Topic (follow-up to Thursday, 12th August 2010): How do we assess whether or not mathematical concepts have been grasped and understood?
As it happened on Monday, 16th August 19:30 - 21:00 GMT

7:31 pm
ColinTGraham:
Hello everyone, welcome to Monday's #mathchat
7:32 pm
ColinTGraham:
Tonight's topic: "How do we assess whether or not mathematical concepts have been grasped and understood?" #mathchat
7:32 pm
padgets:
@ColinTGraham #mathchat hi everybody!
7:32 pm
ColinTGraham:
If it is your first time, a special welcome! Focus on one or two tweets and interact. Don't forget the hashtag: #mathchat
7:35 pm
ColinTGraham:
This is quite a general issue - assessment! Let's try to focus on assessing mathematical stuff...! And assessing understanding! #mathchat
7:35 pm
ColinTGraham:
Shall we start by itemizing the types of assessment we could use, whether or not we do! #mathchat
7:36 pm
padgets:
#mathchat I would like to know besides paper pencil how you assess math, I teach science and am looking for ideas :-)
7:36 pm
ghewgley:
Hello to all the people in #mathchat
7:36 pm
Caro_lann:
Hi all #mathchat
7:36 pm
cybraryman1:
Some math assessment sites on my Math Reference page: http://bit.ly/1PAeOz #mathchat
7:38 pm
padgets:
#mathchat ok, I use drawings of concepts by students, models students create about a concept, the making of videos, stories written
7:38 pm
ColinTGraham:
Some suggestions: oral explanations, maths journals, videos, portfolios, mini-presentations #mathchat
7:40 pm
ColinTGraham:
It's always a good idea to keep in mind the concrete->pictorial->abstract progression and recording all three stages #mathchat
7:40 pm
Caro_lann:
Observation; Q&A; student posters & presentations; completed tarquin puzzles #mathchat
7:41 pm
ghewgley:
@ColinTGraham I agree that a good mix of assessments is best - if nothing else, it changes things up for students and teachers. #mathchat
7:41 pm
ColinTGraham:
@Caro_lann What are tarquin puzzles, Carol, for those who don't know? #mathchat
7:42 pm
padgets:
#mathchat I use concept mapping
7:43 pm
ColinTGraham:
Can you expand on how that works, Sharon? RT @padgets: I use concept mapping #mathchat
7:43 pm
CoachGinsburg:
Questioning is key. E.g. : ask what and why before how; read my post Assessing Thru Asking for morehttp://bit.ly/atxwV0 #mathchat
7:44 pm
ghewgley:
I would also argue that lots of formative assessments and feedback are crucial as concepts are being taught. #mathchat
7:45 pm
ColinTGraham:
@CoachGinsburg Do you see that questioning as being primarily from the teacher or do you encourage student questioning? #mathchat
7:46 pm
ColinTGraham:
@ghewgley How much of the formative assessment process do you record or keep, Gary? #mathchat
7:46 pm
CoachGinsburg:
@ColinTGraham Definitely both directions, but it starts w/us as models #mathchat
7:48 pm
ghewgley:
@ColinTGraham A question I wrestle with. Currently not much as I use data for pacing, reteaching, extra practice, etc. #mathchat
7:49 pm
ColinTGraham:
@CoachGinsburg So does the "Why?" cause problems for younger students who prefer to ask it rather than be asked, David? #mathchat
7:50 pm
ghewgley:
@ColinTGraham Formatives are kinda like eyes in surgery - they guide where we are and help us get to where we need to go. #mathchat
7:50 pm
Caro_lann:
Sorry - not Tarquin, Tarsia. http://bit.ly/bVoryR #mathchat
7:50 pm
ColinTGraham:
Let's throw out a general question, then, How much of your assessment is formative and how much do/should you record it? #mathchat
7:51 pm
ColinTGraham:
@Caro_lann ;-) Thought that's what you meant! Don't worry about following links everyone, they will be recorded in the archive. #mathchat
7:52 pm
ghewgley:
@ColinTGraham Most of my assessments are formative - I like the constant feedback. Record for grades - little. #mathchat
7:53 pm
CoachGinsburg:
@ColinTGraham @ColinTGraham I've worked with kids as young as 1st grade, who were ok w/why--probably depends on what the why is #mathchat
7:53 pm
Caro_lann:
Tarsia puzzles: hexagonal or triangular matching cards. I use them for every level, numeracy up to HND #mathchat
7:54 pm
ghewgley:
@Caro_lann I love those puzzles/cards. Thanks! #mathchat
7:56 pm
ColinTGraham:
Do you think formative assessment should be part of grades, unless you are working on standard-based assessments? What %age? #mathchat
7:56 pm
gsirovat:
RT @cybraryman1: Some math assessment sites on my Math Reference page: http://bit.ly/1PAeOz#mathchat
7:56 pm
cybraryman1:
Listening to children explain how they solve problems is an interesting assessment technique #mathchat
7:56 pm
ColinTGraham:
HND = Higher National Diploma, UK qualification for University entry, in some cases.http://bit.ly/cQavH4 #mathchat
