Showing posts with label perspective. Show all posts
Showing posts with label perspective. Show all posts

Friday, August 6, 2021

Leadership: New Teachers and the Ethical Standards

    In Ontario teachers are governed by the Ontario College of teachers. Part of being an Ontario Certified Teacher (OCT) means that you are held to the standards of practice and the ethical standards, outlined in the hyperlinks provided.

There is so much to learn as a new teacher. It is flat out overwhelming - even when you have dreamed of becoming a teacher for years and feel you were born to do it, once you get started and really see how much there is to thinking about and consider; the learning curve is steep. 

Here I will analyze the ethical standards in the context of Growing Success to show how it is embedded in the 2010 policy. By following the assessment & evaluation policy, you are upholding the ethical standards (care, respect, trust and integrity) of the Ontario College of Teachers.

Care

"The ethical standard of Care includes compassion, acceptance, interest and insight for developing students' potential. Members express their commitment to students' well-being and learning through positive influence, professional judgment and empathy in practice."

"Developing potential" and "professional judgement" make me think a lot about the purpose of assessment: to improve student learning (Growing Success, pg 6). If you are working to improve student learning through a genuine desire for success for each individual student you will show compassion and interest for developing student potential and you will be committed to student well-being. In addition, the phrase "professional judgement" appears in Growing Success fifteen times, starting on page 2.

On page 8 of the policy (which is providing context for the fundamental principles of assessment and evaluation) it states, "In their important professional role, teachers show students that they care about them, and model a love of learning that can deeply influence their lives."

Respect

"Intrinsic to the ethical standard of Respect are trust and fair-mindedness. Members honour human dignity, emotional wellness and cognitive development. In their professional practice, they model respect for spiritual and cultural values, social justice, confidentiality, freedom, democracy and the environment."

The first of the seven fundamental principles of the Growing Success policy is that "...teachers use practices and procedures that are fair, transparent, and equitable for all students." Additionally, you can only have a sound handle on assessment & evaluation when you are able to build trust with students and parents.

On page 147 the policy defines its use of the word equity as "A condition or state of fair, inclusive, and respectful treatment of all people. Equity does not mean that people are treated the same without regard for individual differences."

Trust

"The ethical standard of Trust embodies fairness, openness and honesty. Members' professional relationships with students, colleagues, parents, guardians and the public are based on trust."

Some of this is addressed above in the analysis of Respect, as it uses trust and fairness in its definition. Moreover, we can build trust through openness by making sure to be transparent in our assessment practices. Another of the fundamental principles states that "...teachers use practices and procedures that are communicated clearly to students and parents at the beginning of the school year or course and at other appropriate points throughout the school year or course."

Page 2 (the Introduction) also uses the term trust: "Successful implementation of policy depends on the professional judgement of educators at all levels, as well as on educators’ ability to work together and to build trust and confidence among parents and students."

Integrity

"Honesty, reliability and moral action are embodied in the ethical standard of Integrity. Continual reflection assists members in exercising integrity in their professional commitments and responsibilities."

We use a criterion-based approach to assessment and evaluation in Ontario. It is important to understand what this means and to use this approach, as this is how we help students to make progress in a reliable, research-based approach. When we fail to maintain a criterion-based approach to our curriculum we are comparing students to each other instead of evaluating their learning based on the expectations themselves.

When growing success defines professional judgement it states that " In professional practice, judgement involves a purposeful and systematic thinking process that evolves in terms of accuracy and insight with ongoing reflection and self-correction" which highlights the importance of ongoing teacher reflection.

Wednesday, July 28, 2021

Leadership: Why Every Teacher Should Be a Researcher

    The theme of this module in our course was teachers as researchers. While my previous entry was specifically about action research (AR), ultimately it is important for all teachers to think of their work in the classroom as research and to be intentional about using a framework and making decisions based on data.

Action research uses the following process:

Phase 1: Planning (Come up with a testable question, do some secondary research, design the process) 

Phase 2: Action (Complete the primary research and data collection cycles)

Phase 3: Analysis (What does the data show?)

Phase 4: Conclusion

and from phase 4 we can cycle back to phase 1. Ideally action research would be completed collaboratively (and there are other models we can consider, such as Collaborative Inquiry, which ultimately have a similar process and the end goal - to try new things and learn from it - is the same).

If we are not able to engage in formal AR (collaborative time is not always given, common goals may not be determined) then we should make a best effort to engage in this process on a smaller scale for our own educational practices. I can see this process being used in two ways. Many educators likely are doing this very informally, but we could all benefit (as would our students) from thinking about it in more depth and making sure to complete the process.

In our day to day teacher we are constantly assessing student learning, collecting data and making decisions based on that data. Often this process is based on intuition and anecdotal data that is not tracked. This does not make the  process wrong, but likely we could be making more efficient decisions to improve student learning by being more intentional. I see this process as:

  1. Plan a lesson including intentional decisions for assessment for and/or as learning
  2. Do the lesson and collect the data (it could be fully collected such as a simple exit ticket using Google Forms/Quizzes or it could be as simple as using a thumbs up/side/down survey where you jot down the counts)
  3. Reflect on what the data tells you (record your reflections, especially if it informs something to do differently in the plan next time)
  4. Make an informed decision about student learning and use it to inform the next cycle
By using the process more formally on an individual basis we making an effort to limit our biases (which we all have - and what makes them a bias is that we often don't recognize them).

