’ and get students to practice without really realizing it. It also great for discussion and you can tell very quickly if students have answered everything correctly or not. For more, see Why I Love Tarsia.

8. NRich – Great site for ‘low floor/high ceiling’ problems that will challenge anyone in your classroom. Students may like to explore this outside the classroom, too. Sortable by topic and I believe they are coming out with a common core curriculum map, quite soon.

9. Dan Meyer 3 Acts Spreadsheet – Act 1 –  You show a video or picture prompting discussion, prediction and estimation as well as the all important step of coming up with the variables that are to be investigated. Act 2 – Students get the information they need to solve the problem. Act 3 – Once students have solved the problem in various ways and presented you show them the solution. There is a lot more to it than this and to pull these lessons off well is a true art form. But the only way to get better at these is to try them. So try them! More info here.

10. Mathalicious – Math lessons based on the real world problems. $185 for 12 months subscription (I think currently they are also doing pay-what you can) but well worth it. Excellent for creating the need for the math you teach.

It takes me around 90 minutes to trawl through these websites at the beginning of a unit but is well worth it when it comes to lesson planning and I know half of the activities I am going to do already. As with any of these activities they will need to be (and should be) adapted for your classes and situation but they provide an excellent starting point from which to plan.

What websites are a must-check when you are planning a unit? Leave a comment, below.

Gapminder is Awesome

I wanted something that would open up the world of scatterplots to my statistics students; something where they could really get a sense of correlation and causality. I decided to do a project based around the fantastic GapMinder World and it payed off.

First I showed this video of the master Hans Rosling at work with the graphs his foundation came up with.

I then gave these instructions to my students:

You (and max one other person) are to prepare a 3 minute presentation on a GapMinder graph of your choice.

Instructions:

• On a computer go to the gapminder website by clicking here
• Play around with the explanatory and response variables until you find two that you think show some sort of relationship
  • If you are struggling to find variables with a link, click ‘Open Graph Menu’ and play around with graphs that have already been created.
• Your presentation must include answers to the following questions
  • What are your explanatory and response variables?
  • What is the link between variables at the start (before you click play)?
  • What do you notice happens over time?
  • Are all the countries close together or more spread out? What does this mean?
  • Are there changes to any particular country that are of interest to you?
  • What if you isolate by continent? Are there any changes that are of interest to you?
  • Is there anything else that stands out with your graph?
  • Are there any outliers to the trend?
  • Does this graph bring up any other questions that you would want to investigate further? What information would you need to answer these questions? Is this information available?

Your presentation must include the time series animation (when you press play) as well as PowerPoint slides using screen shots of points of interest.

You will be graded on:

• Content (out of 6)
• Presentation (out of 4)

What went well

• This was a great way to get across a sense of scatter graphs and will be awesome to segway into taking about correlation and causality.
• This was enjoyed by the students and really got them thinking about statistics and global affairs
• It was good to give specific questions for the students to answer. In my experience just saying ‘present for 3 minutes on a graph of your choice does not give great results’

Even Better If

Next time I do this, I think it would be good to model what an excellent presentation looks like. I missed a good opportunity to teach this skill.

How to fake a Jackson Pollock

Convergence (1952) by Jackson Pollock (from about.com)

It’s the end of summer school session 1 and I wanted to give my students a taste of the beauty and power of fractal geometry. Rather than just play a TED talk (although this helped with the introduction) I wanted them to live through the process.

I know that fractal geometry has been used to spot fake Jackson Pollock paintings and thought it would be fun to look at the method behind this and to see if my students could use what they have learned to try and create their own ‘Jackson Pollock’. Here is a summery of what we did, spread out over a 2 day period (in between normal curriculum activities).

1. For a link from Geometry, semester 1 work, we used this nrich task to start them questioning what a fractal was.
2. We had a discussion on where you might see such shapes in the real world, e.g. lungs, coastlines, cauliflower etc.
3. We watched this TED talk from Mandelbrot himself (recommend using subtitles with this, he can be hard to understand)
4. Before getting crazy with the paint, we watched this video on how Pollock painted his work and how people have tried to replicate the motion
5. Time to head out to the front lawn of the school where students were greeted by a large canvas and a lot of paint where they were tasked to try and create their own Jackson Pollock, but not before reading the following quote from Nature Notes to help them think through the process, rather than just splash a load of paint around.

‘There were two reasons to suspect that Pollock’s paintings might obey fractal geometry. Moving around a large canvas laid on the ground, the artist let paint fly from all angles, using his whole body. Human motion is known to display fractal properties when people restore their balance, says Taylor, and films of Pollock seem to show him painting in a state of ‘controlled off-balance’. Second, the dripping and pouring itself could be a chaotic process. 

“Pollock was in control,” says Taylor. The large-scale fractals are a fingerprint of the artist’s body motion, he notes. “But the small-scale fractals are also to do with his choices — his height over the canvas, the fluidity of his paint, angle and force behind the trajectory, and so on.”’

The real magic was when we took a photo of the canvas and zoom in several times to see if we have replicated the infinite properties that Pollock created so well. Here is a video of the class starting the painting (and getting pretty covered in paint in the process).

Here is the end result and the zoomed-in versions.

  

I appreciate we’re not going to win any awards with this art but from a geometry point of view, I was really happy with the results and so were the students. The zoomed in photos do not look all that dissimilar to the painting as a whole.

I will be, of course, asking the school to display this somewhere. There is part of me that hopes they decline so that I can take it home with me. Apart from anything else, it was great fun!

A huge shout out to local artist, Quincy Owens, who helped me to set this up and provided all the materials we needed.

Have you done something similar? Any suggestions on how I can improve on this for the future?

What motivates my students to learn?

I used Google Forms to survey 56 of my students (I know, it sounds like a statistics textbook question already!). I wanted to know what motivated them in my classroom. The survey was anonymous and I encouraged them to be as honest as possible.

The question: What motivates you to learn in the mathematics classroom?

The response: 1 – No motivation, 4 – Highly motivating

Any other comments? (here is a sample):

• I would like to work in groups of my choice
• Competition only puts stress on me
• I find the mathematics interesting, but I feel immense pressure to get a good grade and get into college
• I like working on my own with music playing
• I need one on one help and lots of time to practice

My initial thoughts:

• Clear patterns here are motivations of getting to college and getting a good job. I wish it was the same for ‘the mathematics covered’
• Also clear is that students want lesson activities to be fun
• Not so clear is the motivation of groupwork, individual work and working on practice problems. This just highlights the diverse nature of how my students learn and how to get the best results I need to cater for different learning styles. This is an art form, for sure.
• Also interesting is that not all students appreciate competition. Even more interesting is how this graph changed with different classes. For example, for the first class that took this survey, there was an intense dislike of competition. This leveled out as the day progressed.

Conclusion:

• College and career is more of a motivator than the math. I would like this to level out somewhat; for the math to be its own motivator. I’m still working on this point.
• My students are very different in terms of how they learn and what motivates them. Some appreciate individual work, some appreciate group work. In a math ed world where the group-work-is-the-only-way team is by far the loudest, I have to remember that this is not always the biggest learning engine for all of my students.

This process reminded me of the following TED talk on ‘The Power of Introverts’. An important idea to think about if we want to tailor education to the individual student: