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Part 2: How Do I Assess This New Math Curriculum?


In the last post, we explored how formative assessment is used to guide instruction and how summative assessments can be used to assess the current curriculum, including the competencies and the big ideas.

 

Historically, we have only been assessing procedures and so there needs to be a new approach to assessment that is aligned to the new curriculum.

I gave you an example using square and square roots. I’m going to continue with this and in this post we will dig deeper into these questions:

How are my students involved in the process (besides being test takers)?

How do I assign a letter grade to the assessment?

Here is the assessment sample I used in the last post:

 

 

So, the next question is probably “ok, this looks good but how do I mark it?”. This doesn’t lend itself to marking each answer with a tick mark and counting them up to get a 19/20 or something similar. We need to have criteria and this criteria needs to be shared with and/or co-created with students.

How are my students involved in the process (besides being test takers)?

When I was in high school, English was my least favourite subject area, which it shouldn’t have been because I’ve always loved literature, writing and talking. It was my least favourite for one reason only: I had no clue how to get an ‘A’. I had a very fixed mindset in school. I was your typical high performing girl that the research shows are the most common group to have fixed mindsets. I could usually get a 7/10 or an 8/10 on my essays and paragraphs but that was it. What the hell is a 7/10 on an essay? I had no clue what to do differently to improve. Where did I lose those 3 marks? It was a complete mystery and frustrated me to no end. It still does if I’m honest (LOL!). Most English teachers now use rubrics to mark ….so why aren’t most math teachers using them? My assumption is that they’ve never seen them at work or aren’t at all familiar with them. So here’s an introduction:

Students need to have a clear understanding of the expectations we have for them. This was a whole lot easier with the ‘old’ way of marking – the goal was to get all the answers correct. When we ask students to write to explain their understanding a more complex system of marking is needed if we want to be transparent with our students.

Co-creating this criteria and exemplars with your class is a valuable use of class time (it will likely take a full block the first time through). Here is what it looks like:

Ask each student to show their understanding of square roots (or any other concept) in 4 ways:

1.  Symbols (using numbers and symbol) – for example:because 3 x 3 = 9 or 32 =9

2. Words – for example: the square root of 9 is 3 because a square with an area of 9 has a side length of 3. A square root also means that you multiply the root by itself to get the square number so 3 x 3 = 9.

3. Pictures 

4. Contexts – Zoey built a square box with a side length of 3 ft, what is the area of the base of the box?

After the students have all written their ideas they put their ideas on the board (you can give them sticky notes for each or larger pieces of paper). As a class we then sort through and find the best examples and we discuss what makes them great examples (this then goes into your rubric). We are looking for examples that are clear, well explained and that make sense. Once we have chosen one or two exemplars from the batch, we create an anchor chart that shows each of these 4 ways using the best examples (see sample below). If you find that you have no good examples, you can either redirect the learning to allow them time to create better examples or fill in the gaps with your own examples.

Now the students have a clear idea of what it means to explain their understanding in these 4 ways with clear examples and we can create criteria based on what made the examples the best.

Below is an example of what might be created (click here to download):

 

 

The good news is you do not need to do this for each concept as it is pretty general or can be altered slightly for each concept. The power of this is that it actively engages students in the assessment process in two ways; by helping to create the criteria they better understand what is required of them to achieve a level 1, 2, 3, or 4. Also, they can be self-assessing as they compare their own work to this criteria, thus giving them the power to know how to improve to meet their goals.

Assessment as Learning means that students are a part of the assessment process; they are using self-assessment or peer assessment to evaluate where they are at and identify their strengths and areas of need. In other words, they use the assessment as a learning tool. This rubric allows students to engage in this important process. It gives them agency.

Each new unit could have a new rubric (use the same one and alter for each unit as needed) so that students know what depth of understanding we are expecting.

How do I assign a letter grade to the assessment?

As for the rest of the test, we could use a general rubric like the one my colleague Jenn Reeson and I have been tinkering with (it is still a work in progress):

New Math Curriculum – Rubric
(click here to download):

Please feel free to use some or all of this (thank you to Jenn Reeson for getting this started and continuing to try to make it a great tool for all of us to use). I have added in purple the specific concepts for this unit of study.

Here is another example created by Angie Gagne and Melissa Mawhinney. I’m extremely lucky to have colleagues who are so committed to student learning and who are so knowledgeable about best practices in assessment. Again, they plan to alter this rubric as this is a starting point for them. They will use it with their classes and adjust as needed so that it meets both their assessment needs and those of the students.

Communicating and Representing (click here to download):

Understanding and Solving

If you return to the sample assessment, can you now see how to ‘mark it’ using these rubrics? Students should have this rubric BEFORE the assessment and I like them to self-assess by highlighting where they think they are at (this is part of the reflecting piece) and then you highlight where you think they are at. There are a lot of rubrics for problem solving on the internet and once you understand their power and their purpose, you may choose to use one or more as templates and then create your own. Because this can be time consuming, some teachers just like the generic one (without the purple), or they use this generic one and the add in more specifics for each unit (like I did with the purple). Make it work for you.

The grade comes from a holistic overview of the rubric. I wouldn’t even assign a grade until you have to (i.e.: report card) as the research is pretty clear on this: as soon as we put a grade on it, the learning stops. Instead I give this back to students with the rubric highlighted and allow them to make any changes they want to improve. This rubs a lot of teachers the wrong way because it somehow seems not fair to the students who got it all right the first time but my goal is not to penalize kids who really want to do well and who have fully understood the concepts but have not performed well on the test. I don’t feel like grades should be a ranking of students but rather a way to see how far along the mastery spectrum they are. There is always room for growth and I want to foster this approach so that students continue to revise and edit their work until they have produced something that truly shows all that they know. This approach also promotes a growth mindset.

When I do have to assign a grade it’s pretty easy just by looking at the rubrics from the assessments. They will either be mostly in one column or in between, so mostly 1’s would be not yet meeting or “I”, while in between 1 & 2 would be C-, mostly 2’s = C, in between 2& 3 would be C+…so on with 4’s = A (exceeding expectations). You could also replace the numbers with terms that describe the mastery path, like: novice, apprentice, practitioner, master.

The purpose of the rubric is not only to get a grade but more importantly it is to give students the feedback that they need to improve. In the rubric they can see their strengths and their areas of needs. This can also be shared with parents so that they can support their child. It simply gives WAY more information about where their learning is at than a score of 19/20.

As with all of this new curriculum stuff, I know it can be overwhelming and so a good place to start is to find a rubric that’s created and adapt it to your grade level. I encourage you to do this with colleagues. The rubrics above were not created by one person but rather by collaborating, discussing and revisiting until the rubric made sense. Try a few things and see how they work for you. Please feel free to comment and share your experiences (there may be others who can help you out if you try something and it flops). Also, if you have a created a rubric and you are willing to share, I know there would be some grateful readers. No one is expecting perfection as we are all learning here. I’m a fan of NOT reinventing the wheel so please shareJ.

Thanks again to my colleagues Jenn, Angie and Melissa for sharing their rubrics; this takes courage to put yourself ‘out there’!

My mission is for teachers to feel great about their impact on student learning. I make it easy for teachers to prepare and deliver lessons that will change lives.

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