On a larger scale, as educators we often have a goal for ourselves for a semester or school year. Sometimes this goal is more personal in nature (i.e. to improve work-life balance) and sometimes it is purely about student learning (i.e. to improve on giving descriptive feedback). Although this goal may not be a collaborative effort we can still engage in a more formal process to work through this goal. We are more likely to hold ourselves accountable and, I would guess, are more likely to succeed. The point in both the day-to-day example and this is the same: be intentional!

Plan (don't skip the research)
Collect the data
Reflect (write it down)
Make informed decisions

Where this can (and does) become difficult is that by not being collaborative we can remain stuck in our isolated classrooms. It becomes important to have conversations with others in the building about your work to keep away from that bubble and to seek feedback from others. If we all engage in work like this it will start to lead to some meaningful collaboration, or at least will allow us to support each other in individual endeavours!

Friday, July 9, 2021

Leadership: Inspired to Learn!

    This entry is for my Teacher Leadership course and we were asked to take any topic from the module that resonated with us and describe it along with "its importance to being a pedagogical leader."

One of the candidates in the course has inspired my own learning when they created their AQ course outline titled "Nurturing Learners in the Classroom." The purpose of the course is to learn more about:

  • Science of learning
  • Factors contributing to student learning
  • Myths in learning
  • Executive functioning
  • Content retention
  • Educational system models
  • Teaching students about the brain and growth mindset
The above topics are all ones that I have explored (or at least asked about) in the past and these ideas have sparked me to want to start to dive a little deeper into one or more of them again.

Too often we think of teaching and pedagogy as being based on the topic we are teaching. Too often we make it through our B.Ed programs and still do not really know how people learn or what is required to build classroom cultures and school systems that are actually equitable. It is actually vital to being a good teacher to understand how humans learn (and how this is different depending on developmental age) and to analyze and reflect on our own teaching using this lens.

If you are going to be a pedagogical leader (which can be thought of as "supporting teaching and learning. It includes instructional leadership—supporting classroom teachers in their key role of implementing curriculum" according to Michael B. Abel) then it should be considered essential to understand the science of learning and how we can best take advantage of what we know about the human brain to be effective educators and to lead others into using these best practices.

Thank you, Rachel, for inspiring me to further my learning and return to parts of education that reignite my flame!

Sunday, July 4, 2021

Leadership: 10 Admired Leadership Qualities

    I am currently completing my Teacher Leadership Specialist AQ and it has brought be back to blogging. I am hoping that it will serve to help me build some momentum and bring life back into this blog after some time away. So bare with me a little while I get my writing legs back under me!

Leadership is a complicated thing, and as teachers we are often informal leaders among colleagues and friends. Here are 10 leadership qualities I admire in others and am striving to make qualities that I see in myself:

  1. Build relationships!
    My outgoing department head is very good at making this a priority in his leadership. He always remembers to ask how things are going before he dives into the work and our department meetings always put an emphasis on getting to know each other before sharing information or diving into the learning. This is something I always have the intention of doing, but my outcome-focused personality tends to take over - so it is a work in progress!

  2. Be a conversational wizard!
    My former principal was fascinating to watch. She could take a conversation likely to get heated and turn it into a calm moment that resulted in a plan of action. I am still not entirely sure how she did it but the foundation of her approach was to allow each person involved to be heard and she was firm. I only wish I had more opportunities to observe more carefully before she retired.

  3. Have a clear vision but build it collaboratively!
    Shared visions are always a lot more effective and motivating for the people that you lead. Having a voice in a conversation always makes me more inclined to buy-in and I see the value in making sure others get this opportunity. Some circumstances may make this more difficult (i.e. when change is needed but routine is firmly grounded) so when the vision may not be shared it is important to find other ways to allow voices to be heard, the vision to be clearly communicated and for the vision to evolve as change begins to happen and collaboration is becoming more common.

  4. Always ground the work in student achievement and well-being!
    My former principal always used to say "the students are our clients - it's not about you." It is human nature to feel ownership over what we do in our lives, but it is so important to step outside of that nature and realize that we are not perfect and many of us have experienced a lot of privilege in our lives (so it is even more important to reflect, listen and avoid becoming defensive). Our classrooms should be student-centred and so should our leadership work.

  5. Lead by example - take risks!
    It is vital to practice what you preach. As teacher leaders we should be an example of what we want to see. This is why I feel it is important to continue to work on effective assessment & evaluation practices grounded in policy and to be innovative and reflective about classroom practices.

  6. Be vulnerable!
    This is connected to #5 - to lead by example you also need to share practices and learning with others. Being reflective in a public way allows others to see that you are fallible and that in being innovative there will always be failings but persistence ultimately pays off.

