Wednesday, November 22, 2017

Reflections on Midterm Conferences in "Gradeless" 9-10 Math

This post can also be found on our team's TLLP blog.

It has been an observation of mine that students are struggling to transfer the meta-cognition skills gained in other places into the math classroom. The ideas and structures I am putting onto their math learning seem to be very different than anything they have done in math before that they do not realize they have done it elsewhere. It has made for some interesting reflection on my part.

In continuing with my journey to explore student reflection I wanted to have students self-evaluate at midterm and conference with me to determine their report grade and report card comments. I set this up using an assignment on Google Classroom and had the sign up for a conference time-slot.

My grade 10s were given a reflection document that included a few things (outlined via images below).

Part 1: Identify pieces of evidence and start to identify criteria from the map that were evident in that evidence

Part 2: Highlight where evidence shows that they are for each criteria of each overarching learning goal in the course (the map is a partial map, only including the aspects relevant at this point in the course)

Part 3: Self-evaluate and reevaluate learning and next steps

When this was all said and done I opened this file when students came to me for their conference. Since I was finding that students were struggling with this process in math I ended up spending most of this time looking at their map with them and identifying areas where we disagreed so that we could discuss them. I recognize that I had not done the map justice (did not explain it well enough) and had already known that it would be difficult as it would be their first real exposure to it (I was only able to write the map myself the week before giving this assignment). Needless to say, I learned a lot - and had already planned to get a student focus-group together to help me reword the map more appropriately for students.

So next time I will:
- get students using the map earier
- rework it to use more student-friendly language
- model how to use the map
- have students evaluate using the map before midterm
- continue to build student reflection and self- & peer-assessment skills explicitly

The grade 9s I do not have a map for so I approached their reflection by having them fill in a chart while referencing the parts of the curriculum document that were relevant at this point. They were often able to identify specific expectations that they were doing well on and ones that they had to work on. What ended up lacking was them considering these expectations from a lens that expanded from just the "understand and use" - I need a way to make sure that the 9s consider the math processes as well in the future.

Overall students responded fairly positively during conferences when I pointed out things that had not considered that showed they were struggling with aspects of the course, but the discussions took a long time. The conferencing process was valuable, but I need to seek some ways to make it more manageable and to be away from facilitating student learning for less time.

Sunday, October 15, 2017

Questions Coming From "Gradeless" Math

This post can also be found on our team's TLLP blog.

Going "gradeless" (using feedback-focused assessment) has brought about some great things with students, but often leads to more question than answers about my assessment practices. If you are reading this and have any ideas or suggestions I would love to hear from you!

Overarching Learning Goals & Learning Maps

I have started my year in grade 10 math with a set of learning goals and an incomplete learning map. I went into this process with an understanding that these documents will always be working documents. Changes will be needed depending on the group of students and changing needs of the course/society/etc. I am only 6 weeks into the semester and already envisioning the need for changes just based on pedagogy and assessment policy. Some of the reasons for this will be become more evidence in the topic below.

My learning map only has descriptors for level 3, which is partly by design.
1) I couldn't figure out how to describe the learning for 4 levels since I had not even tried using these goals for standards-based grading
2) I want student language to be used on the map so really need their voice to complete it
Hopefully I can get to a point soon where I have enough student evidence to show them that they can help me with that.

The Achievement Chart

I am grappling with the achievement chart in math - I am a fan of ensuring that we are assessing using all 4 categories (for those of you outside of Ontario those are Knowledge & Understanding, Application, Communication and Thinking) but I am struggling with the "descriptors" that Ontario uses to split them into 4 levels and even more grappling with what it means to have knowledge & understanding at a level 4 (exceeding expectations) when removed from thinking. I cannot get away from the idea that to show level 4 K&U you must also be showing T.

Manageable Feedback

This is the biggest question for me in out TLLP. How do I give students the feedback in math that they need and deserve in a manageable way? If I were to do all of what I think is beneficial I would literally not sleep. When everything is in place I will try to find ways to do it a bit more electronically so there is less hand writing to do, but the idea still baffles me in such a skill-based course (with the sheer volume of skills/understanding they need).

If anyone has any idea I would love to hear them. There is only so much that they can accomplish through self- and peer-feedback.

Managing Conferencing

I love doing interviews with kids about math. It is always an eye-opening look into what they actually understand (sometimes things they have not been able to articulate on paper and sometimes finding out just how much they are memorizing and not understanding). When I was teaching senior courses I usually found the time I needed to have these conferences, but I am having more trouble doing so with junior courses. It is a to harder to get them to be automonous for 3 days so that I can have the time needed.

Any ideas are welcome!