7:57 pm
Caro_lann:
Most formative assessment unrecorded. Written comments on written work (not numerical score or grade). Targets negotiated with ss #mathchat
7:57 pm
ColinTGraham:
@cybraryman1 Would you also record children's explanations too as part of building a portfolio? #mathchat
7:58 pm
ghewgley:
I agree with formatives being better with narratives on report cards. #mathchat
7:59 pm
ghewgley:
Formatives are geared more towards processes - kinda hard to grade that with a letter/number. #mathchat
8:00 pm
ColinTGraham:
@Caro_lann In your case, Carol, you are working with adults. Does assessment have a different sense of importance in your class? #mathchat
8:00 pm
cybraryman1:
@ColinTGraham Yes. It is interesting to see how students solve problems and it should be part of their portfolio. #mathchat
8:01 pm
ColinTGraham:
For me, that is the beauty, no grade! RT @ghewgley: Formatives are geared more towards processes - hard to grade w/ letter/number. #mathchat
8:02 pm
ColinTGraham:
@CoachGinsburg Do you have a set of questions you always use for assessing, David, or is it more spontaneous? #mathchat
8:02 pm
ghewgley:
Formatives are way more work for a teacher, but I think they are crucial to teaching and learning. #mathchat
8:03 pm
Caro_lann:
I don't have to grade any of my ss. Numeracy have a summative external exam and teachers have pass/fail assignments #mathchat
8:03 pm
ColinTGraham:
Let's shift direction a little now and talk about how we actually assess whether a concept is understood. #mathchat
8:04 pm
ColinTGraham:
@Caro_lann So very much a criterion-based situation, either you can or you cannot. #mathchat
8:06 pm
ghewgley:
I assess by student explanations, student teaching others, quizzes, projects, etc. #mathchat
8:07 pm
CoachGinsburg:
@ColinTGraham Spontaneous, and not that clever. Write me at david@ginsburgcoaching.com for a questioning paper I've found useful #mathchat
8:08 pm
drtimony:
Thinkalouds are powerful esp with good doc/eval plan RT @cybraryman1: Listening to children explain how they solve problems #mathchat
8:08 pm
Caro_lann:
@ColinTGraham Some would prefer red ticks and a % score. I train them out of it! They are allowed to "red tick" their own work #mathchat
8:10 pm
Caro_lann:
Numeracy adults still act as if they are in school with all the anxiety etc. Diagnotic work is really important #mathchat
8:10 pm
dazmern:
@CoachGinsburg I would be interested in seeing that paper. bollschweiler.school@gmail.com #mathchat
8:14 pm
Caro_lann:
If ss can explain to a peer, or write a new question it is an indicator that they understand. #mathchat
8:19 pm
ColinTGraham:
@drtimony Would/do you record thinkalouds, or do you see them as a way to encourage a way of helping less able students? #mathchat
8:19 pm
tj007:
Hello mathchat - managed to get on to join in. Tweetgrid seems to be misbehaving! #mathchat
8:21 pm
ColinTGraham:
@tj007 Yes, my TweetGrid decided to stop co-operating too Tim! #mathchat
8:24 pm
tj007:
I'm just trying to quickly flick through what has already been mentioned. #mathchat
8:24 pm
cybraryman1:
We have to be cognizant that some students have reading or learning disabilities so an oral approach would help in assessment #mathchat
8:24 pm
tj007:
I find that if a pupil can explain a concept to another, they are on their way to understanding it. #mathchat
8:25 pm
Caro_lann:
Tweetdeck playing up #mathchat
8:25 pm
drtimony:
RT @ColinTGraham def record for future analysis. Don't have literature with me but good resources for use are available #mathchat
8:26 pm
ColinTGraham:
@cybraryman1 I think an oral approach can also highlight lack of mathematical language too. #mathchat
8:26 pm
tj007:
An exam this yr was multichoice. It certainly helped 2 identify which pupils fully understood and which 'fell' for misconceptions. #mathchat
8:27 pm
ColinTGraham:
RT @Caro_lann: Pt 2 whole class do quick quiz on new topic. Self marked then identify area for group problem & individual targets #mathchat
8:28 pm
Caro_lann:
Agree! Important to develop language RT @ColinTGraham: @cybraryman1 oral approach can highlight lack of mathematical language too. #mathchat
8:29 pm
tj007:
I like 2 use remotes (qwizdom) 2 check pupil understanding. It enables me 2 record their responses and analyse the data generated. #mathchat
8:29 pm
ColinTGraham:
@tj007 Is that not the nature of multiple-choice though? How do you assess levels of understanding with multi-choice? #mathchat
8:32 pm
Caro_lann:
@ColinTGraham @tj007 Talk to the students after the multichoice test! #mathchat
8:32 pm
ColinTGraham:
Does anyone feel that students need to feel a sense of progress too? How does your assessment practice achieve this? #mathchat
