能上谷歌的加速器

I’ve written about my usual SBG scheme here. It works fine and many students take advantage of learning at a slightly different pace but still getting credit for what they know, once they know it. However, I’m interested in keeping small quizzes primarily in the formative domain, yet using an assessment tool that is based on clear learning objectives, re-testable and flexible. This post talks about a possible transition from using a few dozen learning objectives in quizzes to a new, larger goal assessment tool.

能上谷歌的加速器

This year was the first year that I had to put some restrictions on the number of re-assessments students could take. In Term 1 I was getting inundated with re-test requests, I estimate that I had somewhere between 300% – 400% increase in requests this year. It was crazy. I had to stop offering re-tests for a while and then gradually bring them back. I was actually surprised that students didn’t complain about me stopping them, or say that it was unfair. I think this was partly due to them recognizing that the system overall was quite fair.

能上谷歌的加速器

This year had some more challenges of course, because of the pandemic and moving to online learning. Unlike many of my colleauges, I didn’t even attempt to give out anything that could be considered a summative assessment. In other words, nothing was for marks. As far as I could tell, for most students this didn’t affect their overall effort. I say this both through my observations of student work and through a survey I gave students.

It was also pretty obvious to me that we had no way of accounting for summative assessments in the VSB secondary schools while online since there was no chain of custody or invigilation with the assessments. We send out an assessment and at some point it would be returned. What happened between those two events is anyone’s guess. I happen to think that most students would be honest with their work but that’s just a gut feeling.

Looking to next year, I was thinking that my typical SBG quizzes could still be done but kept formative. It then dawned to me that this is really the best use of them anyways. I’ve never liked having to turn a bunch of SBG quizzes into a grade. This of course leads to the next question then: what evidence should be used for a grade?

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Another possibility for determining a grade is to be deliberate with using “performance tasks.” When I think of performance tasks in physics, I think of assessment tools that are comprehensive and could be somewhat open-ended. A typical test could be a performance task but these types of tests usually don’t work well with SBG – they are not linked to learning objectives and the selection of questions and how they are graded can result in very unreliable data. To see how this can happen, look at page 12 of this presentation. When I run ProD workshops on this topic, I get the participants to grade this assessment using points. Without exception, in each workshop the assessment is scored with a range from 45% to 82%.

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It then dawned on me that this could be the type of assessment tool I could use with my students. For learning intentions, there would be a big shift. Currently I divide the course into separate units and each unit has maybe 6 learning intentions. For example, for Constant Acceleration:

While I would keep these learning intentions for clarity and practice with SBG quizzes, the SBG assessment would look more like this where the main assessment goal is the performance task CA:

We would still do on-going quizzes with kin.1 to kin.5, but they would be faster and part of entry or exit slips in the class. Progress would still be recorded as before. For summative assessment, I would use one problem (performance task) like the one written by Knight, shown above. The “score” would be based on how the student performed on the performance task.

能上谷歌的加速器

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My initial thought is that a student would have to repeat their performance twice in a row to obtain that grade. For example, if a student got an “Extending” on the CA task and then two weeks later gets an “Applying”, their score for CA would be Applying. “Applying” in week 1 and then “Extending” in week 2 would also be a score of “Applying.” However, in this case the student could ask to do a re-test and if they got an “Extending” that time, their score for the learning objective would be “Extending.” Overall grades would be determined using the proficiency scale for each unit/performance task, and SBG quizzes can be used for supporting evidence.

There are a couple advantages to this scheme:

1. The SBG quizzes should be a lot faster because students don’t need to endlessly pontificate whether or not they can do the question
2. The SBG quizzes still give good feedback to me and the students on what they need to improve on.
3. I can give SBG quizzes online during COVID and not have to worry about cheating, copying, lates, etc.
4. The grades will be based on overall understanding of a learning objective / unit goal through the performance tasks.
5. The performance task is truly indicative of what I am interested in students being able to do.
6. Doing each performance task twice spirals the curriculum and reinforces the idea that “learning is a transfer of knowledge to long-term memory” and this long-term memory refers to (perhaps) at least two weeks. You can’t just cram for an assessment once and claim to know it.

There are some challenges with this scheme:

1. Even if the SBG quizzes are faster, is this too much time set aside for assessment?
2. Since we have 6 units (I think?), each performance task is relatively high stakes
3. Will I be endlessly giving out re-tests to students so they can get two in a row? Will students give up on an objective if they get two “Applying” in a row, meaning that they will need to do at least two re-tests to increase their score?

