# How Small Nudges Could Have A Big Impact On Math Education

Do you ever notice that many decisions are secretly being made for us? You probably missed them like I did.

Consider this: Last Friday, and much like every Friday our math department headed out for a quick snack and recap of the week at one of our favourite restaurants. We enjoyed stories from a week’s worth of lessons and working with students while looking forward to new stories for the upcoming weekend. Like every Friday when it’s time to leave I get the bill. What do you notice?

The tip was suggested for me!

I didn’t have to think too hard about what to leave. The restaurant has made it real easy for me to include that good tip. How many more tips do you think this restaurant earns compared to other restaurants that don’t have this feature? A bunch more is the answer.

Here’s another example of a subtle suggestion that has a big influence on our decisions. Have a look at this image taken at the University of Pennsylvania.

We have to do a double take and think about what side to place our trash in. We are pushed to consider our trash placement instead of just tossing it in a bin. A subtle suggestion that influences our decision. Recycle or Landfill?

Both of these scenarios didn’t just happen by accident or without careful thought, both are using a branch of behavioural economics to influence decision making called Nudge Theory.

From wikipedia: “A Nudge is a concept in behavioural science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals.”

If we go back to the tipping example: the suggested tip amount on the bill is a small indirect suggestion for me to give a good tip. The restaurant has made it real easy to leave that tip (they did the math for me). Also notice that they didn’t provide tip amounts less than 15%. They nudged me to make a tip of 15% or greater! They nudged me to choose the behaviour that was favourable to them.

In the garbage bin example the creators drew your attention to the negative impacts of putting items in the garbage side. If you toss on the garbage side that trash goes directly to the landfill. They nudged you, very subtly, to think before you toss trash.

The basic idea behind a successful nudge is to make it very easy to do the favourable behaviour and hard to do the unfavourable one. It was easy for me to make a tip of 20% and harder if I wanted to tip less. It was easy for us to make a decision to recycle because choosing the alternative was something we generally want to avoid: filling landfills.

Nobel Prize winning economist Richard Thaler along with Cass Sunstein brought Nudges into the forefront in 2008 with their book: Nudge: Improving Decisions about Health, Wealth, and Happiness and I learned about it from the Choiceology Podcast episode: The Big Impact of Small Changes by Dan Heath. In that episode Heath outlines a great example of a nudge: the power of the opt-in versus the opt-out.

In Austria, more than 90% of their citizens are organ donors. In the neighbouring country Germany? Less than 15%. Are Austrians that much more conscience about organ donation? Nope. In Austria citizens are auto-enrolled in the program and have to opt-out if they would rather not be a donor. In Germany you are not auto-enrolled and have to opt-in to be a donor. That’s a nudge! A small subtle change can have big outcomes in decisions. Auto-enrolling capitalizes on our laziness factor. It’s easier if we do nothing compared to doing something.

“It’s a question of putting the best outcome along the path of least resistance and letting your automatic system do its thing.” Mark W Riepe writes regarding nudges.

What implications does Nudge Theory have in the math classroom?

### Nudging in Math Education

In my opinion one of the most poorly designed calculator features on my smartphone is the percent button.

Students often misuse the % button the calculator and are not sure what is going one behind that it. It’s like a black box of percent calculation. Many misconceptions arise in my grade 9 applied class when students use this button without knowing the math behind it.

Compare that to what Desmos is doing.

Desmos has auto-added the word “of” after the percent symbol. There is no way for a student to delete the word of. It’s stuck there. It forces us to think about how we use that button. Both teachers and students are now auto-enrolled in finding the percent of a number before doing anything else. It’s an amazingly small change that has a huge impact on learning. They have made it easy to do the right thing. And impossible to do the wrong thing. That is a nudge!

Have you seen these charging stations for phones in classrooms?

Teachers are making it super easy for students to choose to put their phone away if it’s a distraction to their learning. A student will gladly get the juice and put that phone away for an hour. Nudge!

I want students to regularly self assess their learning in my classroom. I want them to be more accountable to get what they need. I make it very easy for them to see their own progress on the learning goals in our course. By auto-enrolling them in their Freshgrade portfolios student can access all the learning goals anytime and work towards showing improvement on them! It’s my way of giving them a nudge to make good decisions regarding their assessment.

What kind of nudges are you trying?

