Trying something for the first time

Over the summer, I had the chance to see Darius Rucker (and a few other country artists) in concert and one particular song lyric stuck with me. The song lyric goes "When was the last time you did something for the first time?"

Learning a new skill or idea always starts with doing something for the first time. This happens frequently in my classroom when I introduce a new concepts to the class. Students try things for the first time almost on a daily basis in the classroom when they are in school.

However, it can be challenging to try something new. Doing the same thing is comforting. The fear with trying something for the first time is that I might not be good at it or I might fail at it. People often resist change which can be thought of as trying something for the first time. What if its challenging to do? What if it takes a long time to master? What if everyone else is better than I am? What if?????

Yet as a teacher, when was the last time I put myself in their shoes and did something for the first time?

I kept that in the back of my mind for the rest of the summer. As a self-proclaimed life long learner, it was important to keep trying things for the first time.

So this summer, I had the chance to try SUP yoga for the first time.

I also had the chance to run a trail race for the first time (I've actually run 3 so far this summer).

In both activities, there was some anxiety of not knowing what to expect. But with support from the yoga instructor and friends, both events were enjoyable and I would do both again. This support system made the activities successful to me - and success was defined by me. I deemed myself successful in SUP yoga by finally standing on the board at the end of the lesson and not falling in. I deemed success in the trail run with not winning the race but simply completing it and still smiling.

As the summer holidays wrap up and I prepare to return to the classroom, I am making it a goal for the year to keep trying things for the first time. Be it trying a new activity in my classroom or trying a new assessment tool or trying a new sport, I want to make sure that I keep in mind what it is to be a student of life and keep learning! I want to remember that success, however the individual defines it, seems to always be attainable with a good support team.

So when was the last time you tried something for the first time? 

Demonstrating Thinking on Assessments in Mathematics

As we near the end of another school year, I find myself reflecting on my teaching practice over the last 10 months. A piece of "homework" we have been asked to complete has centered around assessments - reflecting on what we have done in our courses this school year. I know that one of my goals for next year is to investigate (and try) alternative ways to assess in mathematics, beyond just using a test. But before we get to that, I want to highlight a success I had on a test this year in my grade 9 (MPM1D) math course.

The unit we had just completed was on linear equations with a focus on graphing lines and determining the equation of a line given different pieces of information (2 points on the line, the graph, a line parallel and a point, etc.). The test addressed the main concepts/skills of the unit and we usually have 1 question that asks students to extend their knowledge in new ways.

Here is the example of the last question on the test.

Note: we had not discussed collinear points in class before the test - hence the definition of the word in the question.

I was amazed at the variety of solutions that students presented and how their thinking was visible but may not have matched the solution I had in mind. There were multiple ways to show their understanding!

Here are some examples of student solutions to this question:
Student #1:



Student #2:



Student #3:


It is clear in all of these solutions that the students have an understanding of what the slope of a line represents and they have not simply memorized the definition/formula. They were all able to apply their knowledge and clearly demonstrate their understanding of points on a line in relation to slopes.

Using VNPS in my classroom, I have been able to observe student thinking throughout the year. This type of question on a test shows that thinking is also possible to be seen on assessments. Furthermore, I sometimes get stuck trying to create "thinking" questions on test attempting to make them the "hard" questions on the test. This particular question helped clarify for me that these "thinking" questions do no have to be particularly harder than other questions. They should, however, be open-ended enough so that students have different entry points to the question that allows them to showcase their understanding of the content. This will be a lens that I will use when creating assessments next year!

Random groupings - allowing voices to be heard

I'm fortunate to teach in classrooms that have white boards around the room. This means students in my classes are often working at Vertical Non-Permanent Surfaces. I've blogged before about the wonders of VNPS but have recently discovered the power of using randomness for assigning groups.

Last week, my department head came to observe one of my classes and he happen to come by as the class was getting started. Students were working in groups and were solving several non-right triangles. It was a review class for their upcoming test. In this class, I assigned students to groups based on ability level - I created mixed ability groups. Because this was a review period, my purpose for assigning groups in this way was to make sure that each group had an expert in the group to help support each learner.

During my debrief of the lesson with my department head (@Domanator19) asked why I chose groups in the way I did and we had a good discussion about the benefits of random groupings. I know they are beneficial and look forward to hearing about them even further at OAME2018 however I was reluctant to use them in this class. I wasn't sure they would be beneficial for every learner. At the end of the debrief, I made a mental note to try using them in an upcoming class.