能上谷歌的加速器

So far this post has been focused on assessment and knowledge based curriculum. I’m not ignoring curricular competencies, and I do assess them. What I’ve been leaning towards is setting up tasks that are linked to curricular competencies and assessing them and scoring them the same way as other learning objectives. I no longer have separate categories for the tasks, the students’ grade lumps all the scores together. Perhaps I’ll write more about this in another post.

能上谷歌的加速器

I also teach math (this coming year I will be teaching Pre-Calculus 11) and I’m not sure how this new thinking lines up with it. I haven’t taught Math 11 but I have taught Math 10. Looking back to it, I can’t think of very many comprehensive tasks. I seem to recall there being a lot of separate and related tasks but the learning objectives rarely led into a larger, more comprehensive task. I don’t know how this will shake out for Math 11.

能上谷歌的加速器

I recently sent out a survey to Twitter where 50 respondents were presented with series of scores for students. The scores were for individual learning objectives and all the scores are based on a 3 point or 4 point proficiency scale. Each score was indicated by one of four different colours. Users were asked to come up with an overall letter grade and percent for each student based on these learning objective scores. Some guidance was given to the user to ensure that everyone would have a common understanding on what each colour meant. Below is an example of scores for a student.

The main reason I was interested in doing this survey was to find out how consistent teachers can be when grading holistically, and how close their holistic grade would be compared to a calculated grade. For example, a 4 point scale like the one shown above can be averaged and converted to a percent by assigning a 1 to red, a 2 to yellow, a 3 to green and a 4 to purple and then averaging these point. This average can then be converted to a percent using the table below.

For Pam, she had an average of (4×2 + 6×3 + 5×4)/15 = 3.07. This converts to an overall calculated grade of 83%.

The Results

First let’s look at the overall grade results for Erika. Erik’s score results were:

Holistic grading results from 49 users are below.

The overall average for Erika’s holistic grading was 79% with a standard deviation of 5.7%.

The graph below shows the average and standard deviation for each of the 15 students analyzed. The standard deviation is quite consistent across all students. The average standard deviation for students rated on a 3pt scale was 4.9%, for a 4pt scale it was 4.5%, and for a mixed 3pt/4pt scale it was 5.2%.

Next I looked at how the average holistic rating compared to the calculated average.

These results were very close. The average percent difference between a holistic grade and a calculated grade was only 2.1%

Summary

Overall I would say that on average, a person is able to holistically choose an overall grade that matches a calculated grade. This is important when you consider how a calculated grade was created in this task: an average was found from individual learning objective scores and then this average was compared to a conversion chart. Here in Vancouver most teachers use the gradebook that is included with our SIS, “MyEducation”, and this gradebook is not able to calculate a grade in this manner. Therefore, if a teacher wants to use a proficiency scale where the first level (1, red) equates to a 50%, the gradebook will not be able to calculate a correct average. What this survey tells us is that we can have confidence that a teacher does not need to use a calculated average, and that a grade determined holistically will give the same results.

However, for any given student there was a relatively wide range of holistic grades, even if the average closely matches the grade. I’m convinced this standard deviation can be greatly lowered with training. For example, consider Jackson’s score results below. With a bit of training, a teacher should see that mostly yellow gives a grade of 75%. Jackson mostly has yellow with one green that mostly balances out with two red. Jackson should probably be given a grade close to 75%, yet two survey results gave Jackson a holistic grade of 50% and 55%. Clearly these grades are two low and I bet that the person was thinking that red is 0, yellow is 50% and red is 100%.

Using a survey like the one presented here not only informs on how well teachers can create a holistic grade, but it can also be used to help with training teachers and calibrating their grading ability to an agreed upon scale. Whether a person would want to use this holistic grading, that’s another question. I wonder how well this process scales? Would it be harder to choose a grade if a person was evaluating 40 learning objectives instead of 15? What if you can’t visually see all 40 learning objectives on the same screen or sheet at once? I don’t actually think it’s a good idea to have 40 discrete learning objectives, but these are the types of questions that need to be considered prior to deployment.

Last night I was at a district meeting on Communicating Student Learning. There are a few different CSL projects going on in our school district and these meetings are good places to share our individual school experiences and collaborate on new ideas.

