Assessment and Instruction!

From Bell Curve to J Curve

Did you ever feel like your teachers or professors were never reading your work and just giving you a random grade? I know I definitely have. There have been times were I put my best effort only to be given a mediocre grade meanwhile the person beside me handed in essentially nothing and managed a high grade. There have been times even the opposite happened – I get stressed, hand in mediocre work (strategically choosing assignments) but getting an amazing grade.

We’ve all heard of it, the infamous “bell curve” or “grading on curve”. What this meant was certain amount of percentages or letter grades were reserved for a specific amount of students. “In a system of pure curve grading, the number of students who will receive each grade is already determined at the beginning of a course” (K12 Academics). You probably notice this more in university. I mean, did anyone else ever notice the class average was primarily in the 70s? Overall, some of us probably got higher or lower than that but getting above 79 was definitely something to celebrate.


The bell curve, for obvious reasons, is an unfair method of assessment. Predetermining how a student is going to achieve before they even step through the door of your classroom is clearly not the right way to do things!

So what then, have most educators started to head toward? There’s this little theory that was developed originally for economic purposes but has been adapted to many other fields including education. This curve is what some people are referring to as the Jcurve.

The J Curve

This model is not limiting toward student success rather, it focuses on the belief that “with proper instructional practices over time, there is an unlimited capacity for successful students” (ASQ). obamaholdup

Let me put it another way:


That means, that no matter what the odds are against the student, they can still do well and still be successful. What can we do, as teachers, to make sure we are following this model over the bell curve?

Connecting Assessment and Instruction

Please follow the link and watch the short video 🙂

So what did that little video tell us?


That everything we assess guides our instruction and everything we use as instruction will be assessed in some way (pre, formative, summative).

If the video didn’t really explain the Big Ideas well enough, you can follow think link to an article that will clarify some ideas 🙂

So how do we design assessment and instruction together?

1. Connect to the learning goals and evidence

2. Integrate continuous assessment seamlessly the instruction (pre, formative, summative)

Students need to be able to understand what they are learning and what they are doing, which means all learning experiences need to be connected to curriculum expectations and learning goals.

Students Need to Become Independent Learners

In order for students to become independent learners, there are a few things that we can do as teachers

1. When we ask questions, we need to give them more think time

2. Give students a chance for self assessment by providing them with the success criteria (I can, I have… statements)

3. Provide ongoing assessment (formative) and descriptive feedback.


In order to become more independent, students also need to learn through peer and self assessments. As noted in the video, self and peer assessments are not going to happen overnight. Students don’t just magically know how to do assessments. I mean, we’re taught how to do it and even some of us struggle!

The purpose of these types of assessments is allows students to

1. clarify learning goals

2. co-develop success criteria.

When and How do we decide to include students?

1. Plan Ahead – What do they need to remember/review?

2. Have them think about the big ideas from previous activities to activate prior knowledge.

Why is Involving Students a Good Thing?

1. It connects the learning and the instruction.

2. The students are required to gather information about their learning.

3. It provides the teacher with the opportunity to employ alternative groupings (mixed over similar ability)

4. Activities revolve around the knowledge and skills of ALL students.

5. Students become resources for learning – they help struggling students.

6. It provides the teacher with multiple opportunities for feedback.

7. Students can engage in peer and self assessments regularly.

“assessment that is consistent with principles of learning and understanding should:

  1. mirror good instruction
  2. happen continuously but not intrusively as a part of instruction
  3. provide information about the level of understanding that students are reaching.” – Bransford, Brown and Cocking (2000).

Fair and Authentic Assessment 

I know, there’s probably someone thinking “okay thanks for the long post on assessment, but can you tell me what I can do to be fair?”

First of all, you want to plan tasks that can be connected to real life. If students cannot see the connection to their lives, they’re not likely to learn it.

Second, you need to create tasks where students are challenged but it’s not too difficult. You need to figure out what they can do on their own and what they can’t. There’s that Zone of Proximal Thinking again.