What are you doing to make the right behaviours easy and the wrong ones hard? What are you doing to affect choices your students make in your classroom?

# Gaining Insight

As the year closes down I think back on 2017.  I was curious about some of the stats on this site and was blown away at some of the numbers. I never thought that when I started sharing what goes on in my classroom that I would have over 150000 views in a single year! Amazing….and thats all because of you! I dug a bit deeper and found the three most popular posts from this year.

At first glance I thought, “Yeah, those top 2 posts make sense. Their kinda gimmicky and fads. We search for those relevant topics our students are into; games and bottle flips! I’m sure if I wrote a post on fidget spinners it would be up there too.”But after thinking back on those activities and comparing them I think both their value come from being able to gain great insight into student thinking. And it’s that ability to assess our students deeper thinking here that teachers are drawn to.

Take the Angry Birds lesson for example, the creativity that is embedded  throughout the lesson is everything. Students get to choose how their flight paths look and act. There’s a story behind every arc they put into their activity. Their thinking can’t help but spill out all over, and I get to use that knowledge I gain to help push them along. Take away the angry birds and you still have a great creative lesson.

Replace it with a drawing, or trace of a picture or even a marble run and students experience the exact same creativity and learning goal expectations. The activity still allows me to have those insightful conversations.

The bottle flipping activity is a formative assessment gold mine. Again take away the bottles and replace with paper balls or card tossing and this lesson is identical, and I have just as much success at seeing into my students thinking.

It’s this insight that we all want. It’s this insight we need. Insight allows us to what Kyle Pearce and I have been calling ignite our moves. Seeing how a students thinks in live time allows us to act. We may act to address a misconception. We may act to push learning further. We may act to plan our next lesson. We may act to change our planned lesson into something that the students need at that moment. Lessons that allow insight into student thinking must be our norm.

This fits with the 3rd top resource. Spiralling Grade 9 Math. The file found on this post give us a day-by-day to teach with lessons just like the ones above. Not gimmicky lessons —  Lessons that spark curiosity! They are lessons that provide great insight so I can ignite my moves and fuel my students sense making. And fuelling sense making has to be our main purpose.

Have you used any of these resources? Comment below to share how?

# Formative Assessment & 3 Act Math Tasks

This post references the 3-act math task structure. If this is unfamiliar to you read about it here from Dan Meyer, and here from me.

A common question I get about using 3-act math tasks from teachers is “How do you assess that?” And I’ve found it’s both hard and easy to answer this question mostly because for the last few years I’ve felt like I’m ALWAYS assessing!

Let me explain.

“3-act tasks are formative assessment machines.” They’re naturally structured to give you the teacher rich information about your students understanding and knowledge.

From Wikipedia,

Formative assessment is, “a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment.”

Keys words: “during the learning” and “modify teaching

When I first started teaching I asked about the difference between formative and summative assessment. I was told to think of it like: formative assessments were quizzes and summative assessments were unit tests. Both of which were marks that got recorded in a markbook. It was like the going mantra was, “Why are we marking it if I’m not going to count it?”. I’ve grown to believe that formative assessment isn’t just a packet/booklet/worksheet/homework/quiz that we count or don’t count for marks…..Formative assessment should inform us.  It should give us information to use to help craft our next instruction.

### 3-Acts and Formative Assessment

A teacher while observing one of my lessons commented: “Wow! Your students were so engaged during that task with the movie.” Most teachers I see are seeing 3 act tasks as a way to engage our students. In my opinion thinking that the power of 3 act tasks starts and ends with student engagement greatly undervalues the task structure. As a teacher you can learn so much from what your students show you during those first two acts. You just have to listen.
Those acts are all about assessing where you students are and designing, on the fly, where to go next!! And I totally I agree, That is definitely hard! It’s hard to plan to be flexible.

“plan with precision so we can proceed with great flexibility.” – Tom Schimmer

Act 1 is about  Being curious, Wondering, Estimating, and being informal. Listen to their estimates. Insist on having students share their reasoning. Don’t let them off the hook when they say “I just guessed”. You gain valuable feedback on their ability to use our Mathematical Processes. Listening to their reasoning will give you insight into possible strategies they will use when solving the problem. It will help you prepare on the fly possible scaffolding questions to push your students thinking.
Act 2 is for watching what your students do. This is your chance to carefully craft a plan. What strategies did you see? What strategies need to be shared and discussed? What strategies didn’t see and need to be introduced and modelled? For me, gone are the days where I develop a “lesson plan script” that I follow for the first 25 minutes of class. I need to know where they are before proceeding.

