Assessment

Polygon Pile Up

by Jon Orr

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

  1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
  2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

Addressing #1

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student). 

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

 

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Addressing #2

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle

Click to download a PDF copy to print.

And to really challenge yourself or your students here is a blank one. Can you fill it in so it’s “hard” to determine that indicated angle? What is the least amount of info you can give to bring out the most amount of thinking? Share them out! 

 

Being Picky – Ignite Session OAME 2017

by Jon Orr

Giving an Ignite talk can be a rewarding but also super terrifying experience. For me it was both. Session participants create exactly 20 slides which will auto-advance every 15 seconds giving a total time of 5 minutes. This year, for the second time OAME invited me to participate in their Ignite session at the 2017 conference in Kingston, ON (my home town).

I wanted to share with you my talk:  Being Picky: How we choose lessons and tools for our classroom.

You can read the transcript with slides below.

I was inspired for this talk by fellow teacher Andrew Stadel and it begins with coffee makers. Here is the super deluxe coffee maker that I was looking to buy for a long while! It has all the bells and whistles, timer, auto shut off, and even a grinder.
and then this baby slides in which is arguably the easiest coffee maker to use in the world, it has only three buttons. I had to make a decision. I wonder? Which would you choose? Why? The why is most important part of the conversation it’s what dictates your choice. That’s because we humans are picky. We’ve got lots of reasons to like what we like. We create a set of criteria based on our wants, needs, beliefs, values. I could swap out coffee makers here for
tv shows or computer choices or hair styles and you’d have lots of opinions, conversations, disagreements, maybe even regrets. How many of you had those haircuts……come on….don’t be shy! I knew you did!

We could also swap those out for our lessons and activities. It’s important that we think about what we want in our lessons to create good student learning opportunities. We need to think critically how lessons we get from others fit into our core beliefs of good learning. For me, I have four criteria I use to evaluate all of my lessons
I want ALL my students to show me their thinking and understanding in interesting ways. I want them to show me what they think first instead of just telling them what to think! I want to open up the questioning that goes on in my room. So I look and create lessons that allow for this.
I want my students to discuss, collaborate, argue, defend, and justify with each other. I believe this helps clarify their learning and understanding so I must make sure that discussion and collaboration happen in my best lessons.
I am always assessing! I’m constantly looking to see who gets what we are doing and who needs help. I need to be able to assess quickly the abilities in my room so I can use that on the fly to decide where to go next. Assessing easily must be apart of my lessons.
Every lesson or activity must have a ratio between the cost of set up and the payoff where the payoff heavily out weighs the set up. Nothing is worse than spending a huge chunk of time, making, cutting, designing and then when you run it the learning outcome wasn’t worth it. The payoff must out weigh the set up.
These are things I value in my lessons so naturally I must select lessons and tools that allow me to meet this criteria! One tool that I use regularly and meets all of these criteria is

A whiteboard. Students can easily show off their learning. They are quicker to get to writing on a whiteboard than on paper. Especially when the boards on the wall. Students get to defend, argue, justify their thinking with each other. I can easily see if students are understanding and the set up ratio is a no brainer. Here’s a whiteboard, marker….Go!
As technology advances it becomes a bit more difficult to choose what we want to use. There are literally thousands of apps, websites programs that are in ED tech and globally it’s an $150 billion dollar industry!! And I know that all of those companies out there didn’t create their software with my criteria in mind. I only want tools that fit my criteria!! So I throw away programs/apps/websites/tools that don’t meet it and keep the ones that do meet it. I want to share two tech tools that meet my criteria and one that doesn’t. First up…

The activities on teacher.desmos.com are amazing and meet my first two check points. Through carefully set up prompts my students can easily show me their thinking in a variety of ways. Their new conversation tools make it easier for us to consolidate and class discussions have never been more interesting.


It also meets my second two criteria. I can see in live time what the students are working on. It gives me the feedback I need to decide to go further. The set up can’t be easier. There are hundreds of pre-made activities ready to just click and run. Just grab a device.


Freshgrade is online portfolio tool that meets my criteria. Showing thinking through pictures is the beauty! Discussions can occur easily and assessment is a snap…which drives where we go next.


Kahoot has been pretty popular lately. Students answer multiple choice questions in a game like format competing against the rest of the class. However, It doesn’t allow my students to show their learning in interesting ways…..just a right/wrong selection. We can have discussion about the ideas but the questions are timed putting a rush on my students thinking and I don’t think that helps good learning.


Assessment is tied in but I see class scores not individual achievement. But hey, its super easy to set up!!! Since it doesn’t meet most of my criteria I decide not to spend time creating on it.


These are my four criteria for lessons and tool selection. If a tool doesn’t meet the criteria then I don’t use it. Our time is valuable. I don’t want to spend time on learning something if it doesn’t fit into they way I think good learning happens.

Going forward you have homework. You need to decide: What kind of lessons do you want in your room? And then create the criteria that will help you evaluate the lessons, activities, tools you get from co-workers, friends, online, or at conferences like this. Be picky! We trust you!

End of transcript

I’d like to thank Andrew Stadel for this post on his Tech Tool Criteria and also Kyle Pearce for feedback and  suggestions and listening to me rehearse!

What are your criteria for activities and tools? Feel free to share them with me through email, twitter, or here in the comments.

Formative Assessment & 3 Act Math Tasks

by Jon Orr

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.

Further Reading.

 

Assessment in MFM1P – Update

by Jon Orr

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

Get your own copy of the Google Sheet (You’ll need a Google account).

Sign up for a free Freshgrade account