## Required Reading: Improving Learning In Mathematics

February 3rd, 2011 by Dan Meyer

This is essential. On commission from the UK in 2005, Malcolm Swan wrote a guide to great math teaching [pdf] that's as good as anything I've read at this length. It is, explicitly, a collection of activities — full explanations of resources a teacher can use for floatation in her first year — but the document also goes into exquisite detail about what *theory* motivates those activities. It outlines excellent pedagogy while at the same time keeping your head above the waterline.

This is a fast read — big type, thin margins, lots of color, etc. — and from now on, it'll be the first thing I recommend to new math teachers. I hope you'll do the same. But help them make sense of it also. Some of this only may look so brilliant in light of my abundant early-career failure.

on 03 Feb 2011 at 2:36 pm1 PhilAlso check out the latest project he (Malcolm Swan) has been involved with: http://www.bowlandmaths.org.uk/index.htm

A package of ICT enhanced enquiry learning packages. Some brilliant stuff here.

on 03 Feb 2011 at 6:49 pm2 serafinaThanks for another great resource, Dan!

I look forward to reading this over the next couple of days.

on 03 Feb 2011 at 10:53 pm3 NordinThanks for the link – a brilliant resource for a new maths teacher (me)!

on 04 Feb 2011 at 5:38 am4 Marilyn Knight JustDan & Phil — Thanks for the lead! I’ve included links to these resources on my home school web site & will explore methodologies & materials in search of ways to better reach my students :)

on 04 Feb 2011 at 5:59 am5 simon walshThe bowland approach sounds good. I think that giving kids and alternative way to learn is a big part of the battle won. I am a huge believer in activity based maths. You can see me teaching a class sequences with this method on our website. The lesson idea was not mine, it is a classic, but it shows the level of energy and enthusiasm that you can get in a maths class if you abandon text books.

video on this page..

http://mathsdoctor.tv/Maths-tutor/about-us/our-story/

on 04 Feb 2011 at 7:42 am6 ncetm_administratorThe whole Improving Learning in Mathematics is available online. More details at https://www.ncetm.org.uk/resources/1442. We’re also on Facebook and Twitter (search on NCETM).

on 04 Feb 2011 at 9:56 am7 blaw0013Hi Dan. Thank you for the resource. I agree that this can be a very powerful tool for a new teacher as they work to develop concrete examples of pedagogical and curricular materials for the classroom toward a vision to transform mathematics education.

I hope all of my students who find value in this resource will recognize the fatal flaw in its organizing premise, that there is one mathematics and one way to think mathematically that is worth knowing. This author decries the notion of pursuing a “discovery” approach to mathematics, yet the entire pamphlet has students working to know someone else’s mathematics, i.e. to discover something already known.

A humane way to teach mathematics reverses the role of “discovery,” charging the teacher with discovering how the child/student is thinking. What did the student make of the problem situation posed? i.e. What is the question in the student’s mind? Then, what is the conclusion/solution to that question and what reasoning rationalizes/justifies that conclusion?

The next step in the teacher’s role is to bridge the child’s thinking with that of their own–that which is representative of the discipline we call mathematics.

Try Dewey’s 1902 essay “The Child and the Curriculum.” http://www.archive.org/stream/childandcurricul00deweuoft

on 04 Feb 2011 at 2:29 pm8 Elizabeth SThank you for being in grad school (oh, and also for sharing this stuff!). :-)

Elizabeth (aka @cheesemonkeysf on Twitter)

on 05 Feb 2011 at 12:03 pm9 Pwolf“A humane way to teach mathematics reverses the role of “discovery,” charging the teacher with discovering how the child/student is thinking. What did the student make of the problem situation posed? i.e. What is the question in the student’s mind? Then, what is the conclusion/solution to that question and what reasoning rationalizes/justifies that conclusion?

The next step in the teacher’s role is to bridge the child’s thinking with that of their own–that which is representative of the discipline we call mathematics.”

This article says just that, and posits that there are concrete ways to get meaningful responses that will help teachers get a good picture of that student thinking.