Let’s consider the proportion problem Turbo Texting (See the whole lesson here). See the act 2 video below.

Have a look at the student work after showing act 2.

What do you see? What information does this tell you? What would you ask this student?
Does the student know why they divided? Do they know what the 0.1125 means? Can they interpret to see who is faster? How can you use this to help craft your instruction when you bring the class back together?

Then when you see this answer, it’s clear that they knew how to interpret their calculation, but also informs you that you’ll need make sure both of these solutions are shared to the class. A great class discussion can occur here on how each solution shows who is faster and why we would want to find each rate.
Without allowing your students try their own strategy here in Act 2 it is most likely that both of these calculations would never have popped out. It’s allowing your students to show what they know that allowed for this discussion to happen.
Or take this example from the popcorn pandemonium task (read here first). View Act 2 here:

and a student’s thinking,

and another,

If the learning goal is to “Connect various representations of a linear relation” then seeing this strategy from our students allows us to take what they know and connect it to something new! We should build on their understanding not dismiss or overrule it. This can be powerful in their learning process. But without seeing their thinking first you wouldn’t know exactly what to build onto. To help our students the most we should be continually assessing where they are and where they need to be then design our instruction to make that happen. 3 Act tasks are amazing structures to assist you in this journey, they’re not just videos to engage your students……they’re so much more than that. Go ahead…… plan with precision.

# Assessment in MFM1P – Update

Here’s a short update on my grade 9 applied course. I’ll try to explain this as clearly as I can…bare with me.

An integral part has been our weekly mastery days. I’ve written about those days along with the tools that make them possible here. These days have been so important to our learning and we will definitely be doing them again next semester.

### Allowing For Differentiated Learning and More Student Accountability.

Having these days allows students to have more responsibility in their learning not less! We are using a web based and app based tool called Freshgrade (You can read about how I set that up for mastery days here – this post will be mostly about the benefits). On our mastery days students have to scan through their portfolio and decide which learning goals (expectations) to improve on….then, they, the student, has to go and make that improvement happen (Each LG in Freshgrade has links to questions for them work on). So our mastery day is filled with students all working on different expectations from the course — according to their need. With the encouragement I give them they know it’s up to them to work towards mastery on each learning goal.

Student view of a learning goal to improve:

An activity in Freshgrade I’ve called a learning goal. Each one shows student achievement and next steps to improve.

### Capturing Growth Informs Instruction & Assessment

The portfolio tool in Freshgrade is amazing. It captures and holds all of their work. It provides me great insight into their learning. As students work to improve their learning goals (expectations) they upload pictures of their work through the app. I get to see that work and provide audio or written feedback also through the web/app or in person. What I love is that I get to see all that interaction for each learning goal (expectation) forever. I can see the growth that my students are making. My old spreadsheet tool never tracked past work…only most recent. I love being able to see a student’s thinking progression as they attempt problems. It makes me as a teacher more confident about that student’s ability on the course expectations.

For example, this student uploaded a picture of their work on solving a proportion. They were confused on the nature of proportional relationships. After a comment and talking with the student they made corrections and re-uploaded. Their next step is to attempt a new problem to show consistency. That progression of learning stays in their portfolio for us both to see!

A student view of their portfolio:

Can’t see the video? Click through to the post

Capturing all of their progress and achievement in Freshgrade also provides me a ton of data. Since I set up the categories in Freshgrade to be the strands from the curriculum and each learning goal is assigned to one of those strands I get to see my class’ achievement on those strands. For example, If I filter the activities (learning goals) to only see the ones for linear relations I can see if we need to work more on linear relations. This has been great in the spiralled course. We can spend more time on what we need.

Gradebook view showing learning goals and student achievement.

I hope I explained our mastery day process clearly……now, onto an updated day-to-day plan for MFM1P.

### Planning:

Each semester I’ve spiralled I’ve kept a spreadsheet that outlines my day-to-day. In the links below you can see those outlines in detail. I’ve included each semester on it’s own tab.

Webpage view of the outline