Today, I used random grouping for the second time in a row with the same class and had a powerful "AHA" moment.

For information purposes, groups were working on problem solving with the midpoint and length formula:
1. Find the length of the line segment from A(-3, 15) to B(5, 12).
2. Find the midpoint of the line segment from C(6, 10) to D(17, -4).
3. G is the midpoint of the line from F(-6, 8) to H(4, 19). Find the length of the line segment from G to H.
4. Point M(-8, 15) is the midpoint of the line segment from L(-15, 2) to N(x,y). Find the coordinates of point N.

My "aha" moment came when I noticed students that were often quiet in class were now contributing and talking to their group members. When I purposefully make groups of mixed abilities, the strong students often spoke up and directed the conversation. They sometimes took over the problem and presented their solution as the one and only solution. In these situations, quieter students or students that did not have as much confidence in their ability often had a more passive approach to learning. They didn't have time to digest the problem before the solution was on the board. Today, using random groupings (I generated my groups using https://www.randomlists.com/team-generator) these students were randomly placed in a more uniform ability group and had their voices heard. Today, these students had the chance to lead the solution and present their understanding. All students walked away from the lesson with a deeper understanding of midpoint and length.

I guess you can now say I'm converted to using random groupings!

How am I resilient?

"The only real mistake is the one from which we learn nothing." - John Powell

"You miss 100% of the shots you don't take." - Wayne Gretzky

"If at first you don't succeed, try, try again." - Thomas H. Palmer

These are all famous quotes that I often hear and have often said. I've often read about and heard talks on helping students in our current classrooms to be resilient. Merriam-Webster defines resilient as "tending to recover from or adjust easily to misfortune or change".

However, making mistakes, failing, rejection... these concepts are often associated with negativity in our own lives. How many people are anxious just reading these words? How many of us are resilient when faced with these ideas?

I write this post as I ponder on my own resilience. 

Today, the 3rd cohort of the Desmos Fellowship was announced and I was not one of the lucky 40. I am disappointed and wonder what I could have done differently in my application.  So how am I going to be resilient? 

I fret hitting the "Publish" button on this post. How will I be resilient if someone challenges one of my ideas? 

If I want my students to be resilient, should I not be modelling resilience as well? In my teenage years, my father would often be heard saying "Do as I say, not as I do." This was especially true when I was a young driver and my dad was nervously sitting in the passenger seat. If I am not able to be resilient, am I not just telling my students "Do as I say, not as I do."? 

So what does resilience look like for me? Just a few things would be...

I will re-apply next year for the Desmos Fellowship and for other PD opportunities. There is still great learning from the application process and reflecting on my teaching practice. This would be similar to a student not making the team and trying out again next year.

I will teach with my classroom door open and invite colleagues to visit my classroom as often as possible. I don't just want feedback when I think the lesson is perfect - I want continuous feedback along the journey. This would be similar to students showcasing their work and not just focusing on the perfect product. Using VNPS in my classroom allows this to happen frequently.

Memorizing or understanding?

My Grade 10 Academic class wrote a unit test this week assessing student's knowledge of quadratic relations when the equation is given either in vertex form or factored form . 
They were expected to 
- graph the parabola given the equation in either form, 
- determine the equation, in either form, given details about the parabola

Here is an email exchange I had with a student while they were studying:
  
Student Question:

I was looking through the review that you handed out to us, and as I was going through it, I had never seen over half of the questions on it. 

Some of the questions that I was completely confused on were:

Please let me know if questions like these will be on the test, as I have never seen any questions like these in the work that we have done leading up to the test so far.

My Response: 

1.

We have seen questions like this. Rewrite it as . This is a parabola that opens down and has a vertex at (0, 9).

2.

Not a focus on this test. We will see these in Unit 4.

3.

Not a focus on this test. We will see these in Unit 4.

4.  
We have seen questions like this. Rewrite it as . This is a parabola that opens down and has a vertex at (3, 7).

5.

We have seen questions like this. This is the equation in vertex form however the vertex has fraction values . 

Student Reply:

I did not know that we were able to re-write equations, as well as I did not know that x and y values could be fractions that large.

Thank you very much Ms. Gravel!

The reply took me by surprise. Because none of the examples I used in the unit had the vertical shift come first, the student had memorized the "formula" for the equation and not understood the separate parts of the equation. (Disclaimer: Most of my lessons did involve investigations however all the written examples had the equation in the same order).

I shared this exchange with a colleague and they recalled a similar experience with one of their students a few years back. My colleague was teaching the Pythagorean Theorem and a student stated that his example


was not a right triangle.