At one point in the meeting, two concerns about proficiency based assessment/reporting came up. I wanted to write about them because these are two issues that I see raised with regards to assessment and Standards Based Grading (SBG) quite often and they are great questions. The first concern was asking how teachers can decide whether a student is ready to progress on to the next grade level when using proficiency scales. The second concern was asking if we have research evidence to show that proficiency scales improve student learning.

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While I believe we are mostly interested in using a proficiency scale to communicate what a student has done, there is more to it than being a one-way communication tool to parents. Proficiency scales are tightly associated and tied to criteria based formative assessment. All formative assessment schemes involve proficiency scales at some level. We also know that formative assessment is one of the best and most cost effective ways of increasing student learning. In this regard I feel confident in saying that as long as proficiency scales are part of a thoughtful formative assessment methodology, then student learning will improve.

Proficiency scales are often used and required in formative assessment, and formative assessment improves learning. Therefore proficiency scales often play a role in improving student learning.

As for the first concern mentioned above, it’s common for people to ask how we decide to pass or fail a student if we are using proficiency scales. The inference in this question is that a 100 point percent system is very clear because everyone knows that 50% is a pass. You get 50% or more, you pass the course.

Before I describe how proficiency scales can be used to determine a passing grade, I first would like to point out the absurdity of the 50% pass. I’ll start with an anecdote. Generally speaking, I don’t think I’ve ever seen a student with 50% that can really do anything correctly in a course. The 50% student pretty much doesn’t get the course skills or understanding. This is especially true for students that have 50% purely based on judging assessments, not because of late marks or other behavioral reasons. I suppose if a teacher deducts points/percents from a grade for behavioral reasons, a student could have less than 50% but still be skilled in some learning objectives.

In terms of accuracy, no one can grade classroom work to within 1%, especially if we want the grade to reflect student knowledge, skill and understanding. There are many reasons that we don’t have this kind of accuracy. The day of the test/assessment might be a bad day for a kid that is sick/sleep deprived, caught between fighting parents, anxious, preparing for a intense out-of-school competition, etc. The assessment itself might be invalid because the questions and tasks don’t fairly represent what the students were explicitly taught. A test that involves a broad range of topics can have test items that are biased in favour of a few topics, and therefore different students will get different grades depending which particular topic that are better in. This last point is one reason why I dislike teacher developed “final exams” that are meant to cover 9 months of content and understanding in a one hour long test. I believe that many tests used in the classroom are simply not robust. Assessment accuracy depends on a balance between robustness (did one student do well because the test happened to be weighted on the one topic they knew really well?) and sensitivity (does the assessment actually allow us to make good inferences on how much the student knows?). Test robustness and sensitivity require comprehensive test items that cover all topics in varying degrees of difficulty.

It is very difficult to write a valid assessment whether we are using a 100 point scale or proficiency scale. What we need to do is recognize the faults in our assessments and not attribute a perception of accuracy that is not there.

The last reason we should be wary of the 100 point scale is the idea that a 1% change is the difference between pass and fail, and reconciling that with what a student has to do to make a 1% change. For example, suppose a student has 49% and they just have to hand in one homework set to get the additional 1%. It’s likely that the student’s understanding and knowledge will not have changed from before handing in a homework set to after handing it in. If their knowledge and understanding hasn’t changed, why would their pass/fail status change? A teacher could instead have a student re-do an assessment in order for the grade to improve but the assessment would have to be carefully crafted so that an improved grade relies on the student improving on something they weren’t good at previously. Even if this is accomplished, there is still the problem of accuracy in the assessments. If we can’t measure better than +/- 5%, how can we say that 49% is a fail but 50% is a pass?

The pitfalls of the 100 point scale don’t speak to the concern on passing and failing using proficiency scales, but it can be useful to compare the two. Let’s compare examples of clearly defining what constitutes a “pass” for a course.

The 100-point scale describes what a student gets whereas the proficiency scale describes what a student can do. The proficiency scale example gives a better description of what constitutes a pass.

There are many different ways to describe a pass using proficiency scales, the above example is just one. In my experience, when a student has a portfolio of work assessed using proficiency scales, it has always been very clear on whether the student should pass the course. In the time leading up to a final report, suggested actions can be given to a student so they will clearly know what is required to pass. “Sally-Jane needs to improve on the learning objectives X, Y and Z in order to successfully complete the course.” In this example, the student is given clear and specific guidance on what needs to be done, and the action directly relates to knowing and understanding of the course’s curricular goals.

