Why you should use Visualpatterns.org, every week

I used to teach high school. I would often see students who struggled to see:

• How to generalize patterns and extrapolate
• The meaning and usefulness of a function
• That the cartesian plane was just two number lines stuck together, useful for comparing two quantities changing at the same time
• The difference between a linear relationship and an exponential relationship

Thanks to teacher and activity creating genius Fawn Nguyen, we have a way to address this problem. I now run a visual pattern activity at the start of my lessons, every Wednesday. Just a few weeks into the semester, I am already seeing the above gaps filled!

We have started mainly by mainly using linear patterns with constant differences. Now that this link is pretty strong I have started to introduce increasing differences and they are quickly getting the idea of a curved relationship on the graph. I have created this sheet to help organize the students thinking. I give them 4 minutes to think on the problem by themselves and 2 minutes to discuss their ideas. Then as a class we ask and discuss:

• Can you describe in words, how this pattern is growing?
• What do you notice about the numbers in the table?
• What would be a really slow way of calculating the number of blocks/objects in step 43?
• What would be a quicker way of calculating the number of blocks/objects in step 43?
• Using this rule, what would step 1000 look like?
• If I saw a step with [     ] blocks, which step would I be looking at?
• If I were to graph steps against blocks/objects, what would the shape be? Why?
• Ext: What would step 0, step -1 look like?

I am quickly finding that, by accident, students are solving equations and building up a sense of the need for processes such as factoring, finding the inverse and finding the slope of a line. I have found I am able to coherently validate the need for calculus, 5 years before they take it. I believe this will really help my students when I run lessons such as Dan Meyer’s toothpick activity, later in the year. Sure this is just similar to the explicit/recursive rule section of particular algebra textbooks, spread over a year, but I think a regular discussion on this idea is crucial to making connections and getting the deep understanding needed for algebra and beyond.

I am excited to hear if it has made much of a difference, next year and into the future. I suspect it really will.

Ep. 11 feat. Prof. Jo Boaler on Having a Growth Mindset for Learning

The MathEd Out Podcast

Jo Boaler is an author/speaker, and is Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting mathematics education reform and equitable mathematics classrooms. She is the CEO and co-founder of Youcubed, a non-profit organization that provides mathematics education resources to parent and educators of K–12 students. She is the author of several books including, What’s Math Got To Do With It?(2009) and The Elephant in the Classroom (2010), both written for teachers and parents with the goal of improving mathematics education in both the US and UK. Her 1997/2002 book, Experiencing School Mathematics won the “Outstanding Book of the Year” award for education in Britain. Currently she is the Research Commentary Editor for the Journal for Research in Mathematics Education.

Jo Boaler Website

How to Learn Math: For Students

How to Learn Math: For Teachers and Parents

YouCubed

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Within 10 years, every math classroom will have one of these

It’s a cool trick, you think of something and then you can make it. But a visit to 3D printing company 3D Parts Manufacturing quickly convinced me that this could be a hugely powerful tool to help build understanding in mathematics.

Think about it:

• After considering volume and surface area of 3d shapes, you could see your ideas come to life
• After considering the coordinate plane, you could see your ideas come to life
• After considering maximization and minimization problems, you could see your ideas come to life
• After considering solids of revolution, you could see you ideas come to life

Using this well will be an art form. The temptation to be ‘hey, look how cool this project is because we used 3D printing’ will be strong. If used well, this could be an incredibly powerful tool to make more abstract ideas become more real. like an extreme version of Desmos, this visual, hold-in-your hand manifestation of mathematics will bring us ever closer to answering oh so common question, Why?

Ep. 8 feat. Dr. James Grime

The MathEd Out Podcast

James is a mathematician with a personal passion for maths communication and the promotion of mathematics in schools and to the general public. He can be mostly found doing exactly that, either touring the world giving public talks, or on YouTube.

After working in research in combinatorics and group theory, James joined the Millennium Mathematics Project from the University of Cambridge. On their behalf James ran The Enigma Project, with the aim to bring mathematics to life through the fascinating history and mathematics of codes and code breaking. Spys! Secrets! And secret messages!

James travelled extensively giving public talks and visiting schools, colleges, universities, festivals and other events, and reaching 12,000 people, of all ages, every year. Touring took James all over the UK, and the world, and involved talks for Google, Microsoft, RSA conference, Maths Inspiration, Maths in Action, BrainStem (Perimeter Institute Canada), and various science festivals. James’ aim is…

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Top Tech Tip – Rowmote Pro iPhone app ($4.99)

 

I avoid my desk whenever possible during a class and like to be moving around or up at the board. This proves difficult when my computer and powerpoints are at the back of the room and I need to change between slides. Of course I can just buy a clicker (good ones fetch $50-70). However, I looked at the app store and found Rowmote Pro ($4.99), an app that not only works as a clicker but does pretty much everything your keyboard and mouse can do.

I’ve just finished a unit on spreadsheets and scatter plots and I was able to be at the board or walking around the room the whole time whilst working a functioning spreadsheet. It was awesome.

There aren’t many apps I can say this of (if any) but I now use Rowmote Pro in every lesson and it means I can be where I want to be at any point during the lesson.

What apps make your teaching life easier?

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.

#NCTMIndy day 1 feat. Dan Meyer

The MathEd Out Podcast

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He currently studies math education at Stanford University, speaks internationally, and works with textbook publishers, helping them move from education’s print past to its digital future. He was named one of Tech & Learning’s 30 Leaders of the Future and an Apple Distinguished Educator. He lives in Mountain View, CA.