After many minutes going back and forth, the student finally exclaimed that it wasn't a right triangle because it wasn't in this orientation.



It was then, like for me in this situation, that my colleague realized that he needed examples of right triangles in all orientations to emphasize understanding and not memorization.

Food for thought for the next unit...

Students reflecting on their learning

In order to take the emphasis off of the final mark on the unit test, my colleagues and I decided to try something new in our last grade 9 unit. We were going to have the students reflect on their learning before seeing their final grade on the test.

The day the students wrote the test, we photocopied their completed test before grading it. On Friday, students were provided with the photocopy of their own test and a sheet that looked like this:

They then spent the class time working through each question identifying what content of the unit was assessed in that question along with a reflection of how prepared they felt for the question. 

At the end of the period, students were provided with their graded test. 

Some of my take aways from the activity:

-  Students focused more on their own solutions and not just the number of marks they got. Often students who do well on the test only focus on the few questions that contain mistakes and do not take the time to reflect on what they also did well. 

- The conversations between students were focused on learning and not just on marks. If two students got different answers, they worked together to determine where the mistakes arose.

- When the marked tests were returned, there were no surprises or emotional responses to lower than expected marks. And as mentioned above, the students who did well looked through their test with a critical eye as opposed to seeing a good mark and filing it away in their binders. 

I'll admit that this was in reaction to students writing the test and identifying that they felt it was a challenging test. In the future, it would be beneficial to have students go through this reflection activity before the test (even before the review period) so that they can focus their studying on the content of the unit where they feel least prepared. It is definitely something that I would consider doing before the final exam. 

Finally, we did have the benefit of having time to use a class to go through this process. In other units, I hope to use this same reflection activity but may have to assign it for homework the day before I return the test. I could envision students going through this process at home and arriving to class with an educated guess as to how they think they did on the test. 

MDM4U Games - choosing player A or player B

The last few classes have been used to consolidate the concepts we have been working with thus far. Students were asked to ensure they had a definition in their notes for: probability, bar graph, histogram, probability distribution, random variable, discrete random variable, continuous random variable, and probability histogram. I did hand out a worksheet to practice probability and measures of central tendencies. 

Today we played several short dice games (I created these off the top of my head looking for some that have an equal probability of occurring and others that do not). Students were paired up and played each of the following games recording who won each game. 

Game #1:

• Roll the pair of dice. (2 standard dice)
• If sum is Even, Player A gets 1 point
• If sum is Odd, player B gets 1 point
• Play the game 10 times

Game #2:

• Roll the pair of dice. (2 standard dice)
• If the product is Prime, Player A gets 5 points
• If the product is not prime, Player B gets 1 point
• Play the game 10 times

Game #3:

• Roll the pair of dice (1 6-sided dice; 1 12-sided dice)
• If the sum is even, Player A gets 1 point
• If the sum is greater than 7, Player B gets 1 point
• Play the game 10 times

Game #4:

• Roll a set of dice (1 6-sided dice; 1 30-sided dice)
• If one number is even, Player A gets 1 point
• If one number is odd, Player B gets 1 point
• If both numbers are even, both players get 1 point
• If both numbers are odd, both players lose 1 point
• Play the game 10 times

Game #5:

• Roll the pair of dice (1 6-sided dice; 1 12-sided dice)
• If one number is prime, player A gets 2 points
• If the sum is less than 6, player B gets 3 points
• Play the game 10 times

Game #6:

• Roll the set of dice (2 standard dice)
• If the sum is odd, Player A gets 1 point
• If the sum is greater than 10, Player B gets 1 point
• If the sum is less than 5, both players lose 2 points
• Play the game 10 times

Game #7:

• Roll the set of dice (2 standard dice)
• If the product is less than 10, Player A gets 4 points
• If the product is greater than 18, Player B gets 4 points
• If the product is between 10 and 18, each player loses 2 points.
• Play the game 10 times

We gathered the data as a class to see if Player A or Player B had an advantage in each of the games. Based on our results, only game 6 had a clear advantage for player A - all other games were pretty even.

Students were then asked to determine the probability of each player getting points in each game. An interesting outcome was in game #2 where the probability of player A getting points is MUCH less than player B but our class results when playing the games showed that each player won the same number of times. 

This lead nicely to the start of a discussion of fair games and realizing that it is about more than just the probability of an outcome but what the point values are in a game. 

Our next class will be used to define a fair game and look at the mathematics behind determining if a game is fair or not.