8:33 pm
tj007:
@ColinTGraham not sure about levels of understanding - depends on how Q is asked or presented perhaps #mathchat
8:33 pm
ColinTGraham:
Yes, well that works so long as the test isn't summative! RT @Caro_lann: Talk to the students after the multichoice test! #mathchat
8:35 pm
tj007:
@Caro_lann Most realised their mistakes afterwards, but one test enabled us to explore limits of accuracy further which was great! #mathchat
8:37 pm
tj007:
'how we actually assess whether a concept is understood' can they apply their knowledge to a situation that hasn't been taught? #mathchat
8:37 pm
ColinTGraham:
One approach suggested on Thursday was getting students to make the questions for tests... do any of you do that? #mathchat
8:40 pm
ColinTGraham:
@tj007 That was a point I raised last week too. For me a big step is: being able to apply vs knowing when to apply knowledge #mathchat
8:41 pm
ColinTGraham:
RT @Caro_lann: My trainee tchrs have 2 evalu8 accessibility of various maths tests ( lang, context). It's useful for me to do too. #mathchat
8:41 pm
tj007:
I've not asked students to create questions before, but would happily try it to see how it works out #mathchat
8:41 pm
Caro_lann:
@ColinTGraham #mathchat Tests are external but ss could write qs for mock tests. Good idea - will try
8:43 pm
cybraryman1:
I had students keep journals with their diagrams & explanations. Also kept math glossary in them. #mathchat
8:43 pm
cybraryman1:
Like the idea of having students compose questions. #mathchat
8:44 pm
ColinTGraham:
One of the beauties of student-generated quizzes or tests is that it gives you an idea about how they think as well as language #mathchat
8:46 pm
tj007:
How would you encourage the students to create a unique question, rather than copy one they have done - or does it not matter? #mathchat
8:46 pm
edudemic:
RT @ColinTGraham: One approach suggested on Thursday was getting students to make the questions for tests... do any of you do that? #mathchat
8:47 pm
CoachGinsburg:
The resource is "Asking ?s" from Assessment Alternaties in Math http://bit.ly/aqd27o turns out I don't have reprint permission #mathchat
8:47 pm
ColinTGraham:
@tj007 I think if students are just reframing previous questions, it suggests a mechanistic or concrete level of thinking. #mathchat
8:49 pm
ColinTGraham:
@tj007 One way round this is to encourage 'trick' questions or exploring distractors. Earlier errors are good for this! #mathchat
8:49 pm
CoachGinsburg:
I did a stump Coach G In-Out table activity with Gr 6-8 that was fantastic--EVERY student created one, and a few stumped me! #mathchat
8:50 pm
ColinTGraham:
@CoachGinsburg OK, thanks for sharing the link, anyway David! #mathchat
8:53 pm
ColinTGraham:
In the last five minutes or so, are there any areas where you feel you could be doing more or less assessing and/or recording? #mathchat
8:53 pm
Caro_lann:
Ask them to write a multichoice question with distractors. Class discussion of what distractors are first maybe #mathchat
8:54 pm
tj007:
@ColinTGraham 'trick' Qs and exploring distractors sounds gd - will prob make me think more about what I wish the ss to learn too #mathchat
8:55 pm
ColinTGraham:
@CoachGinsburg Could you give an example of one of your In-Out activities, so we get the idea how they work, David? #mathchat
8:56 pm
tj007:
14 rules for writing multiple choice distractors (just googled) http://bit.ly/cnfDqu #mathchat
8:57 pm
ColinTGraham:
I don't advocate teaching to the test... but I have found that getting Ss to write ?ns actually helps to clarify their thinking #mathchat
9:00 pm
Caro_lann:
Will try to do more recording next term. Maybe post its for quick notes in class. Helpful for target negotiation. #mathchat
9:00 pm
ColinTGraham:
As a parting thought, it is also worth stating that multiple-choice is only one possible approach to assessment! #mathchat
9:01 pm
tj007:
The Multiple choice exam was the first we have done. With the new specs, it was also the last! #mathchat
9:03 pm
ColinTGraham:
OK, everyone. Thanks for another great #mathchat. The archive will be online in about 30 minutes. Don't forget to vote for the next one!
9:04 pm
CoachGinsburg:
@ColinTGraham See my post re: best way to prepare kids for m/c tests is to NOT give m/c in classhttp://bit.ly/cPBwyK #mathchat
9:04 pm
tj007:
At KS3 we have small tests at the end of topics (approx every 2 weeks) - not convinced that I am happy that they have understood. #mathchat
9:05 pm
tj007:
Will look to apply ideas mentioned tonight to try and help with that (prev tweet). #mathchat
9:05 pm
Caro_lann:
Good chat tonight. New stuff to ponder as always. See you next week! #mathchat