Whether we are talking about representation of accuracy, communication or improved student learning, the use of proficiency scales is an improvement on using a 100 point scale. I would be interested in hearing any counter arguments to this in the comments below.

Today in physics 11 I tried a new lab using our motion and force sensors, carts and tracks. The lab idea is from New Visions and I believe that the script that I was working from was written by Kelly O’Shea and Mark Schober.

I was pretty excited to give it a try because I’ve always just told my students that the area under a force-distance graph is work. With this lab, students develop the idea from direct evidence.

Students set up a tilted ramp such that they pull a cart up a delta h of 20 cm. The angle of incline can be anything, and this will play into the discussion after data is collected. The students pull the cart up the ramp and analyze their graphs. From their previous experience working with data and graphs, they look at average forces, trendlines, slopes of the trendline. After a short meeting where we try find a pattern, we all agree that there isn’t a strong pattern. I then challenge them to think of another way we analyze graphs and a few students said that we can look at the area under graph. That’s where we left it today.

Next class we will re-run the test and the area under the graphs should all be really close. I’ll then have them calculate the delta Eg for a cart that is raised 20 cm. From my own experiments, the results will be within 10%.

There were some problems with today’s lab though and I wish I could do a do–over. Overall it took the students almost 60 minutes to collect one run. Two groups did it in about 10 minutes, which is a lot closer to what I expected. The students were paralyzed by their data. Some groups had a negative slope in their trendline (their cart pull was slowing down), and that didn’t sit right with them. Other students were taking a very long time to plot a perfectly scaled sketch of their graph on the whiteboard, when the instructions were (and have been all year) to make a quick sketch. It was a bit tortuous and I showed some of my frustrations in class.

Looking back, I’m not sure if there is any advantage to not tell the students straight up that they should collect their data and analyze the area under the graph. I don’t any reason to have them first try and find a slope or whatever else they might try to find. I think I could frame it a bit different and allow for some exploratory time, but we didn’t need a full cycle of data collection that doesn’t deliver a useful result.

Another thing I could have tried is to show them an example graph and have a deeper conversation about why the graph looks like it does (accelerations and jumps in the pulling force). I did actually show them a graph from a demo pull but we didn’t discuss it in detail.

Overall I like the lab but that 60 minutes just about killed me, especially when a few groups finished in 10 minutes and we will need more time again next class. It was a sign that too many students didn’t understand the purpose of the experiment.

Research has long shown that fraction arithmetic is difficult for students.  We also now know that success when working with fractions is one of the best predictors for success in post-secondary education. With this in mind, one of my prime focuses in math 8 is to do the very best I can with teaching fractions to my students.

The research on fraction arithmetic tells us that by grade 8, students have a success rate of around 50% when adding fractions.  For some people in BC, this issue with fractional arithmetic is compounded by what they see as a weakness in the new BC Curriculum. In their minds, fraction arithmetic should start much earlier in the curriculum.  In BC we start working on equivalent fractions in grade 5, but we don’t do any addition, subtraction or division until grade 8.  The research on fractions and university success is used to convince people we should be starting earlier.  The argument that we are falling behind other countries in standardized tests (Singapore, Japan, China?) is also used.

While I completely agree with the issues mentioned in my first paragraph, I strongly disagree with the opinions that I mention in the paragraph preceding this one.

1. Success with fractions is correlational to university success and has not been shown to be causational.
2. As far as I know, the early success with working with fractions is predictive because it is selective, not because actually knowing fraction arithmetic at a young age is in itself important for later success.
3. Research back in the 1980’s shows almost the exact same success rate with adding fractions in grade 8 as it does now.  If starting fraction arithmetic earlier is better, we would expect to have more success in the 1980’s.
4. The concept of adding fractions should be simple.  Kids can add numbers, and my experience is that kids are good at finding equivalent fractions.
5. Research done by Rober Siegler and others has emphasized the advantages of seeing fractions as numbers, rather than parts of a whole.
6. In terms of standardized test scores, I believe it’s impossible to say that Asian teaching methods are better.  Any comparison needs to consider that their school systems incorporate many more instructional minutes and institutionalized tutoring.