Here is a short interview with Dan Meyer following his opening session at the 2014 NCTM Regional Conference in Indianapolis

[audio https://dl.dropboxusercontent.com/u/82726094/MathEdOut/10-30-14%20NCTM%20Indy%20-%20Dan%20Meyer.mp3]

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Ep. 7 feat. Prof. Malcolm Swan

Malcolm Swan has been somewhat of a hero of mine since the beginning and so it was a great pleasure to be able to interview him for the latest episode of MathEdOut. Enjoy!

The MathEd Out Podcast

Malcolm Swan is Professor in Mathematics Education at the University of Nottingham and has been a leading designer-researcher since he joined the faculty in the Shell Centre for Mathematical Education in 1979. His interests lie in the design of teaching and assessment, particularly the design of situations which foster reflection, discussion and metacognitive activity, the design of situations in which learners are able to construct mathematical concepts, and the design of assessment methods that are balanced across learning goals – and thus have a positive backwash effect on teaching and learning. Diagnostic teaching, using ‘misconceptions’ to promote long term learning, has been an ongoing strand of this work.

He has led design teams on a sequence of internationally funded research and development projects including work for UK examination boards and the US NSF-funded Balanced Assessment project and the Mathematics Assessment Resource Service(MARS). He has designed courses and resources for…

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Walk the Line – Adding and Subtracting with Negative Numbers

I wanted an activity that would give students a deep sense of adding and subtraction involving negative numbers. Both. At the same time. I figured the best way would be for them to actually walk through what happens to a number when it goes through these operations; so began ‘walk the line’.

The idea is simple, have students walk through various sums increasing from adding two positive numbers, going through to subtracting two negative numbers, reviewing each time.

They will first need to stand in a line, then using sidewalk chalk, draw a zero on the floor and draw out a number line to the right and left of where they are in the positive and negative direction.

Here is the general dialogue that happens:

• I am going to call out a sum and I would like to see how quickly you can get to the result. You start with the first number I call out and are permitted to move before I have finished calling out the sum.
• 3 + 2 (call out slowly to give students time to move)
  • Review Questions
    • Now, what did you do when I first said 3? – Run to that number
    • What did you do when I said “add”? – Got ready to run away from zero
    • What did you do when I said 2? – Ran two spaces away from zero
• Next:  5 – 8
  • • Review Questions
      • Now, what did you do when I first said 5? – Ran to 5
      • What did you do when I said “subtract”? – Turned to face the zero (Why? etc)
      • What did you do when I said 8? – Ran 8 spaces and ended up at -3
• What about  5 – ( -8)    (call out slowly)
  • Review: What was different when I said subtract -8 instead of 8? – Had to go the other way (Why? etc.)
• At this point I bring student thinking together and explicitly clarify the rules:
  • Whatever number I say first is where you start
  • If I then say “add” you face this way (pointing in the positive direction) and if I say “subtract” you face the other way (pointing in the negative direction)
  • If my second number is positive you walk forward by that amount, if my second number is negative you walk backward by that amount (for example: 4 would be four steps forward, -4 would be 4 steps backward)
  • Let’s try this out
• 3 – 8 (call out slowly to give students time to think and move)
• -4 + 10
• 2 + (-5)
• -9 + 12
• 2 – (-5)
• -4 + (-7)
• -6 – (-10)
• etc
• Then return to classroom and do the same sort of thing but students write (just) their answers on their mini whiteboards. We review each time going through the 3 step process.

This activity really worked and students were doing this all in their head by the end of 50 minutes which is what I was aiming for. There was no separation of addition and subtraction or positive and negative numbers. They were just different points on the number line and different ways to move.

How do you introduce adding/subtracting negative numbers?

Classkick Review – Thoughts from the first day

I first heard about Classkick through Dan Meyer’s blog and thought ‘I have to give this a try!’ The idea is simple but the implications could be huge. A platform that lets you see what students are thinking and writing, in real time! It is so simple I can’t believe it hasn’t been done before.

So, as soon as I finished reading the article, I downloaded it onto my iPad and emailed my students to do the same ready for the next day. I didn’t want to go another day in my classroom without trying this out.

The punchline: It’s a great idea, but it needs some work.

The interface is clean and pleasant to use. The tutorial videos are helpful as some elements are more intuitive than others. For example, i assumed that students would sign up once to a class and after that would stay signed in (as is the case for many other education apps). But with Classkick, students will sign in to each assignment you set, separately with a different code. I think this could get a little cumbersome when I am setting activities every lesson.

The idea behind the app is phenomenal and when it worked it was magical. To be able to see what students are writing, provide immediate feedback and pointers is a very powerful tool. This could be used for in class work or for homework.

The students loved knowing that I could see their work, I could give them instant feedback and they responded very positively. They jumped into the learning from my feedback. I could not only look at their answers but circle and ask questions about mistakes in their thought processes. This is so exciting!

However, on first use I did find the app a little slow, at least from the teachers side of things. In one lesson it took around 4 minutes for the students’ work to appear on the screen when the network was working just fine. Sometimes it took a while to recognize my writing, impeding my ability to give as many students as I could, feedback. It can also take a little getting used to writing with a stylus. I found if I wrote too quickly, it simply didn’t recognize my writing at all.

This is a new app; there are going to be bugs. I for one am excited to stick with it as the wrinkles are ironed out or I find something that is doing the same thing but better. One day, this sort of app will be part of every classroom and hopefully, very soon indeed. The best of luck to the Classkick team!