Finally, you need to plan backwards. Think about the end first and work your way back. I’m pretty sure this was all in my little video but just in case you decided to skip out on it, there it is again!

In other words – you need to focus on the student not the studentS. You need to capture your student when they are learning their best. Take their most recent, well-polished work to define them. When kids are in school those letter grades, levels or percentages become all they represent and they feel like that is all that they’re worth. But isn’t it interesting that once you get out into the real world the marks you got in school are no longer really that relevant?

So what’s the difference between the traditional methods and this “authentic” I speak of?

Traditional Assessment ——————————— Authentic Assessment

Selecting a Response ———————————— Performing a Task

Contrived ————————————————————— Real-life

Recall/Recognition ——————————- Construction/Application

Teacher-structured ————————————- Student-structured

Indirect Evidence ——————————————– Direct Evidence

If you click on the link, you’ll get a detailed description of each difference!

If you’re still interested in different types of assessment and how they link to instruction (which I’m sure you are!), you might want to check out this article that discusses the shift from high standard tests to games! The basic idea is that instruction and assessment can take place at the same time through the use of games.

“game-based learning provides moment-to-moment opportunities for learners to apply their knowledge and demonstrate competency while solving problems in a relevant context. Assessment data reflecting player decision-making can be used to present a personalized learning experience as the game adapts to the learner’s strengths and weaknesses.” – Dave McCool.

Sidenote: Anyone with the last name McCool is obviously someone we really need to be listening to! His name has COOL in it!

But in all seriousness, this concept isn’t too far off from what we already do in the classroom as teachers. I highly recommend you read the article.

Questions for You

  1. How have you previously connected assessment and instruction in your classroom?
  2. What does authentic assessment look like for you and your students (hypothetical or real)?
  3. What are the pros and cons of having game-based learning in the classroom?
  4. How do you decide to assign a grade to your students? What pieces of evidence do you collect?


This is the plan that never ends…

Math is important and that’s why it takes forever to plan for. At least, that’s what I keep telling myself. I actually do believe it. Despite my greatest attempts at avoiding math in every day life, it’s everywhere. My students refuse to believe me and when I tried to mention the importance of fractions and making sure things are in equal parts (ie. birthday cakes, pies, class pizza party), my students kindly put it,”tell them to suck it up!” 

So what am I going on about? Math is connected to everything. 

Big Ideas

Big Ideas are one of the concepts that I have to get my head wrapped around. Having been taught how to teach at the I/S level in specific subjects, the term “Big Ideas” was relatively new for me – when it came to math. 


In a nutshell, they are key concepts that you want students to learn. They are way more than just our overall and specific expectations from the Ontario CurriculumThis concept has been extremely helpful in my planning (once I was made aware of it!) This past school year, I had a 2 grade split and next year I will have a 3 grade split! Rather than planning for three separate grades, I can focus on the big ideas and differentiate as needed. 

For more information on Big Ideas that includes some examples, I suggest looking at Marian Small. This powerpoint, was extremely helpful when I was trying to figure out what “Big Ideas” meant (I was making it a lot more complicated in my mind!). She also has a number of books that would be AMAZING to have!

Determining your “Big Ideas” will definitely make planning long range, unit and lesson plans so much easier!

Long Range Plans

Long Range Plans are the perfect opportunity for me to see where I want my math program to go by the end of the year. It’s also the perfect time to see where I can make some cross-curricular connections. Since math in integrated into almost everything we do on a daily basis, developing a long range plan for each subject allows myself the opportunity to see HOW I can make everything connect. For instance, when it comes to data management I can easily make a connection to Geography as my students are required to read different types of graphs in both subjects. It also provides that “real world” opportunity so I can hear less “I’m never going to need to read a graph! I want to work for the MNR!” Instead of planning two separate units – 1. how to make graphs and 2. climate, patterns, etc., I can just combine the two and make the lessons that much more engaging!