  7. Seek feedback!
    Part of being fallible is realizing that there is always room for improvement and being proactive to ask for feedback from others. This is another aspect of leading by example and being vulnerable but it important to recognize on its own. All of the best leaders I have had were ones who found ways to seek feedback from students and colleagues.

  8. Have courageous conversations!
    Change is not created by shying away from what might be difficult. I have learned that allowing these conversations to stay away from "getting personal" involves careful listening in combination with bringing a "third point" to the conversation. This is usually in the form of a resource that is impartial so that it can be referred to when the conversation needs to be grounded.

  9. Empower others to lead!
    My outgoing department head's expertise was not in my subject area, so he was very good at asking us to lead professional learning for our group when we had something to offer. He knew that it would be more valuable and meaningful coming from a colleague than coming from him. By helping others around us develop leadership skills we become stronger leaders ourselves.

  10. Be knowledgeable!
    It is pretty difficult to create buy-in when you don't have the vital knowledge to support it. Knowledge of best practices including instructional & assessment practices, knowledge of policy (curriculum, Growing Success as well as board and school policy) and knowledge of school & department protocol/processes (where to find things, who are the resources in the school). Leadership is not likely to be respected if the people being lead have more knowledge (a leader can still need to learn, it helps to be open about that learning but needs to be acted upon in a timely fashion).
At this point I feel pretty comfortable with myself for #4, 5, 6 and 10 and that given some more formal opportunity to lead that I am getting more comfortable with #3, 7 and 9. I am continuing to work in the short term on #1, 2 and 8.

Friday, July 6, 2018

"Gradeless" Math 2.0

Well the blog updates got pushed to the bottom of the to-do list in second semester (not unusual) so this is a tad overdue, but I wanted to share some of the changes that my reflection on first semester lead to.

Some context:
- first semester did not have a learning map with descriptors until after midterm (I did not find I was able to write clear descriptors that I liked until I had evidence of student learning to use to write them)
- the learning map was not clear to students and since they had not engaged with it during the semester having them do final reflections and self-evaluate their course mark was difficult for them
- students relied heavily on the teacher for feedback

And so I set out in the second semester to make some changes. As many of you will be able to relate to, my thought process was more ambitious than life would allow for.

The new iteration (Gradeless 2.0):
- I added to my deconstruction of curriculum to include the learning map (read here for a description of the first week of class in Semester 1, I kept the math processes part and then the grades 10s did the following instead) by cutting up the map into pieces and giving it to them to put together (this forced them to read at least parts of the map and start to become familiar with it)
- Trying to spend more time modelling the use of criteria and feedback for students and giving them more dedicated time to do assessment as learning (trying to help them be less reliant on the teacher)
- Having students engage in the learning map by self-evaluating at the end of each set of summative evaluations (admittedly, this happened after the first set but did not get done in explicit class time after that)

New reflections:
- The new iteration was time well-spent. Students definitely had a better grasp of what the map was intended to do and were more comfortable using it (not all of them, there is still some work to be done, perhaps a more pointed effort to conference with students more often)
- I want students to refer to the map more to increase their focus on identifying where they are and what their next steps might be (keep the focus on noticing and naming the learning and reflecting on their progress)
- Students seemed to appreciate the transparency. One going as far as to say "I finally know what it means to be a level 4 in math" and used this as a way to help himself set goals
- The feedback at the end of the course from my students shows that even the ones who rated the learning map on the low side liked the idea of it, they just found it confusing at times

So it seems like the learning map is something I should continue to pursue and should put a focus on helping to make it more student friendly - I am just not sure what that would look like yet. I wonder if there is  way to make it a bit more interactive so that students can see examples of some of the more confusing parts or read explanations of terms.

If you have any suggestions they would be welcome!

Happy summer!

Thursday, February 15, 2018

Reflecting on "Gradeless" Math - Modelling Life-Long Learning

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

As the title of this entry may suggest this entry is serving as a place to express my thoughts around how last semester went and the changes I am hoping to make. My desire is that this "public diary" will help me to be accountable to my goals, will inspire someone else to take a risk, and will model that we (teacher) practice what we preach - we are all learners.

What worked well that I will continue:

  • Having students engage in deconstructing curriculum (specifically the math processes and instructional language)
  • Making students reflect on their learning (often!)
  • Having a grounding document for evaluation (learning map with overarching learning goals)
    • evaluation is based in criteria
  • Having students analyze their evidence of learning to determine their grades (and conferencing about it)
  • Constructing success criteria with students
What I will strive to do better:
  • Engage in curriculum deconstruction more frequently (not just at the beginning of the course)
  • Doing more explicit instruction around reflection (how, when, why)
  • Helping students understand where they currently are (map was not ready until midterm last semester, students did not know how to use it or make meaning from it) so they can better match evidence of learning to the map and, therefore, determine a midterm and final term grade
  • Teaching students to self- and peer-assess and give appropriate, meaningful feedback
  • Spending time getting students to co-construct criteria for types of questions or tasks (and for daily topics)
  • Getting students to self-identify as needing help and committing to getting that help (perhaps with a simple Google form)
  • Collecting student feedback on my practices
What I will do differently:
  • Provide a copy of the completed learning map from the start of the course to each student
  • Engage students in the use of the map frequently
  • Scaffold student note-taking based on investigative learning (i.e. in the early stages I am publishing a "note outline" that asks prompting questions indicating that there is something they should take note of/think about
Future goals and desires (that are just not realistic right now):
  • Have a usable learning map for the other course(s) I am teaching 
  • Engage same-subject colleagues in work around assessment practices [we are engaging in some "department" professional learning time in the coming weeks that may help with this]
  • Be better at recording observation and conversation assessment data of student learning

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!