Tuesday, September 26, 2017

Week 2/3 in "Gradeless" Math - Self & Peer-Assessment and Reflecting on Progress

This post can also be found on our team's TLLP blog.

In the second full week of school I put a lot of focus on starting to develop student's skills in self- and peer-assessment. Without these skills the idea of developing an environment that creates more autonomous learners likely would not happen (and the burden of giving descriptive feedback would fall entirely on me - and I also have a goal to get more sleep this year).

Here is the gist of the steps I attempted to take last week:

1. Give students questions to use when reflecting on their work (such as "Have I written my solution so that someone else can follow it?"). I put these on the board and uploaded a photo of them to our Google Site for student's to reference.

2. Introduce the model I am using for descriptive feedback (Acknowledge what you are doing well; Describe what your next step should be; Determine how/when you are going to work on your next step). I also put this on the board and uploaded a photo to our Site. In the future, I would like to provide students with exemplars and discuss what good feedback looks like.

3. Assign students to choose a question they have done and use the questions from 1 and the model from 2 to write descriptive feedback for themselves (and asked them to upload to Sesame so I could give them feedback on their descriptive feedback).

4. On the next opportunity I modeled how I used the success criteria to write the reflection questions for students (this time we were looking at problem solving).

5. I then assigned a question for them to do as practice and when most of them were finished I had them swap with a neighbour and peer-assess using the questions and write descriptive feedback for their partner.

6. For homework that night I asked them to choose one of the questions they did at home to upload to Sesame and include descriptive feedback for themselves. I followed up with those who posted one to give them feedback on their self-assessment.

I plan to have report conferences with students at midterm and the end of the course to determine their report grades together. To help them prepare for this I also implemented the next two steps at the end of the week.

7. I created a chart (pictured below) with instructions for students for them to use to help them summarize what we had been doing. I filled in the overarching learning goals (OLGs) that I wanted them to focus on and they needed to list the evidence they had of that learning (i.e. quiz, homework, activity) and then list the corresponding success criteria from our learning map as ether "met" or "still working on".

8. Based on the instructions students sent home an email that summarized the chart (on my Google Classroom assignment it stated that they should: Tell them what they learned/were able to do; Inform them of what is still being worked on; Summarize how the student feels they are doing so far).

Once students started to send the emails and I looked at a couple I realized I needed to get them to do a reflection portion to help consolidate a bit better. Upon this reflection I decided to add this to the bottom of these reflections.

This will make sure students are reminded to revisit their goal and will hopefully lead to students setting some relevant goals for where they are at the time.

I will definitely be continuing to get students to use self- and peer-assessment and will continue to work on using the above style reflections to see how they go. Right now the tough part is convincing all of them to complete it (I gave them time in class, but probably not enough).

Wednesday, September 13, 2017

Week 1 in Math - My Motivations & Understanding Expectations with Students

What, Why and Where

I am finally embarking on my vision of a "gradeless" classroom. What does that mean? It means that my students will receive feedback that is feedback-based. Learning becomes about learning. Grades take a step back and are determine for reporting periods.

Why am I going here? I am giving the ownership of learning back to my students. For too long I have been the owner of the learning. It was believed that the teacher "gave" marks and students always wanted to know what they needed to "do" to get an 80. The shift is simple - I give feedback based on set criteria that students need to work toward and they reflect on their learning and act on a next step to meet those criteria. 

Where am I now? In the past 2-3 years I have done some work with creating overarching learning goals and reformatting evaluations (i.e. taking marks off of quizzes, using one-point rubrics to give feedback, etc.). Ultimately these changes have led me to need to go to a fully feedback-based classroom so that I can focus on doing this well. So this year (my grade 10 classes in particular) will learn math through feedback based on 5 overarching learning goals.

Our First Few Days

After spending a period on vertical surfaces solving a problem in groups we started to attack the curriculum. I wanted students to have a chance to find out what the curriculum was and to understand the lens through which the curriculum is taught. In fact, I wanted them to own it.

The Math Processes - the lens through which the Ontario math curriculum is taught

Students were in 7 groups of 3-4 students and each group was assigned to one of the processes. They were tasked with rewriting their process in their own words. I gave them two prompting questions to consider to help with the process: What does it mean? What will it look like in class?

Groups then rotated around and had a chance to add or suggest changes to the work of the other groups. When they returned to their own group they were to look at the suggestions made and decide on their final sentence - sharing their final work in a shared document.

As a group we looked at the final sentences which was my chance to ask them questions about their choices of words. This lead to us making some changes (I tried to make sure we were keeping as much of their wording as possible) and agreeing as a class that we understood what it looked like.