I recently discovered Canadian Teacher LRP Tool and I’m definitely interested in using it once my planning kicks into full gear! I don’t think I’d use it as my only resource but I think it can definitely have some uses.

Unit Plans

I’m really good at making Unit Plans – in theory. I just can’t stick to them. At least, I couldn’t this year. I could barely plan 2 days in advance because the needs of my students were constantly changing. Finding out at the end of May that they can’t round or divide is frightening (I started teaching them in March!). Obviously, the Unit I had planned was put on hold. But the most important part of my unit always stayed the same – what did I want in them to be able to do at the end? 

Backward-down design is crucial. Thinking about the end of the unit is so much more important than the start. When you’re planning that next unit, think very carefully about what you want your students to know at the end. Everything else you do before the end can change (and it probably will).

Once you have the end in mind, think about where you want to start. Next think about how you plan to do your assessments? What kinds will you be doing? How often? 

Finally – the most important thing I learned – is think about where their gaps might be, especially if you’ve never taught them before. Don’t assume they know anything. The best thing I did was stopped assuming they knew how to do something and started thinking like they didn’t. If they know how to do the concept you’re about to teach them – they’ll tell you and you can pass it off as review. I have a feeling there’s a student in your class who will be grateful that you reminded them how to multiply two digit numbers!

Here is a useful template from the “Ontario Curriculum Planner” 


 Daily Lessons

This is going to be your meat. This is where your 3 Part Lesson that I told you about is going to come in. This is also the area that you will probably constantly be changing. No matter how much you plan, students can and WILL surprise you. Maybe they are completely clueless and you need to take several steps back to fill those gaps or maybe they catch on a lot quicker to a concept than you thought they would.

For example: I had one class during my practicum that struggled severely with using a protractor. So, when I went into my next class, I was prepared! I planned an elaborate lesson on how to use protractors and it was engaging! It was perfect… Except my students thought I had completely lost my mind and were extremely insulted that I thought they needed to learn how to use such a simple tool. Luckily, I had my next lesson ready and we moved on. It would have been an extremely long hour!

If you’re looking for a template to get started with this website has a complete list of useful ones. I particularly like Template 14 because it’s designed with the 3 Part Lesson in mind. 

What’s Next?

When I think about the upcoming year and the amount of information I’ve learned in such a short amount of time, I know there’s things I want to change or incorporate. 

  1. Include Big Ideas. While I might have been doing this anyway, I think it need to make it more clear in my planning.
  2. Use 3 Part Lessons Again, I was doing this but I need to make it more evident. 
  3. Long Range Plan This year, I’m not being thrown into a class. I have so much more time to do this and I need to do it. I’m good with my unit plans, I just need to make sure I have a LRP as well. 
  4. Include Guides To Effective Instruction This will help better understand not only my thinking but as well as student thinking.
  5. Continue to Plan Cross Curricular. Nothing beats hitting two birds with one stone. It’s more engaging for the students and so much more can get done.



Planning for Math

This is definitely my weakest subject to plan for. By weakest, I mean most time consuming and frustrating. It makes me want to tear my hair out and crawl under my desk. BUT! That’s a good thing. It’s a challenge and I’m always up for a challenge. The reason I hate planning for math is, as I’ve previously mentioned, it was a subject that I hated in school. It frustrated me to learn. Now as a teacher, I’m so aware of the problems that can occur with a lesson and I want it to go perfectly. 

Traditional vs 3 Part Lesson

Traditional teaching is exactly what it sounds like, traditional and boring. Alright, maybe not all traditions are boring but when it comes to education – it almost always means boring! It means desks in rows, the teacher talking and students sitting quietly and “absorbing” what the teacher is lecturing about. In elementary school, I was lucky enough to have teachers that didn’t spend a whole lot of time lecturing but I still remember a lot of images similar to: 


Okay, so maybe it wasn’t that intense in elementary school but I imagine to a struggling student in math, the image is pretty close to what they are seeing. With traditional teaching, the struggling student doesn’t really matter. That student just needs to do more worksheets, practice questions from the textbook and have more homework. Eventually, they’ll get it. Right? 


