I’ve received some emails recently from teachers asking about Diagnostic Assessments, so I’m going to dedicate this blog to my experiences and thoughts on these, what I have tried, the issues I have had and what has worked well. I have also included links to download pre-assessments and answer keys for Whole Numbers for grades 3,4,5,6,7 &8.
“I love the idea of them and think they are very valuable but in my
experience, I had a lot of trouble getting decent data from them“
Why Should I Use a Diagnostic Assessment?
The purpose of a diagnostic assessment is to see what your students know or retained from previous years and where their gaps are. We also use them often as a way of identifying students who may need more support or intervention so they can be used by a whole school to help the learning support team know where their services are most needed.
My Struggles with Diagnostic Assessments
I love the idea of them and think they are very valuable but in my experience, I had a lot of trouble getting decent data from them. Here were the problems I kept running into:
Some students simply didn’t do it, or very half-heartedly because it wasn’t for marks they just didn’t care (incidentally, Canadian students ranked third WORST on how hard they tried on the most recent PISA – so maybe it’s a National problem!). When they aren’t trying their best the results don’t give us the information we need.
1.) Many students forget procedures until they are reminded or reintroduced. I have found that after a few minutes of reviewing a concept they actually do remember it. We obviously can’t spend a few minutes on each question on the assessment so when students don’t answer because they don’t remember, is it really that they don’t know how to do it, or understand it, or is it that they haven’t been given enough time/support to retrieve the information?
2.) Test anxiety/overwhelm. So many kids are so anxious about math and when given an assessment, especially with multiple pages, even if they are not for marks. This again causes inaccurate information.
3.) The diagnostic covers so much material – it was hard to tell how much they knew about the topic from one or two questions. I also found that many kids just guessed on the multiple choice questions, took hours to do the computations page and couldn’t attempt much of the problem-solving pages. All giving me good information about their lack of skills, but not giving me the specifics I was looking for.
For several years I would use the VIDMA (Vancouver Island Diagnostic Math Assessment) at the beginning of the year and the end of the year. In my attempt to get better data I tweaked the VIDMA for years; changing and deleting parts to try to simplify and just focus on number sense and I questioned whether students actually attempted the multiple choice questions or just guessed.
I looked for other diagnostics but the VIDMA was the best one I found and I was frustrated that I couldn’t make it work
A New Approach
Because I thought that the diagnostic was too long and cumbersome, I tried something else: pre-assessments for each concept.
I used resources like Leaps and Bounds (and intervention program by Marian Small), Marilyn Burns’ intervention resources and VIDMA and created pre-assessments for each grade at my middle school (grades 6-8) for each concept that had been taught in previous years such as Whole Numbers, Decimals, Fractions, etc.
The benefit here was that we were just looking at ONE concept at a time rather than the whole curriculum. The other huge benefit we found by using them was that we realized we had often been under-teaching or over-teaching many concepts. If you, as the teacher, assume they all come in with the skills from the previous year, or you assume you will need to go back and start from the beginning of the concept, you will also likely be over or under teaching.
One example was when we used the fraction pre-assessment in a grade 6 class. The teacher told me she always starts with fractions of sets (from grade 5) and then moves forward from there BUT we discovered that literally every single student in her class understood this concept so we didn’t have to bother, saving her a couple of lessons. AND we also discovered that the whole class didn’t have any conceptual understanding of equivalent fractions (also a grade 5 concept). There were 3 students who could find equivalent fractions numerically, but couldn’t show them using pictures or number lines, nor could they explain how they were equivalent other than to state the rule “whatever you do to the top you do to the bottom”, showing us they had no conceptual understanding. This was valuable information for us so that we could then differentiate our lessons to ensure that those 3 students were focussing on the conceptual understanding piece, not on the procedure.
A Flexible Approach
It is not always necessary to do a whole big pre-assessment, you could just diagnostic questions and break it down more. For example, if you are about to teach multiplication of double-digit numbers to grade 5 students, you could give them a few questions to see the strength of their prior knowledge:
1.) Show what 4 x 3 means in a picture or number line AND write a story problem that would be solved by 4 x 3
2.) Ask students to solve 4 x 30 and 4 x 300 and discuss the similarities and difference by using math vocabulary like place value.
These two questions alone will tell you
1) If they understand what multiplication means and when it’s used. This is pretty crucial so if they don’t yet have this understanding, now you know where to start.
2) If they understand the place value system. Using base 10 blocks is hugely helpful when showing them how 4 x 3 is related to 4 x 30 and then 4 x 300. If they are just ‘adding zeros’ they haven’t quite figured it out and that will come back to bite them in Grade 6 when they multiply decimals.
How to Explain their Purpose to Students:
I spend time explaining to students that this pre-assessment is a guide for helping me to help teach them better. I tell that I wish I was a mind reader but because I’m not, I need as much thinking on the paper as possible. Even if they know they’ve done it wrong or aren’t sure, I want to see where they go, what they’re thinking and what steps they’ve tried. When they commit to doing this – you will find their assessments to be incredibly valuable for you in terms of formative assessment. They will also help you plan partners, teams, differentiated tasks/lessons etc.
Benefits for Students:
The other benefit to using the pre-assessments is for the students themselves. It shows them exactly where they are- what they know and what they don’t know yet AND it is a nice tool that they can use to measure their growth. You could give the same assessment again part way through the unit and let them see their improvements. I find it a nice self-assessment tool and because it’s not for marks, it doesn’t create added stress. This is a nice way to develop the core competencies of self-evaluation.
They can be time-consuming – often taking at least one full class, sometimes more, but I find the time well worth it. You could always do a shortened version too if that suits you better. Sometimes I give the students the assessment and ask them just to do questions 1-3, or 5-8 and then I can see where they are at for that particular skill. I can then give them back the assessment at a later time and ask them to do other questions. This makes the process quicker and still gives me useful information about my students.
You will find pre-assessments for Whole Numbers here.
Please use what you want from them as they are far from perfect and I am tweaking them each year. If you have suggestions I’d LOVE to hear them – just like I tell my students “more minds on the problem creates a better solution”.