Building #ThinkingClassrooms

Almost 3 years ago now, some math teachers in our school board returned from a conference with two concepts from the research of Peter Liljedahl; vertical non-permanent surfaces (VNPS) & visibly random grouping (VRG). I was blown away by these 2 strategies & implemented them in my classroom immediately after learning about them.

Peter tells a great story about a Math teacher saying upon meeting him “Oh, you’re the vertical surfaces guy!”. While he’s happy that teachers are finding benefit from implementing VNPS in their classrooms, he hopes those teachers will be inspired to go even further and delve into the 11 conditions Peter says will help us build “Thinking Classrooms”. A thinking classroom is . . .

“a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion” (Liljedahl, 2016)

In his chapter titled “Building thinking classrooms: Conditions for problem solving” Peter outlines 11 practices teachers can adopt in order to build a Thinking Classroom. Actually, I think that chapter proposes 9 of them, and Peter has an upcoming chapter to be released that details all 11 practices that his most recent research has unveiled. Here is my sketchnote summary of those practices:

Thinking Classroom.PNG

Building a thinking classroom:

  1. Begin with problems/tasks
  2. Visibly random groups
  3. Vertical non-permanent surfaces
  4. Oral instructions
  5. Defront the room
  6. Answer “keep thinking” questions
  7. Build autonomy
  8. Hints & extensions to maintain flow
  9. Level to the bottom
  10. Student-created notes
  11. Assessment

That last one is the one I am the least clear about what it entails. I heard Peter say in a talk that it would take him another 3 hour session just to cover that piece alone. I’m hoping that the more I explore his publications, the more I’ll learn about what he proposes for assessment as I am keen to get away from tests & make my assessment match my classroom time.

For more of my posts on Peter’s Thinking Classrooms work, click here.

Peter’s Thinking Classroom research can be found here.
He provides some “good problems” so you can start with the 1st step, here.
You can watch a 1-hour archived webinar by Peter on the topic here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Self-verbalization & Reciprocal Teaching

I’ve been selected to participate in a lesson study at my school this semester linked to Ontario’s “Renewed Math Strategy”. My homework after the first meeting was to read up on two of John Hattie’s high-yield strategies; self-verbalization & reciprocal teaching.

Our next meeting is tomorrow so I did some last minute reading & put together a couple of sketchnotes to summarize what I read:

reciprocal-teachingself-verbalization

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Studenting & Visibly Random Groups: #Sketchnotes #ThinkingClassroom

A few years ago I started using visibly random groups & vertical non-permanent surfaces in my Math classroom. I got so excited about these strategies when some colleagues brought them back from a PD they had attended and immediately changed my classroom routines & setup. These strategies come out of a body of research by Peter Liljedahl on the Thinking Classroom.

Peter came to Ottawa last week for our Math PD day. He keynoted our event as well as offered workshops, both beginner & advanced, on how to apply his research findings in our classrooms. I tell everyone I can about how much Peter’s research has changed my classroom for the better, and so after his recent visit I decided to work on sketchnoting & sharing his research.

Here are my first two sketchnotes:

Visibly random groupings:

visibly-random-groups-vrg

Studenting behaviours around homework & studenting behaviours in the “now you try one” teaching model:

studenting-homework-now-you-try-one

Stay tuned for more sketchnotes about the Thinking Classroom!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Buying Calculators Problem #MFM1P/#MPM1D #PrBL

As an introduction to linear direct variation, I put together a quick problem-based learning task that was proportional for my combined academic & applied class:summary-2017-02-15-m9-1

Scenario:

Buying calculators.jpg

What do you notice?

Capture.JPGI had to use the Pear Deck dashboard to hide some responses that involved calculating the price per calculator as this was part of solving the later problem. I suppose I could have left them up, but I wanted to leave the calculating part until later when students were in their groups.

What do you wonder?Capture.JPG

How much would it cost to buy a class set of 25 calculators?
Best estimate: ________$
capture

Solve:

You can find the Pear Deck slideshow in this folder. Also in the folder is a follow up slideshow exploring the concept of Direct Variation.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Yard Space #MPM1D/#MFM1P #PrBL

I took the typical “find the largest area given a specific perimeter” problem and created a hands-on, problem-based learning task for my combined grade 9 Math class (academic & applied combined):summary-2017-02-13-m9

Scenario:
capture
Ms. Wheeler wants to build a fenced in yard for Sally to run around in.
She buys 16 1-metre long sections of fence.

What do you wonder?

Physical & Visual Representations:

The yard must be fully enclosed. Use toothpicks to create show different ways of placing the 16 pieces of fencing (I forgot to take photos of this part but they made stuff like this):IMG_20170220_112029-01.jpeg

Draw your shape & label its dimensions:

Capture.JPG

How should the pieces be set up to create the largest enclosed area possible?

What shape offers the largest area?

square.JPG

We discussed that while a square was the largest rectangle possible, there were other shapes possible with greater areas.

How should the pieces be set up to create the largest enclosed area possible if Ms. Wheeler uses a wall of the house as one side of the enclosure?

We have some more exploration to do here. I left this pretty open and they explored various shapes. But I’m not sure they’ve drawn any solid conclusions just yet for the case where we have 1 side of the shape already accounted for.

Get the Pear Deck slideshow here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Kahoot: game-based learning

Kahoot.PNG

Kahoot is a game-based learning system for the classroom. My students love playing Kahoot; it’s a great way to practice & review material.