Overall Expectations - the content

Students were given the curriculum for one of the strands of the course and were tasked with rewriting the overall expectations in their own words. When they were finished I had the groups working on the same strand get together and come to an agreement before sharing it on our shared doc. We then looked at it as a class.

With my second section I made a better point of talking about the language in the document, defining words they needed and talked about what words were important to leave in.

Learning Map - putting them together

I reworded my overarching learning goals to use the students words from the above and then shared my learning map with the students. The 5 goals on this map are where we will focus our attention for the semester. Instead of having 7 processes and 10 overall expectations students how have 5 goals to manage and reflect on.


While I am at a school where deconstructing curriculum is not new to grade 10 students it was their first time doing it with math "jargon" so the struggle was largely around the vocabulary used. When I do this again with students who are new to this process in math I would spend time at the start looking at math and instructional vocabulary and make sure that we know what they mean and which ones are important to keep.

Saturday, September 2, 2017

Everyone has an Opinion

As a math educator there is nothing I dread more than the wrath of opinions sent my way when standardized tests scores are released (not to mention the fact the it seems to get worse every year...somehow the media gets hold of results before they are public). Everyone has an opinion. And they are entitled to one.

But it does not make them an expert.

It is easy to sit at the sidelines and put blame on someone else - teachers, the curriculum, and the like. Currently most of them blame is on the curriculum and/or so-called "discovery math" instruction.

The Curriculum

Standardized expectations set by the ministry that is publicly available here.

Now I do not ever call myself a math ed expert. My experience is limited to Ontario in grade 9-12 with a bit of tutoring at the grade 6 level. This is the only experience I can speak from. But I am sure I could find many colleagues (elementary and secondary) that would agree that there is too much emphasis on math content. Every grade level is loaded with content that is needed and content has always been in the drivers seat. Elementary grades have to cover content in 5 areas each with a multitude of specific expectations to get to.

Flip to the front matter of either sets of curricula and you will find 7 Mathematical Processes. These are supposed to be the lens through which math is taught - and we need to remind each other of this. Perhaps a redesign of curriculum to make this front matter the meat of each grade would be beneficial. Check out BC's new curriculum - it is competency focused. I am sure it is not perfect, but frankly, it is genius.

You won't catch me claiming that the curriculum does not need to be revisited.

"Discovery Math"

I use the phrase discovery learning in quotations because it is misunderstood by most people. It is over-simplified into this little box definition and believed by many to mean that we give students a problem and then never help them. This is a myth.

I am sure that there is a lot of support needed for teachers to embrace the research behind "purposeful struggle" and I am also willing to go out on a limb and guess that there are many teachers teaching math who are not comfortable doing it (I have friends who would attest to this) and are probably even less comfortable with embracing a different way of teaching. But discovery math is not to blame.

We absolutely need learners to play with numbers and learn ways that they are related. They need to find the number sense within them. Math is not as simple as we make it out to be. It is not a bunch of facts that we memorize and use without understanding (lack of understanding leads to mistakes!) - hey you might be good at arithmetic, but this does not a mathematician make. We need to develop a future filled with people who can problem solve, use logic, reflect and communicate - we do not need a future of human calculators.

Using traditional teaching forced me to always tell kids what to do and how to do it. I could tell them why, but to them why was not important. Students got a lesson and then practiced that work. They only worked on that one skill and never made connections to other ideas. Traditional teaching forced me to teach to the middle of the class and made differentiation nearly impossible.

Discovery math allows me to do a variety of things and to differentiate my classroom. Research supports learning as a complex structure that requires much more than memorizing (and even the parts you do need to "remember" need to be forgotten and recalled many times to bring them into long-term memory). In fact, learning is one of the most counter-intuitive things I know. I bet most people can come up with at least one example of something they thought they had learned only later to realize they had tricked themselves into it - only their short term memory had any idea at the time. By using a discovery approach students have to struggle with ideas (makes learning seem like it takes more effort to achieve - because it does - but lasts a lot longer and leads to making connections to ideas already understood) but they get to do it in an environment with 29 of their peers and a learning coach to help out when the "struggle" moves from purposeful to frustrated.

Don't get me wrong. I don't have an answer. And there isn't a simple one. I cannot tell you why only 50% of last year's grade 6 students met the provincial expectations (but I can tell you that these tests are not straight-forward and disadvantage many groups of students).

I have rambled at this point and could keep going. I could justify every decision that I made in deciding how I would be running my classroom this year. We don't make these decisions on a whim. We do not do them just because someone tells us to.

One opinion writer this week wrote that the one thing that has not changed are kids - that kids are still kids, capable of learning. This is an oversimplification of a very complex discussion - I could easily disagree with her. But one thing is for sure.

We do it for the kids. Every day.