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Those are three basic understandings that are either self-evident or at least easy to remember.  In terms of methods for adding fractions, we would simply use our existing skills and understandings (pre grade 8) and apply them to a new situation. I am very much against trying to have kids follow a prescribed algorithm because I believe it is unnecessary and evidently not successful. I used the word “prescribed” for a very deliberate reason. A basic intuitive approach to adding fractions based on two principles (numbers are easy to add, and fractions are easy to add when they have the same denominator) is the same as the algorithm, but presented in a conceptually understandable way.

The last piece in the puzzle for success in fraction arithmetic is taking advantage of some general teaching methods.  We should incorporate spaced practice (practice adding fractions over a period of time) and we should interleave the practice.

With the above ideas in place, I think it’s easily achievable to have well over 80% of a grade 8 math class correctly answer fractional arithmetic questions on pop quizzes.

Lesson 1

The lesson starts with me tying a piece of string across the classroom.

“Mr. Smith, why are you putting up that string?”
“I have some wet clothes to dry.”  Hey, days are long when you’re a teacher. Humour helps.

Everyone knows what a number line is, right?  Have a short discussion with your neighbour and come up with some properties of number lines.

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– they’re usually straight lines.  “Good! straightish is nice, but they can probably be curved too” (my clothesline is curved!).

– integers and numbers go on them

– you put dash lines on the number line.  “What do you know about the spacing of the dashes?”

– the dashes are evenly spaced

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<the numbers are a mix of integers, mixed fractions, proper fractions and mixed fractions. There are duplicates written different ways such as 2-1/2 and 5/2>

<5 – 10 minutes pass as kids place their numbers, argue, move numbers, etc.  This is the easy 10 min of my day.>

Alright, let’s all look at the number line.  Does anyone see any mistakes? Is there anything we could improve?

<we always have some things to fix.  Typically there will be two numbers in the wrong spot and at least one spacing that is done more poorly>

Fantastic. Looks good.  There is one huge lesson to learn from this.  Fractions are numbers.  We can take a fraction and put it in an exact position on a number line, just like a natural number or integer.  It doesn’t matter if it is a part, a whole, a mixed fraction, whatever.  Fractions are numbers.

Back your desks please.  Now take a look at these four numbers.  Talk with your neighbour and decide Which One Doesn’t Belong, and why it doesn’t belong. I’ll randomly pick someone to tell me what they think.

– 17, it’s the only prime number

– 44, it’s the only one that has the same two digits

– 65 because the other ones have their digits add up to 8 (1+7, 2+6, 4+4) [my favorite answer!]

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<I got these numbers from http://wodb.ca. The idea is to discuss properties of fractions, review.>

So you already practiced ordering fractions on a number line.  I know have a series of questions I’d like you to work on with the whiteboards.  I want you to identify which one is greater.

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Take a look around the room.  It looks like most of you agree on your answers. There is one that is quite different though.  Which is it?

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Who can explain why they think 3/8 is bigger?

– I know that 1/8 is bigger than 1/10 and since 3 is only 1 smaller than 4 and the 8 is bigger, I think 3/8 is bigger

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That sounds pretty convincing to me!  Ok, everyone needs to go back to their seats. What I want you to do is to write down one or two things that you learned today, or things that you had forgotten and now remember about fractions.

Following up from my previous post, here is another brief set of notes on the action and dialogue in my grade 8 math class.  We start the day out with some voting questions where we use Plickers and Peer Instruction.  My general instructions for all classes when doing voting questions are as follows:

1. No talking allowed while voting.  No sharing of answers or ideas. I want to see what your thinking and if you take your idea from someone else, I won’t know if you get it or not.
2. After you vote, we’ll see if there is an overwhelming consensus.
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Voting question: Which statement is true?

1. Adding a negative number makes the sum negative;
2. adding a negative number makes the sum smaller;
3. adding a negative number makes the sum bigger;
4. adding a negative number makes the sum more negative.

Voting question: find the sum of (-4) + (-9)

1. 5
2. -5
3. 13
4. -13

<the students overwhelmingly answer both questions correct, which is a good sign>

Whiteboards, try these questions. It won’t take long. Use a number line if you need to.
5 + (-2)
5 – (-2)
-4 – (-10)
How did you know that 5 – (-2) was 7?

– Because 5 + (-2) made jumps to the left on the number line so this time we jumped to the right.

<-4 – (-10) has a lot of different answers so we take some time to distill this one. Below is brief overview on what the discussion looks like. For every sentence below there were probably 10 more in the actual class.>

I see three answers to -4 – (-10). Which one are you confident in?

