A+ Education: Lost in Interstellar space

How can diagnostic, formative and summative assessment be undertaken in an inquiry learning experience in Mathematics?

For my last question I will be searching A+ education. A+ education looks like a smaller database: 214,755 records instead of the millions available on ProQuest.   This time my inquiry question is focussed on assessment.

I know a little bit about assessment from resources found on Google in my first question, but I’m interested in finding a few more concrete examples from mathematics. In my first google search the Inquiry Maths page used the terms assessment for, as and of learning to describe diagnostic, formative and summative assessment, so I will keep this in mind as I search.

Keeping the smaller size of this database in mind, I’ve decided to start with a simple inquiry or “problem-based” and then list my terms for assessment.  I tossed up just leaving it at “assessment” but I decided that I would really like to see some examples of assessment at the different stages.

(inquiry OR “problem-based”) AND math* AND assessment AND diagnostic AND formative AND summative 0 results Next step: delete “maths
(inquiry OR “problem-based”) AND assessment AND diagnostic AND formative AND summative 2 results The first is about science, the second, called “Understanding and assessing inquiry-based learning” looks very promising.

Understanding and assessing inquiry-based learning (Brach, J.L. 2004).
The abstract listed the following helpful information :

Diagnostic assessment is used to find out which skills and strategies students know and can use, and then to build on these strengths, or target weaknesses for improvement. Formative assessment can help teachers identify the development of students’ skills and strategies, and monitor students’ planning, retrieving, processing and creating during the inquiry activity. Summative assessment is carried out at the end of the inquiry activity to provide information about progress and achievement. It assesses both the content and the process of the inquiry.    (Brach, J.L. 2004).

This was a good overview of the purpose of these types of assessment, but there was no full article for this so there was no further detail.

(“inquiry learning” OR “inquiry based” OR “problem-based”) AND math* AND “assessment of learning” AND “assessment for learning” AND “assessment as learning” 0 results I tried to search using the terms using by Inquiry Maths.  

Nothing again! Unfortunately, I’m going to have to delete my assessment modes.

(“inquiry learning” OR “inquiry based” OR “problem-based”) AND math* AND assessment 50 Finally some results! Scrolling through the first page there were a few that looked relevant, although many again were based around science.  I am reluctant to include a NOT science as search field, as many useful resources have been about science and maths together.

Assessing inquiry learning : How much is a cubic metre?

This is a very well-written article by Australian educator Kym Fry, with links to literature and concrete examples. This also helps to answer my first inquiry question as well!

Amongst the methods of assessment, the author mentions

  • Joint construction of criteria
  • Journalling
  • Sharing successes and challenges and receiving peer and teacher feedback
  • Students justify and communicate solutions, students judge and compare effectiveness.

As I was taking notes on this I also noticed that the subtitles for each lesson were based on Makar’s stages of inquiry that I had found way back in my first question, on the Inquiry Maths page.

(inquiry OR “problem-based”) AND math* AND assessment 90 This time I went broad.  I found a lot more irrelevant results but also one great article that had slipped through the cracks of my last search.

Formative assessment in mathematics inquiry : principles of feedback deepening mathematical understandings.

Another brilliant article again by Kym Fry, and again referencing Makar’s 4Ds.

This one talk about the need for assessment to be broad and flexible just like inquiry learning. She speaks about summative vs formative assessment and also the key phrases: where are you going? Where are you now? How are you going to get there?   Aligns five strategies of formative assessment (William, 2011) to 4D model of inquiry. (Almond, wells and makar 2010).  This is very explicit and makes assessment in inquiry learning easy to understand.

Screen Shot 2017-09-18 at 6.23.31 pm
Source: Fry, 2012


This result did not turn up in my initial search because it does not contain the word “diagnostic” or “summative” – just “summatively”!  If I had deleted those two terms from my search string or used a wildcard at the end of summativ*, I probably would have found this excellent article straight away.

Overall, I have mixed feelings about A+ education.  While I feel as though it was easier to search and find legitimate results because of its smaller database and focused content, I missed the flexibility that Google provides.  Having to guess exactly the terms found in an article made searching difficult, and really illuminated for me just how much Google adjusts for its users.



Brach, J. L. (2004). Understanding and assessing inquiry-based learning. In S. La Marca & M. Manning (Eds.), Reality bytes : information literacy for independent living (pp. 99-113). Carlton, Vic: School Library Association of Victoria Inc

Banner source: Pixabay 2017


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