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.

Reflection

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.

Thursday, August 10, 2017

Portfolio: Who Do I Hope to Become?

As part of my Teacher Leadership Part 1 AQ we are to build a portfolio of artifacts that reflect who we are as a leader and who we want to become. In this entry I will be reflecting on who I hope to become as a leader and where it might take me.

I would like to be able to feel more confident with dissonant conversations that come up in the office/lunchroom going forward. I find that when I am able to prepare for these types of things I do a little better but I do not always think well on my feet and come up with diplomatic but pointed ways to say things. I will be working to improve this aspect of my leadership-related skills in the near future.

I am planning to complete Part 2 and the specialist of this 3 part AQ course going forward and hope to continue to build myself up as a leader by getting better at seeking feedback from others about my practice. This is a good portion of the data we will need to collect for our TLLP project, so I believe that being the lead of this project will help me to do that more often. I particularly feel that it is important for me to learn to take action based on that feedback.

Going forward I continue to believe that leading by example is the most important thing that a teacher-leader can do. We need to share our triumps AND failures with colleagues (deprivatize our practice), be willing to take risks (and learn from each part of it along the way) and, most importantly, we must be willing to ask the difficult questions (just because we have "always done it this way" doesn't make it the best/only way).

We must be willing to stand up for students, to seek change and be willing to learn from others.

Here is the leadership philosophy I developed for the course that I think reflects who I hope to be as a leader.

Portfolio: Future Endeavours

As part of my Teacher Leadership Part 1 AQ we are to build a portfolio of artifacts that reflect who we are as a leader and who we want to become. In this entry I will be reflecting on a role that I might like to take on in the future with my board.

I used to talk a little about seeking a department headship position. And there was a time where I thought the instruction technology resource teacher position was of interest to me. But in the past couple of years I have come to realize that I am not sure that a headship is what I would really be passionate about and the ITRT position might be fun but is not where I would find excitement.

What my journey (much of which is outlined in the previous portfolio posts) has lead me to realize is that the instructional coach position in my board is really what would interest me. The co-learning stance that they seek, the current focus on numeracy (and, by the way, numeracy does not equal math!) and the ever growing focus on assessment and evaluation speak way more to who I am as an educator. And I think that I would learn a lot about myself and about the profession.

I was fortunate enough to be exposed to this position by a great role model for a few years. She was very good at building capacity in the school and had a great learning stance (she was also an elementary teacher so felt she had a lot she could learn and also brought an interesting perspective to our work).

Last year I called on our IC so that I could bounce ideas off of him to build my first conversation-based evaluation for a senior math course. The result of this interaction was him sharing this gem of a resource with me.

Monday, July 31, 2017

Portfolio: Leading in a Group: Courageous Conversations

I am taking the Teacher Leadership Part 1 AQ. Our culminating task involves creating a leadership portfolio by choosing items from each module of the course to share and reflecting on its contribution to my growth as a leader. I have chosen to share my portfolio as part of my blog.

This entry is from the module entitled Leading in a Group where we looked at how adults learn, the importance of having difficult conversations to give people real feedback, mentorship (the NTIP program), considering cross-curricular lesson planning and coming up with staff meeting agenda.

In this assignment we were asked to collaborate to develop a dialogue around a courageous conversation. My partner and I chose to make a dialogue between a teacher (who had not made necessary changes to assessment practices and was still relying on quizzes and tests) and an instructional coach. Creating this dialogue forces us to think about ways to have a courageous conversation in a way that made the teacher's experience valuable while finding out what they needed so that we could gauge how to move forward. We tried to phrase things in a way that asked for the teacher's input instead of making assumptions about what they needed to move forward in their practice.

I chose this assignment for my portfolio because I believe that having difficult conversations - confronting uncomfortable things - is the skill that needs the greatest improvement. It is something I have often avoided throughout my life, but I am working on it and felt that this portion of the course helped me to reflect on it in a more concrete way.

Our readings/videos suggested these steps for having courageous conversations (for giving feedback to an employee in a business):
1. Prepare them
2. Get to the point
3. Link to business
4. Agree on action
and I felt that in starting this dialogue that we knew:
1. The teacher was prepared because of past conversations with department members/head and knew they were meeting with the instructional coach and why
2. To get to the point quickly
3. To relate the work to the teachers own goals and ideas and give choice
4. To come up with a plan for follow through

Here is the conversation we developed:

Issue or Problem:
Some possible ideas could include - despite multiple conversations a teacher is not making progress in terms of assessment practices (relying on quiz & test data and department/course team discussions have resulted in little change)


Roles: Teacher & Instructional Coach (dialogue is making the assumption that department head made connection between T and IC)


Dialogue:


IC: Hi T, my name is IC, I don’t think we have formally met yet.
T: Hello. It is nice to meet you. We can work in here.