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I think I agree with your idea but I think some of the words can be confusing.

– “Adding a negative makes jumps to the left, so this one must be jumping to the right.”

– “On the number line instead of starting at 5 we start at -4.  But then we make jumps just like the one before it.”

Ok, I’m convinced.
Normally I would let you write down what you just learned but I want this to be very clear to everyone because this is an important rule we will use a lot. Subtracting a number is the same as adding it’s opposite. Let’s think of some examples…

<we go through a bunch of examples in whole class discussion where I pick random students to answer>

Ok there is 15 min left.  I have some practice questions for you.

<individual accountability part of the day>

I’ve seen lots of pictures of math Thinking Classrooms on twitter and I’ve also come across a few videos.  I haven’t seen anything that followed the dialogue in a classroom, so I thought I’d try to capture a bit of that aspect in this blog post.  What I have below isn’t all that different from a lot of lessons except that you have to visualize how the students are situated.  They are not copying something down from me.  They have to write everything themselves and chances are that at some point they will have to justify what they’re doing to the others in their group.  The topic for today was adding integers.

OK, I’ve put everyone in their random groups.  Remember, one pen per group and switch the pen after every question.

On your whiteboard, write down the sum of 5 + (-2) . Use a number line to show your reasoning.
Now try 5 + (-7)
Now try (-1) + (-4)

<kids worked pretty fast, about 1/2 needed number lines>
Let’s see what everyone did… what pattern do you see? Is there a rule that you can use?

– Adding a negative makes the number negative?
– Adding a negative number makes the number smaller?

What about (-1) + (-4)? Is the (-1) getting bigger or smaller?  What does this look like with money?

– If you owe someone a dollar and then owe them 4 more dollars, then you owe them more money. So adding a negative number is like increasing how much money you owe them.

Yes, in all cases the number is becoming more negative. Let’s go back to your seats and write down that rule in your own words.

Ok, try these Suduko type puzzles: Integers Two Ways

<lots of success, some good arguments and collaboration around solving the puzzles, making corrections, sharing>

– can we use a number line?  You bet you can.
– Mr. Smith, we’re done

If you’re finished, make your own puzzle.

Ok everyone, I just gave you a piece of paper. Put your name on it and try the three puzzles that your classmates made. Individual work and hand it in to me when you’re finished so I can see how you’re doing.

<this is where we have some individual accountability>

Last thing today. Who can add 48234 + (-1454) in their head in less than 2 seconds? Who can add 4534 + (-340823) in less than 2 seconds?

<lots of head scratching, no one can do it quickly>

What about 9932 + (-9932) ? Why is that so easy?

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Yes, they are opposites. Opposites add together to 0. We call them additive inverses but opposites is easier to say. We’ll talk more about them in the days ahead.

Kids these days don’t know as much because of grade inflation.

That makes no sense to me. Kids may, or may not, know as much as they use to but what they “know” is a result of the teaching that happens in the classroom. After the lessons, learning and practicing a student is assessed and typically given some number. Whether that number is 70 or 90, the learning has already happened. For a fun experiment, change your student’s report card marks by making everything 20% smaller and next time you see them, see if it changes what they know and don’t know.

I suppose someone might make the argument that an inflated grade makes students complacent with where they are at in their learning. I think this can be alleviated by creating a different classroom culture where students always try their best. My top students, whether their grades are inflated or not, are working extremely hard. I do have students that are complacent with their grades, but these are kids that are in the low B’s and lower and not competing for the best university spots.

Too many kids are getting into university that shouldn’t, because of grade inflation.

Not a chance. If University of Your Grades Are Inflated has 4000 openings for first year students, they’re going to let in 4000 first year students. Whether the average grade of the best 4000 students that they can attract is 90% or 70%, they’ll take the 4000 students. FWIW I haven’t heard of higher failure rates of first year students so I guess universities can’t be that upset about inflated grades.

Grade inflation makes university admissions unfair.