There are 4 types of Kahoot games:

  1. Quiz – multiple choice questions
  2. Jumble – choose the correct order of the 4 answers
  3. Survey – a quiz with no right or wrong answers, no scoring, no leaderboard
  4. Discussion – a single-question survey

How it works: The teacher presents the questions on the projector. Students (using their own device or grouped to 1 device) choose their answer. Points are assigned for correct answers, with more points for quicker responses. After each question, a graph is displayed with the results of the class, showing how many responses were chosen for each answer choice. Before the next question, a leaderboard of the top 5 scorers is displayed to the group.

Why Kahoot is awesome:

  • Increases student voice, engagement, & accountability.
  • Students get immediate feedback as to whether or not they got the answer correct.
  • Spurs class discussions; teacher facilitates discussions when results show many students are struggling with a certain question or topic.
  • Try playing in Ghost Mode where students play against their previous attempts, trying to beat their previous score.
  • There’s a bank of quizzes created by teachers to choose from, you can create your own from scratch or even duplicate then edit someone else’s.

My favourite way to play is to put the game on “randomize order of questions” and play the first 10 random questions from a large bank of questions I’ve created for my entire course as a warm-up to start class.

Here are my Kahoot question banks for MPM2D and MFM2P.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Height VS Foot length #MFM1P/#MPM1D #3ActMath

As an introduction to Linear Relations with my combined 1D/1P grade 9 Math class we investigated height VS foot length and the guinness record holder for the tallest woman:Summary 2017.02.08 (1).jpg

I asked students to measure their height and foot length and record it on a Google Spreadsheet we had up on the projector:

Capture.JPG

What do you notice?Capture.JPG

What do you wonder?Capture.JPG

I posed this question:

Zeng Jinlian was born in 1964 in Yujiang village in the Bright Moon Commune, Hunan Province, China. She holds the record as the tallest woman. She measured 2.48 m (8 ft 1.75 in) when she died on 13 February 1982. How long were her feet?

Estimate: _____ cmCapture.JPG

Students were sent in their VRG groups to their VNPS boards to solve. Here are their boards:

Since it is still early in the semester I scaffolded the activity a bit by instructing them to create a scatter plot of the data on their board to help them solve the problem. I did not however instruct them to use a line of best fit, although many groups used that strategy to help them come up with an answer. Some groups had graphs with a Height axis that went high enough to lookup Zeng’s height and find the corresponding foot length from the line of best fit. Other groups made an educated guess based on the trend the points were showing.

Each student was asked to determine her foot length based on their graph:Capture.JPG

Her real foot length was 35.5cm!

The following day students were assigned some individual practice with scatterplots on Khan Academy.

Activity materials (include a slide deck for Pear Deck) available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Chicken & Goat Legs #MFM2P #PBL

Summary (scroll down for more details):2017.01.11 summary.png

Scenario:Capture.JPG

I asked some questions on Pear Deck to get students thinking about the parameters of the problem:

captureWe discussed some of the above responses that did not meet the criteria of a total of 70 legs and why.

Students went to their boards in their small groups to solve this problem:

She has 26 animals all together.
There are 70 chicken & goat legs all together.
How many chickens? Goats?

Most groups were very unsure as to how to proceed in their solving. Most were simply guessing & checking various pairs of numbers. After a few minutes of allowing that productive struggle, when I noticed frustration setting in for some, I asked if anyone had considered drawing animal bodies & assigning legs to them? Here are the student boards:

We returned to our seats and our Pear Deck session & I put it into student-paced mode. I asked them to create the equations for the various parameters of the problem: Capture.JPG
They struggled with this so I did some direct teaching about how to build the equation for this and the next slide:
capture

Students were asked to use Desmos to graph their 2 equations & then sketch the graph and point of intersection:capture

Students were asked to develop an algebraic solution using the elimination method:Capture.JPG
Not all of my students are comfortable with the algebra still (even though we’re at semester’s end now).

I like that we used 3 different methods of solving this problem; diagramming, graphing & algebraic. I want my 2P students to know they can always fall back on “less sophisticated” methods to solve these problems at evaluation time (as opposed to the algebraic solution).

The resources can be found here (including the Pear Deck interactive slideshow).

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Flight Costs #MFM2P

I’ve done this activity once previously. I changed how I did it for this second go. I will change it again for next semester.

Here’s how it went this time …

Students were presented with this data:copy-of-lr-flight-distance-vs-cost

Students were asked:

2016.12.21 notice.JPG

2016-12-21-wonder

The task for day 1: Determine the initial value & rate, on average, for flights with Air Canada.

Some groups went to Desmos straight away. Others needed some reminding that Desmos can be very helpful with data like this.

On day 2, groups were asked to determine the distance they could fly for $500 using their equations from the previous day. I only took a photo of one group’s board that day:2016.12.22 summary.png

I think next semester I will change this up. I think I will present the name of a city & ask students to estimate the cost of flying there. Then I’ll give them the set of data for cost & distance for multiple cities, but with the first city blanked out; perhaps allowing them to adjust their estimate if they like. We’ll do notice & wonder, and then proceed to solve for the price. I won’t specify modelling algebraically but will perhaps create a Desmos activity builder they can do to practice that in the case where they don’t use an algebraic model to solve.

Activity available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)