IC: So my understanding is that your department head has put us in touch. Can you tell me a little bit about what you would like to work on?


T: Well, department head seems to feel that I need to review how I give tests in my classes, I guess I’m not supposed to be giving so many tests. The problem is that I am never sure with other assignment types how I know they’re not just copying from each other or sharing the workload.


IC: Ok great, that’s a very helpful starting point. Maybe we can start by taking a look at your course outline so that you can walk me through your units of study and the assessments you’ve planned


T: Sure, well, you can see here that we have 6 units throughout the year and each has a mid point quiz and an end of unit test.  You can also see that the year end exam is the culminating task so it is worth 30% of the overall mark.


IC: OK, are you aware of what the course team is currently doing? Or are you on this course alone?


T: This semester I am the only teacher on this course.


IC: You mentioned that you are concerned about students copying. Is there a type of assessment you have in mind that you would like to try to work through?


T: Well I know that I should be doing some problem-based stuff.


IC: How do you feel about collecting triangulated data?
T: I am willing to try something new but am not really sure what you mean by triangulated data?


IC: Triangulated data means that you’re looking for 3 opportunities to assess student knowledge and understanding and that you’re gathering this data through three different lenses - products, observations and conversation. You are probably doing all of them already but not necessarily making use of them as evidence for individual students.


T: Can they be Assessment for and as learning as well as a summative Assessment of Learning?


IC: Absolutely. Providing students with a formative opportunity to work with the new knowledge allows them the opportunity to test their learning and also helps you to adjust your teaching plans to address areas in which students may be challenged. For example, if you were to use a problem based scenario such as a case study, you can give students the opportunity to work through a case study in class in small groups before they tackle a summative Assessment of Learning case study.  While they are working on the formative case study, you can observe and ask questions as they work through the case study and can jot down some observational notes on how they are using the concepts and skills from the unit. You might also use a quiz as a AoL check in before the AoL case study to check on their knowledge of the key concepts they will need to apply in the case study.


T: OK, so I would take observations of individual students so that I would know what  they know individually? How do you get to every student and how do you actually track the evidence you have seen?


IC: Great question. There is not necessarily one right answer, but I would recommend starting with a learning goal and developing success criteria. That way the students will know what you are looking for and you will have a manageable way to look at the work the students are doing. You could target specific students if you are unsure about getting through the whole class, but every student needs to get the opportunity for feedback. Would you like to try planning something like this?


T: Sure. I think I have some case studies from a colleague who taught this last semester. Do I have to give every group the same case study or can they get different ones?


IC: They can definitely be different ones - as long as you think that you can assess the same learning goal for each one.


T: Ok, that seems manageable.  I would still like to use a quiz to get some reliable individual data on each student too. Is that too much?


IC: If you think a quiz is important, you might like to consider is what is on the quiz that’s different from the formative group work but that they might need in order to complete the Assessment of Learning task.  If a student performs poorly on the quiz but then reviews and works to learn the concepts and is able to apply them successfully on the Assessment of Learning case study, you can acknowledge their progress on the AoL Case Study.  


T: So when I determine their overall grade for the unit, do I average the quiz and AoL case study?


IC: You will continue to use the practice of most recent and consistent. The great thing about triangulating your results is that you are able to acknowledge the student’s overall learning. For example, If a student misses the mark on one part of the AoL case study but you have evidence from your observations and quiz results that they do understand a particular concept, you can acknowledge that in terms of the overall mark.


T: So I need to decide on a learning goal and success criteria, identify some case studies that will allow for those expectations to be met and then will need some kind of tracking mechanism to record my observations/conversations.

IC: Sounds like a great start. I can share some sample tracking sheets with you if you like and would be happy to work through those steps with you - or if you would like to have some time to work individually and then to do some feedback via email I can make that work too.

Wednesday, February 15, 2017

MHF Cycle 2 Reflection

I have previously posted a reflection of our first cycle here.

Here is the plan that we used for our first cycle.
(Most of the activity credits go to Jamie Mitchell and Steph Girvan in the Halton Disctrict School Board - Thank you for sharing your resources - including your blood, sweat and tears guys!)



One of the things we have found as a department is that students often struggle with the algebra portions of this course. Because of this I offered my students an "algebra crash course". I attempted to remind them the core of algebra and solving equations through manipulatives and a clear reminder of what inverse means (i.e. that log is a function, so has an inverse). These should be ingrained ideas that these students have and I find myself often wondering how to best help students at the high school level with these skills. If anyone reading this has any ideas please share!

As you can see in our plan we had two traditional tests in this cycle. We split the algebra portion up into two sections, polynomial & rational functions and logarithmic & trigonometric functions. The last part of the cycle has students explore combinations of functions through investigation of graphs and getting students to do their best to generalize rules for different types of combinations. As a final evaluation in this unit we had student-teacher conferences.