This one has some legs but I think they’re pretty short legs, and maybe even quite hairy. Which isn’t a bad thing. Come to think of it, I just described my legs. But I digress… I have heard of one case where a friend’s son, who basically finished at the top of his IB program in high school, didn’t get into University of Toronto engineering (I think that’s what it was). He is now pretty much at the top of his class in 2nd year engineering at UBC. Presumably grade inflation has something to do with this. How much, I can’t say. There was also a recent article in the paper about how some Canadian universities weight applications based on what high school they are from, because they think they have identified varying degrees of grade inflation. So, if there is a grade inflation issue, perhaps they have a solution. In my own experience, I feel that my top students get the best grades in my classes, and the grades reflect what I think represents their relative achievement. If I’m close to the average teacher, I think it’s reasonable to think that there aren’t many “less qualified” students leap frogging over “more qualified” students. Furthermore, we’re lucky in Canada because of the high equality/parity we have in our universities. There are maybe a few exceptions because of particular fields of study offered by a few universities, but in general I believe that most universities offer a very similar quality education.

Too many students are graduating because they don’t have to do provincial exams and because of grade inflation.

This one gets into the area of what we think is the role of public education in society. I believe that the primary goal of public education is to help create an informed, functioning and healthy society. To this end, I believe that the longer that more students stay in school, the better off we are as a society. I don’t think high school graduation credentials offer any kind of free pass to grand future endeavors and careers. No one is going to leap frog over someone else because they have an inflated average of 58% instead of 49%.

Grades are inflated because teachers get pressured, or because admin change grades.

I suppose this happens to some degree. However, I think that students today have a lot more supports around them and a lot more pressure to produce high grades. When I graduated, I think a 78% average would get you into UBC sciences. School was hard, probably about the same as it is today. However, we didn’t have to worry as much about school as students do today. Think about it… In 1988 a student needed a 78% average among students that ranged from 78% to 98% ish. There’s a lot of room for errors in there. Today a student needs maybe 92% in a range that goes up to 98%. That is super competitive. Grade inflation or not, one bad test is enough to take you out of the running. Let that sink in. In 1988 a kid could have a few bad tests. Today, one test is enough to turf your chances. It doesn’t matter if there is grade inflation, one bad test is enough to sink you.

Back to the supports. Kids may have tutors, options to re-do assessments, more personal awareness and self-reflection on how their learning is going, etc. Of course their grades are going to be higher. I also think that it would be surprising that students actually learn much more than they did 30 years ago. We are creatures bound by our biological and cognitive traits, after all. Most gains made by new teaching methodologies are small and often applicable to only a subset of the student population

This blog is not meant to be pro or anti final exam, I’ve written how I feel about exams elsewhere on this blog.  Furthermore, I am not condoning what I perceive to be a lack of direction from our Ministry of Education and the fact that they have not published any achievement standards in either the new curriculum or our previous curriculum.  I will say this though – if people think that BC’s previous curriculum was vastly better than our current one, I suggest you take another look.  The old IRP documents are lengthy and stacked with boilerplate text.  There were more learning objectives and I don’t think that is a good thing.  What they didn’t have, and still don’t have, are working standards on student achievement.  I never saw any teachers use the IRPs for anything meaningful, other than as a checklist of learning objectives.  The most used teacher resources I’ve seen in action are: passed down work from co-workers and teacher resource kits from textbooks.

At a recent “Communicating Student Learning” meeting in Vancouver we were presented with a proposed 4pt scale for recording student progress.

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The proposed grading E-D-P-E scale also seems reasonable in terms of having an upwards bound of “extending”.  It makes sense that we want our students to strive for excellence and recognize when this happens.  However, when I start to think about the word “extending” I start to see some problems.

If one of the goals and purposes of SBG and similar systems is to provide clear learning intentions to our students, exactly what does “extending” tell them?  Are all learning objectives “extendable”?  If we’re clear on what it looks like when a student extends, are we ultimately just changing the learning objective?  Consider a learning objective for Math 8 which could be “I understand where positive and negative integers fit on a number line, and I can add/subtract positive and negative integers.”  Let’s suppose that a student extends this by adding/subtracting positive and negative decimal numbers.  Is there any difference in the following grade scales?

As you can see, asking a student to extend a learning objective is no different from asking a student to master a slightly harder one.  If in fact you want your students to add/subtract positive and negative decimals, why not just tell them?  Of the above two grade scales, the latter has the advantage of being very clear because the Mastery level will be the explicit learning goal.

Working with scales and learning objectives for seven years, I have seen the advantage of being more clear on the expectations from the grade scales.  For good backwards design, we need to be explicit on the learning goals and then work backwards from our assessments.  Trying to design an assessment around allowing for students to “extend” is difficult at the best of times.

