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.

Further Reading.

 

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

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

Sign up for a free Freshgrade account

Teach Math with Spiralled 3-Act Tasks – a full course

This semester was my first go at spiralling a course through problems instead of units. Traditionally we teachers follow the chapters and sections from the textbook. Well why not? It’s all laid out and organized nicely….most times in 1 day chunks….no planning needed, am I right???

How exciting is it though? How much do students really need to think? Are they really solving problems and learning mathematics.

After reading about spiralling from Alex Overwijk and bouncing ideas back and forth with Kyle Pearce we decided to give spiralling 1P math with 3 act tasks a try.

Each day or two I would  introduce to a new 3-act math problem (read Teaching with 3-Act Tasks) to solve with students. We would use that to stimulate wonderings and finally narrow down to a particular goals I wanted to cover.  Each of these lessons is taught with a 4 part math lesson (From Kyle Pearce) which always has students working on solving problems on their own FIRST, and then we step in and teach skills (“math teachery” way) after.

We did not teach within units. We mixed up our 3-Act tasks and problems throughout the semester.

I kept a list of all lessons, and order I used, along with any resources like blog posts, video files, handouts, etc. I wanted to share that list below.

Spreadsheet design was by Kyle

The spreadsheet shows for each day,

  • the strand we covered,
  • the learning goal (LG – for my assessment sheet),
  • the topic, notes for planning,
  • the inquiry lesson portion (3-Act math problem(s))
  • connections to other strands (a place for me to remind myself to tie this piece to other strands)
  • the consolidation/practice resources/links
  • other resources like blog posts, handouts, links, tweets, etc.

Screen Shot 2015-05-21 at 11.50.42 AM

You may notice the bright pink row. These are our assessment/mastery days. We had one whole class each week for this.

The first half of an assessment/mastery day class was handing back of past paper assessments that look like:

Assessment

Each one consisted of 4 questions that covered the learning outcomes of the last week or so.  I wrote feedback for any question that weren’t completed perfectly. They were to read the feedback and re-do those questions.

I let them know that everything counts…..I consider all our conversations, my observations and anything they hand in for their grade.

Also during the first half of class students worked towards upgrading their skills. They access their customized spreadsheet which shows their achievement on each of the learning goals. They choose a learning goal to upgrade. Based on their prior achievement they are given another task to try. After I assess this new task I go and change the mark for that learning goal.

Screen Shot 2015-04-16 at 4.20.29 PM

Both Kyle and I have written posts on this sheet a few times. (here, here, and here). An idea we extended from Alice Keeler.

We spend a good chunk of time working at getting better on our skills always promoting growth!

The last half of the class we do this week’s paper assessment (that looks like the one above). I mark it and give it back so that next Tuesday we can do that all over again.

Here are some benefits I have noticed from both spiralling and teaching through problem solving:

  • Almost no need to review at the end of the year. We reviewed all through.
  • Students see how math connects together. (Proportional reasoning shouldn’t stand as a lone unit when you have linear relations and algebra to teach too!).
  • Students were more confident in math than I’ve ever seen them. (And for 1P’s too!). When teaching in units, students know that whatever problem we will solve today HAS to do with what we learned yesterday. When we teach through spiralling students are always wondering what math they can use to solve the problem at hand. My students became great at risk taking! They would try! How many times has it been where we give a new problem to our students they complain that you haven’t shown them how to do this. My students were given new problems everyday and they became great a trying strategies. Whiteboards help immensely with this too!
  • A time saver! You may think that I would run out of time teaching this way…..I couldn’t possibly teach through problem solving and still cover everything, let alone booking a whole day dedicated to growth EACH WEEK! We had lots of time. Since each lesson tied multiple expectations and learning goals together, we could cover more in one lesson than we could in two lessons the old way. The growth/upgrades each week allowed students to practice skills from all over the course. Around mid-term time I gave my students an old final exam to see how they would do, and they did great!!! I was amazed. We still had half a semester to go!

Since we are coming close to the end I wanted to share my experience! Feel free to check out my daily plan from grade 9 applied

As always, if you have any recommendations or feedback for me I would love to hear about it!

 

 

Ready for round 2?

Second semester is starting tomorrow and I just wanted to get down my ideas on things I will be changing and things I will be keeping…..

New things…

I’ll be using the spreadsheet I modified from @alicekeeler. Although I plan on using Kyle Pearce’s further modified version.

I have slightly modified old my assessment approach (again). I’ll share later.

Kyle and I have been Tweeting back and forth all weekend about spiralling our grade 9 applied classes. We have been teaching using an inquiry based approach (4 part math lesson) and thought that spiralling would fit right in. We’ll keep you posted. Here is my day-to-day plan by topic and task, so far .

I’ll Continue….

a ton of stuff….but here are a few

Keeping my students curious.

Strengthening the connection between algebraic representations and graphical representations using Desmos! 

Documenting my class by taking a picture/tweet for every school day.

Warm ups – To start every class we do a warm up / starter. Most of these starters are math related but for me the most important part is that the starters allow our class to “Gel”. My buddy @Regan_bio is an advocate for always saying we should show our students that we are human and remember they are human too. Take the first 5 minutes of class and be a good human with your kids…..maybe they will be more ready to do some math!

Recently Mary Bourassa has shared her great list of daily warm ups for her grade 10 applied class. Check out her warm ups.

Here’s what we have been doing…

Monday’sEstimation180 – As a class we complete one of these great challenges (10 minutes). We track our progress on Andrew’s / Michael Fenton’s provided handout.

Tuesday’s – Visual Patterns. I choose a pattern for us to determine the equation.

Wednesday’s – Pictionary – Our class is split into two teams. They take turns drawing and guessing objects, sayings, math ideas that I have picked out. Most of the time this is a non math game. (10 minutes)

Thursday’s – Throw Back Thursday — I choose a question / skill that my class has been exposed to in the past and we work on our whiteboards on this as a review question.

Friday’s – 20 Questions. — I pick something and the class has 20 yes or no questions to try and guess what I have picked. We then play a second round where the class together picks something and I try to guess. (10 minutes).

Have an exciting second semester everybody!