Students had a conference like this one during cycle one as practice (for all of them I was using Google Forms to track and DocAppender to give student immediate access to feedback). For this conference students were given two functions in small groups. They were asked to identify the characteristics of those two functions and then to as a group predict the superposition characteristics of those two functions. On the day of their conferences students rolled a die to get a random second combination. Students were given 5 minutes to prepare and then had 5 minutes to share as much as they could about that combined function. The key was that they were to explain why they believed those were the resulting characteristics, not just to list them.

I found this evaluation very insightful into student reasoning and understanding of characteristics as a whole. It also provided insight into the emphasis that I should consider putting onto the graphical representation of functions in earlier courses. I have started to think that we take for granted what students take away from graphs.

I really enjoyed the experience with conference with these classes and definitely plan to continue working on using them in other courses. Getting students to explain things verbally has an ability to show student learning that reading a written response just cannot do. The power of triangulation of evidence.

Wednesday, February 1, 2017

MHF Cycle 1 Reflection

As mentioned in a post early first semester we made an attempt to spiral the MHF4U0 curriculum at our school. I will try to create some more posts to share more details, so for now this post will just focus on the first cycle we used.

If you missed the planning post, you can find it here.

I personally started off with a couple of classes where we did some collaborative problems solving. I wanted to introduce my intention to use visible random grouping (VRG) and vertical non-permanent surfaces (VNPS) in the class. I used this with a couple of fun tasks (such as the Tax Man problem) and then continued with them working on the boards while having them do some review problems together (factoring, radicals). It was a rough beginning. My madness was very new to the students, particularly since I was completely new to the school.

Here is the plan that we used for our first cycle.
(Most of the activity credits go to Alex Overwijk and his team in the Ottawa-Carlton District School Board and to Jamie Mitchell and Steph Girvan in the Halton Disctrict School Board - Thank you for sharing your resources - including your blood, sweat and tears guys!)


The textbook references made above are for the Nelson Advanced Functions book. I very rarely assigned work from the book but students were given the sections as a reference for if they needed it or wanted to do extra practice.

Part way through the cycle (probably about 2/3rds of the way through) I asked the students for some feedback. They were struggling with my use of Desmos Activities and lack of "traditional lectures". We added some more structure to the daily work we were doing. At the start of class we went back to the previous day's lesson (took any questions, which we were already doing) and then co-constructed success criteria based on what they had done. This criteria was added to the lesson plan that the students had access to. I also made a pointed effort to make them read that day's learning goal and asked if anything needed to be clarified. This seemed to help students realize that they were learning.

In retrospect, the vast changes they were going through were a lot. I would create brief google forms for each Desmos Activity the next time to help students consolidate their learning (which would have helped them build their functions portfolio we had asked them to do), essentially they would be exit tickets of some sort. I could collect data for myself while giving students a chance to reflect. And the form could be attached to student documents via DocAppender so that they could have a copy of their own responses.

Our formal evaluation for this cycle was a large group stations task. Students were in groups of 3-4 such that there were 8 groups in one class. There were 8 stations in total (we did 4 per day) that were designed to last approximately 15 minutes each. Of course there turned out to be some they spent more time on than others. Students were to use the time in their groups to work through the problem (i.e. match a graph, table of values, and equation and justify the match) and then record their answer in their own words on their answer sheet.

Students found this to be a very valuable learning tool and, for the most part, the results seemed to align with what we, as teachers, thought that student had shown they knew and could do. They were not big on the fact that it was the only formal evaluation we had done in the first 6 weeks of the course, but appreciated that it was less stressful than a unit test.

In retrospect, the task was too huge for the teachers to deal with all at once. We each had 2 sections x 2 days worth of tasks to go through. It took a lot longer than we anticipated. I would love to do something similar to this again, but would definitely consider splitting it up somehow so that it is not all happening at once. Suggestions are welcome if you have any!

Reflections on cycle 2 to come!

Wednesday, August 17, 2016

Finished with the Status Quo

I am currently making my way through Starr Sackstein's Hacking Assessment: 10 Ways to Go Gradeless in a Traditional Grades School. I will likely do a blog when I am finished and will include my takeaways in more detail but one of her lines has inspired me to bring up some provocative conversation.

As are many of you, I am tired of the argument "We have always done it this way." It may be true that there are some thing in our lives that can stay the same year after year and still be the most efficient way to do things but life changes, and often things need to change with it. Most of the stages of my life have come with pretty significant changes and I have also watched the world evolve - computers, internet, cell phones - and would be significantly behind in current knowledge if I had ignored those changes.

Of course, I have also watched the world fail to evolve (lack of change in carbon footprint despite the research and negative effects we are experiencing; decades long wars (in so many cases started by some misunderstanding and a failure to learn from history) that are sometimes ignored by the rest of the world; etc.

I can no longer watch education become something that does not change.