I would argue that neither of the above two examples for grade scales is appropriate for tracking individual learning objectives.  I think that if the learning objective is “I understand where positive and negative integers fit on a number line, and I can add/subtract positive and negative integers.”, then the scale should be:

I still want to see students showcase their understanding and this is where performance tasks come in.  I see performance tasks as being summative which produce a single grade in a holistic manner.  A performance task can take on many different shapes and forms, such as a unit test that gives one overall grade for several learning objects, or a project that is graded holistically against some set of standards or rubric.  I prefer to grade against a standard.  For example, students may be given an exemplar to help guide them in their work and if the student’s project is better than my exemplar, I give the student a grade of “extending.”  I also caution against using rubrics with many scales.  The scales are inevitably either too vague and don’t really help with the grading, or the rubric is too prescriptive and doesn’t do a good job of assessing anything other than the prescriptive list.  I believe that the “one column rubric” is one solution to this problem.  Instead of making a rubric, I prefer to make a list of features that I want to see (similar to a one column rubric) and then rely on an exemplar to give the students an indication of the quality of work I’m expecting.

In an earlier post I wrote about how I felt that I tend to move slowly through curriculum.  One of the things I do that slows things down is frequent quizzing and post-quiz self/group assessment.  Usually once every 5 classes (or less) we will have a quiz that can take anywhere from 10 minutes to 25 minutes.  Once everyone is finished, the quizzes are handed back to the students and we go over the solutions. Students make corrections and ask questions as we go along.  This whole process can take 40 minutes of class time.  Adding up all the quizzes, it’s a big chunk of time.

There’s reason to think that these quizzes are good use of time – it is a retrieval practice and there is timely formative feedback to me and the students.   However, in my Math 8 classes I’ve been doing something a bit different.  Every couple of days I give the students a very short, fast quiz.  There will be 4 to 6 questions covering topics that go back to the beginning of the year. They get about 10 minutes to do the quiz and then we quickly go over it.  We don’t use quiz dividers and we’re not recording the results. The purpose is fast retrieval practice with interleaved topics.  It is very effective.

These two different types of quizzing have their pros and cons.  For pros, the SBG quizzes have more in-depth questions on a particular topic and allow for tracking progress on the topic whereas the quick quizzes interleave topics and give relatively fast feedback.  SBG quizzes also allow students to focus on specific skills that require work.  For cons, the SBG quizzes take up a lot of class time and often do not synthesize topics.  The quick quizzes have a con in that they aren’t useful for tracking progress because each different topic only touches one or two partial aspects of the learning objective.  For example, on a SBG quiz on adding integers I will ask several questions to cover an array of situations or variations but on a quick quiz there will only be one or two questions. From this quick quiz we can’t infer much about student progress on a learning objective of adding integers if the only evidence we have is from 2 questions.

Adding to this mix, I continue to struggle with finding the best way to produce a summative grade.  For several years I’ve mainly been relying on converting SBG progress to an overall grade.  This makes it easy for students to track their progress and gives them many opportunities to improve.  The downside to this is that the grade doesn’t necessarily reflect overall performance because the learning objectives are done in isolation from each other.  To improve on this I’ve used various “performance tasks” that require the students to pull from several different skills, bodies of knowledge and competencies.  Once again though, time has been my bogey man.  A proper performance task requires 1 to 2 days every 4 to 6 weeks.  As a result, I’m often skipping the performance task in order to keep my classes moving along and the student overall grades are mostly made up from the SBG progress.

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Here are some possible schemes for tracking progress and grades.

There is also the idea of using a performance task as an example of student work to include in a student portfolio or report card, as opposed to reducing the task to a grade. I like this idea because it solves the problem of developing a shared meaning of where the student is at.  By including a piece of student work along with an exemplar of similar work, anyone that reads the report card should have an understanding on the student’s progress.  IIn the end though, we are required to report an overall grade whether it’s on a 100 point scale, a 4 point scale, or anything in between.

FWIW, the performance tasks I am using are shifting more towards individual tests or even 2-stage tests (individual + group).  While I have a couple of lab-like performance tasks that are really authentic, interesting and challenging, they cannot be done individually.  Since the performance task is used to make overall/summative inferences, I don’t think it’s fair to draw this information from a task that is almost all group work.  Furthermore, if I want to allow for students to improve their learning and have their grade always reflect their most recent understandings, it is very hard to use one-off lab performance tasks because they cannot be replicated by individuals and I cannot come up with enough variations to allow for re-assessments.