So what do we do instead? What should we, as teachers, be looking to do instead? Obviously the answer is to move away from traditional teaching. I know it’s hard! Rip it off like a band-aid! It’ll sting at first, but I promise this new method will be more rewarding in the end and your students will love you for it! Take a deep breath…Ready?


Alright. Feel better? Now, let’s get started.

3 Part Lesson

So what is this 3-Part Lesson that everyone in the education world is talking about? Well, it’s a lesson that’s in 3 parts! I know, my students love my humour too! This method is all about the students. It requires students to think about what they already know, what they need to know and how to use the resources around them to solve the problem in a way that works best for them. Do you notice what I don’t repeatedly say? “The teacher is doing this, and this and this”. It’s not about us. We had our education, it’s time for us to help the students with theirs.

Getting Started

This part of the lesson is where students will activate prior knowledge. It generally involves the whole class or small groups. This part might involve the teacher the most but don’t let that fool you! This moment doesn’t last very long! This section of the lesson shouldn’t last more than 10 minutes. 

This is the moment where students are introduced to a problem. In my class, I liked to use Dan Meyer’s Spreadsheet in my classroom. He’s full of ideas and everything has a “suggested question”. Most of the suggestions are open-ended enough that students can arrive at different answers or they can arrive at the same answer in different ways. I preferred using the spreadsheet to get ideas because my students found the questions engaging and they were often in video format so it gave the students someone else to listen to for a change.

During this time, the teacher can be reminding students how to solve a question or prompt students.

For instance, I used this problem during out Percents unit. Students automatically started telling me which coupon was better and which one they would use (most originally said $20 off because it sounded like a large number). I would constantly ask students questions to get them thinking such as “how do we change percents to decimals?”, “how do we multiply decimals” and “how do we figure out how much money we save”. 

Working On It

This portion of the lesson allows students to work independently or in pairs on similar questions from the Getting Started section. This is the longest part of the lesson and should last between 30-40 minutes. The teacher is now circulating the classroom, helping students as needed and paying attention to how the students are working. Think about the language the students are using, the methods the students are using to solve the questions and what resources they’re using to solve their problems. Students should be constantly encouraged to use any manipulative or resource that they need in order to solve the problem. Think back to the Traditional method for a second. What did your teacher used to always say?


Okay, so maybe Primary/Junior kids won’t have a cell phone in their pockets but let’s face it – they will in a few years.

The students are in charge of their learning and they have a bit of independence. I guarantee you, your students will be more engaged and willing to learn. They might not be willing at first, but don’t give up! Don’t put a new band-aid on!

Reflecting and Connecting

At this point of the lesson, all students meet back to reflect on what they learned. Students will use this time to discuss what worked and what didn’t work for them in order to solve the problems. During the Working on It period, the teacher should have been collecting exemplars of student work that the teacher would like to go over during this time. The teacher can guide the discussion to focus on how other students achieved their answers. This opens up a world of opportunities as students may see a “simpler” way of answering a question than their own. 

Now, I don’t know about everyone else’s classes, but mine hated sharing. They had been trained that there was only a few “smart kids” in the class and they always had the answer. So, what I opted to do instead is have students write down, anonymously, what they would like to discuss or their answers my questions and I would go over the common ones and if I had time, I would go through other questions.

I would also include “Exit Cards” at the end of most math lessons. I generally only remembered to do this during the more complex lessons but I hope that I can remember to do it regularly this year! This gave me the opportunity to learn what students were struggling with that I might have missed while I was observing. Generally, my students were pretty honest with their answers.

Hopefully I’ve convinced you to move away from the Traditional Method of teaching because we honestly don’t need any more disengaged students out there.