On page 28 Sackstein had me out loud proclaiming "Yes! This is the articulation I have been looking for!" when she said:
In the industrial era, schools were intended to train good workers, so students went to schools that prepared them to enter the work force. This model of education valued obedience, conformity, and rote learning.
We are no longer in the industrial evolution.

Of course, I will not pretend to believe that we do not need workers who can conform and follow specific steps to complete a task, but the majority of work that we need to prepare students for requires people who can be creative, who can think for themselves, and who can solve problems. This is the world I want to prepare my students for - I want them to find success in whatever passion or skill they find for themselves through the use of transferable, valuable skills (not rote learning they can look up on YouTube).

Hopefully my journey can help to bring along more teachers, students, parents, admin, and community members who want to see a change.

Sunday, July 10, 2016

LGs vs SC vs Task Requirements

Discussing assessment in the education world often leads to more questions than answers and creates a lot of discourse. I have learned that the questions and disagreements are a necessary part of change and that we need to acknowledge and tackle them, not shy away from them. It is easy to feel defensive when our practices are questioned or challenged. It is easy to feel like we are being told that what we have been doing was wrong.

I have also learned that when someone asks "why" they are usually genuinely curious OR they are trying to get me to think about what I am doing. It has taught me to always ask myself why.

I have brought this up because one of the things that has come up a lot recently is the discussion of comparing learning goals (LGs), success criteria (SC), and task requirements. It can be easy to write a a statement that may not clearly fit into one category or the other. But it is also important to try to understand and recognize the difference.

Here is my understanding of each:

LGs are statements that describe what a student should know and do that is specific to a lesson or set of lessons. In Ontario this will often be based directly from the overall expectations of the curriculum.

SC describe what the learning will look or sound like when the student is meeting expectations. They should be based on agreed upon statements formed with a course team but when employed in class may often be co-constructed with the students.

Task requirements are things that a student is asked to do that does not fall under that course's expectations but are necessary to help the teacher focus on evaluating the learning without distraction. These can not be evaluated but a students may be asked to resubmit work when they are not used/followed.

I will be the first to admit that through my journey this year there are times where these things were misused or mixed up. This exploration has allowed me to gain a much better understanding of them and why they are important and have forced me to rethink the what, why and how of my classroom assessment.

Through my use of overarching learning goals, learning maps, learning goals, etc I am hopeful to be able to spend more time giving feedback in the future and less time giving grades. By continuing to build my assessment literacy I can continue to build my students assessment literacy.

My hopes for the future include students who...

  • take ownership of their learning
  • can self- and peer-assess
  • question what we do and why we do it (purposefully)
  • enjoy class more
  • focus on and prioritize learning not marks
and include my hopes to...
  • bring focus to all classroom tasks and evaluations
  • shorten written evaluations
  • grade less
  • discuss more
Comments and questions are welcome and encouraged. Use the comment feature below or connect with me on Twitter :) 

Thanks for reading!

Thursday, July 7, 2016

Math Learning Map Journey

I have been distracted from blogging but am trying to catch up and am back to trying to deprivatize my practice more. And so, I am resolved to blog about my assessment practices (including failures and questions) and hope that I can spark conversation, collect some feedback, and crowd source some ideas. So I have one request - if you are reading these entries, please share them with someone else and/or comment at the bottom and join the conversation. :) The first entry from this series can be found here.

Today I am hoping to share the process and evolution of my experiences working toward a learning map for a math course. I think this is a specific journey worth deprivatizing because it has been a complicated one that involved a lot of lengthy discussions.

This entry requires you to know what an Overarching Learning Goal (OLG) is: I described it in an earlier entry as big ideas that are written as board spectrum learning goals that marry the "know" and "do" that we hope a student leaves a course with. I have discussed OLGs in a number of other entries since this one that can show you some of my journey through understanding and using them as well.

Starting in early 2015 I dove into OLGs and started working with a colleague to write some for a math course. At the time we were both teaching Gr 10 Academic ("Mathematical Principles") so we tried to tackle it. This was both of our first attempts at the process for any course so it was an exploration of the process itself and a discovery that every time we tried to do it we wanted to make different decisions. [One thing I would critique us on looking back was our neglect of the front matter of the curriculum].

Here is a look at the 2 different sets of OLGs we landed on in our two attempts.

In 2016 I had the opportunity to gather with some math and assessment colleagues from around the board to take a real look at designing OLGs and a Learning Map (LM). [I showed a sample LM for my Science course in this entry earlier if you would like some context] A LM takes the OLGs and describes what the learning should look like at each level. This map can then be used for many purposes.

Over the course of many discussions with colleagues at my school, one of our math resource teachers (@MashelleKaukab), and the above mentioned gathering we went through a process of unpacking the MFM 1P (Gr 9 Applied - Mathematical Foundations) course and the Math Processes (Ontario math curriculum front matter). It involved a lot of debate with well-reasoned points - and a lot of learning! Oh how our brains hurt at the end of that day!

Our team decided to create "skeleton" OLGs that focused on the processes that could then theoretically be used to finish OLGs for any course at any level (perhaps with rewording needed). Here is where we landed:

Our team left that meeting still feeling like things were a work in process but I am sharing our draft of our work hoping that you will contribute to the discussion by providing feedback. Please visit a copy of the document here.