It goes on to say that an effective teacher will be able to anticipate that not all students’ lines of reasoning will be correct, and will help students meet these shortfalls of reasoning head-on.

on 05 Feb 2011 at 1:52 pm10 Matt W.I agree with both pwolf and blaw003. It seems like there’s a disconnect between the underlying principles (which are great), suggested teaching strategies (also helpful), and many of the tasks – especially the classifying and matching ones and the ones where kids have to put somebody else’s steps in order.

on 05 Feb 2011 at 5:19 pm11 louiseI think the classifying items comes from some other parts of the UK curriculum for elementary students, which are really rather wonderful as they are not language dependent. I picked them up a couple of years ago on a trip “home”. Someone who is from the UK might tell us what they’re called (mine are at school). Non-verbal reasoning? I have used them in my classes to great effect with ELL students (high school geometry)

I think that if you see the classifying and matching in this context, it will be more cohesive with the whole premise.

on 06 Feb 2011 at 3:54 am12 Whose Learning Should I Be Documenting, Anyway? | Graham Wegner - Open Educator[...] when Dan Meyer points to an outstanding Maths resource, I am interested. But I have to weigh up the benefit to my own practice and the time it will take [...]

on 06 Feb 2011 at 1:09 pm13 PwolfI want to add in here that I’m using lots of these strategies on Monday: using the white boards, having students create problems, and making posters with linear equations.

I spent most of last few semesters trying to include techniques like this in my classes, to little success. I think I’m finally getting the hang of what direction my activities need to go. It’s kind of hard in the beginning to know what type of activity goes with what topic or current level of understanding, and what’s the right ratio of information given to information left out of an activity.

on 09 Feb 2011 at 6:30 pm14 blaw0013@Pwolf. First, let me say (restate) with great emphasis, the classroom strategies advocated in the pamphlet are GREAT, and the pamphlet itself I predict will be a great resource for the preservice teachers that I teach.

My disagreement with the pamplet’s author is not captured in the passage you quoted, rather in the paragraph before: “the fatal flaw in its organizing premise, that there is one mathematics and one way to think mathematically that is worth knowing. This author decries the notion of pursuing a “discovery” approach to mathematics, yet the entire pamphlet has students working to know someone else’s mathematics, i.e. to discover something already known.”

My naming “someone else’s mathematics” is a deeply troubling (form me?) aspect of what we are charged to do as public school teachers. Are we to create divergent or convergent thinkers? A convergent goal would agree with the “discover how you’re supposed to know/think mathematically.” This convergence sees one mathematics, probably those represented by “the standards.”

A divergent goal would engage kids in the mathematical activity of being human, thinking, reasoning, generalizing, deducing, etc. Maybe the Common Core Standards for Mathematical Practice point well to this defining quality of what might be “everyone’s mathematics.”

I don’t know… it is a very slippery idea for me. I know I don’t want to create a roomful of young adults who believe they don’t think right, that is like me.

on 11 Feb 2011 at 4:11 pm15 lizHey Dan! I’m so happy to have found this blog. I’ve only poked around, but what a great resource! Thank you especially for this. I’m in my pre-service year, gearing up for next year, so I appreciate the wealth of knowledge here. I hope your studies are going well. I’ll be checking your site often!

on 13 Feb 2011 at 3:52 pm16 Sam CritchlowThanks for the post – we have apprentice teachers at our school each semester, and I have been in the process of collecting readings, videos, etc. specific to math education to supplement their teaching seminar. Will add this to the collection.

on 14 Feb 2011 at 12:36 pm17 KYoungwe refer to this pack as the Big Blue Box (as that’s what the folders come in)

It has been an invaluable resource to a department who want to encourage pupils to think about maths.

Also it isn’t just about the resource its about how to use it effectively.

on 24 Feb 2011 at 7:35 pm18 lfarringtonJust finished reading this tonight. Lots of highlighter ink was used! Thanks for the pdf.

on 12 Mar 2011 at 5:52 pm19 Audrey Mc^2Hi Dan – thanks so much for this. I’ve now made, and used in my class, 2 activities based on this document. Huge improvement in engagement, even with lots of room for improvement on my design. The kids ended up discussing exactly those things that I wanted them to, only without any overt prompting from me. The activites are embedded in my Mar 11 and Mar 7 posts at:

http://audrey-mcsquared.blogspot.com/

(in case anyone wants to use/improve on them – hey, have at it!)

Audrey

on 13 Mar 2011 at 9:08 am20 Online Teaching Resources #1 « Between the Walls[...] Learning in Mathematics. Dan Meyer described this resource best: “It is, explicitly, a collection of activities — full explanations of resources a teacher [...]

on 16 Nov 2011 at 1:18 pm21 pepsmccreaDan et al.

If you want a greater insight into Malcolm’s thinking underpinning the design of the standards box then this is a good start…

http://www.educationaldesigner.org/ed/volume1/issue1/article3/

on 17 Nov 2011 at 2:54 pm22 KirkWow. Just finished reading it. That is powerful stuff. I think I am going to create a working group at the high school level around this.

on 06 Dec 2011 at 3:59 pm23 dy/dan » Blog Archive » CMC-N 2011 Reax[...] Shell Centre in England, which includes Malcolm Swan, whose exemplary work I've covered here and here. These are exceptional educators and task designers, but you don't have to take my word for it. The [...]