The hope is that this map will become the foundation for every decision, evaluation and report completed for the course. The hope is that it will be the backbone of my backward design for my course.

Thank you for reading and for joining the discussion!
Happy summer!

Sunday, June 26, 2016

Learning Goals & Reflection on Quizzes in 1P Science

I have been distracted from blogging but am trying to catch up and am back to trying to deprivatize my practice more. And so, I am resolved to blog about my assessment practices (including failures and questions) and hope that I can spark conversation, collect some feedback, and crowd source some ideas. So I have one request - if you are reading these entries, please share them with someone else and/or comment at the bottom and join the conversation. :) The first entry from this series can be found here.

In a more recent entry I blogged about the basics of using learning goals (LGs) in my Grade 9 applied science class. You can find this entry here. In today's blog you will find a little more about what I have tried to do with the LGs, particularly related to quizzes.

Here are some of the things I wish to share and/or reflect on:

Challenges of writing in student-friendly language:
It is not always easy to maintain the integrity of the vocabulary necessary for the course while making statements accessible to all students. I try to give them a chance to review the LGs and to ask for clarification if needed, but it is not always easy to get them to admit that they do not understand. And sometimes it makes more sense to revisit the goals at the end of day 1 when the vocab has been introduced through the lesson.

LGs vs success criteria (SC)
It was pointed out to me at one point that the statements I was using were better suited as SC than LGs. The more I have learned and discussed A&E with colleagues I am inclined to agree. I would now zero in on the overall expectations in the curriculum to help with LG writing more and let the types of statements I was writing become the success criteria. But what I was doing did serve these students pretty well as it (but having real learning goals would have benefited me a lot when determining grades for them, but so would editing and knuckling down to use the Learning Map that I started to create for the course as well). I discuss these ideas in this entry.

Quiz layout and using learning levels:
I was inspired by Myron Dueck's book Grading Smarter Not Harder to change the format I was using on written evaluations. I now group things based on learning goal. In addition I no longer give marks on them. Instead I have a grid with the learning goals at the top and I have students reflect on where they think they are (and then I show them where I think they are) and I give feedback within each question. This has led me to write evaluations that much better reflect what I want them to know and do (and I test what is valued without over-testing topics)

Now the unit test is essentially a "re-do" opportunity:
I use the unit test as a chance for students to show me what else they have learned and to give them a different way to show me the same learning goal. I make sure that the goal is tested using a different style of question (i.e. maybe it was a graphic organizer on the quiz and the next time they label a diagram). This was definitely time consuming the first time through, but it was worth it (and creating a brand new (good) unit test is time consuming anyway).

It is much easier to evaluate using levels now than when I gave "marks":
I have been trying to awhile now to think about levels when I mark. For instance, if I am looking at a Gr 11 physics test and the student has problem solved I want to know what level of knowledge and skill they have demonstrated. I then assign a mark based on this level (instead of "taking marks off" for mistakes made, which can be quite arbitrary). Going to levels has removed the idea of getting 1 out of 4 meaning 25% when really it showed the student is starting to get it, but isn't there yet.

Students need better feedback from me than I am giving:
It is still really easy to just circle things, use check marks and question marks. This is not good enough. There is not a level of description being provided when we do this and many students are not asking about them. I know this is something I need to work on, and I also think that by adjusting the LG vs SC aspect mentioned above that this could get easier as I wouldn't have as many things that I think I have to give feedback on.

Most of my 1P students were doing better at midterm than they thought:
There was a lot of surprise in the room that they were doing well. Many of them had never felt like they did well in science before (although they all like the subject). I did notice some of them thinking "oh I can try less now" but it also spurred some of them on to try harder. Some may think this means the course was made "easy" but I believe that they were actually showing knowledge and skill in the course. My practices had allowed me to remove the "noise" from evaluation (i.e. grammar was much less of a distraction) and it was easier to identify students to have conversations with to prove that they knew more than they had written down.

Wednesday, March 30, 2016

We Need to Stop Testing and Start Thinking

I heard something that was music-to-my-ears today. Apparently there was a presentation to senior leadership in my board a few weeks ago that included a prof from UTM and one from UGuelph (both from math departments) that passed on this message (I am paraphrasing of course) that I hope makes its way around the board sooner rather than later:
"We need secondary teachers to stop using tests as a crutch claiming they need to "prepare students for University". Your students are coming to us as great test takers, but without critical thinking and problem solving skills. These skills are vital, and students who have these skills will be able to succeed no matter the assessment environment they are put in."
I have been saying for years now that we are graduating hordes of students who do not know how to think - even the ones getting 90s. This was confirmed by the numerous peers who have become math teachers and admitted that they now realize that they never actually understood the math they did in high school (until they started teaching it). We need to stop testing and to start giving students the opportunities they need to do some true learning and thinking.
To this I add....we need to bring back the Al Geo course! That had to be the course that I did the most thinking for in high school, without a doubt.