It’s exam time and your students are preparing. You’re going around the class, observing how students are studying and, shock horror, they are re-reading and re-writing their notes. The notes are literally going from one notebook to another notebook without going through their brains in-between. As a teacher this is one of the most frustrating things for me to see, and recently I’ve been on a bit of a war path to try to stop it.

This is a short post to celebrate some of my students doing deliberate practice. This year I’ve been stressing the importance of students re-doing questions (as opposed to just re-reading them).

Pictured right is how Ericsson describes deliberate practice (pg. 367)

They way that I’ve advocated for this is to ask students to 1. Identify questions that they got incorrect in our weekly tests, 2. Get a book or another sheet of paper and cover the answer, 3. Re-do the question, 4. Slide the book/piece of paper down and check, 5. Re-do again if they got it wrong, 6. Re-do again a few hours/days later to consolidate.

I’ve felt like a bit of a broken record but then, today, I had my day made when walking around the class I saw these two students!

To attend to the motivational segment of the task, I knocked up this sheet that I gave to students at the start of today’s revision session.

Deliberate practice for the win. Just wanted to celebrate. Hopefully it pays off in their exam.

I’ve really enjoyed working my way through Brian Penfounds series of three (1, 2, 3) blogposts in his Journey to Interleaved Practice series recently. They detail how, prompted by a discussion with the Learning Scientists, Brian has been incorporating interleaving into his integral calculus class.

One particular instrument got me excited, it’s an excel spreadsheet that can be used to interleave questions when you’re planning both lessons and quizzes (see the blank version here (edit: Learning scientists just released a new version here) and Brian’s version here). Here’s a screenshot to give you a taster.

Being the focussed (and sometimes obsessed) learning strategist that I am, I really loved this idea. But it got me thinking, is this better than what I’m already doing? Should I adapt my current practice to incorporate this approach?

I’ve written about my assessment and feedback process before here , in which I talk about the weekly quizzes that I give students, and how they incorporate content from the previous three weeks. This means that students see content for a month in a row (in the teaching week, then in the three weeks after that), then they’ll see it in the unit test (maximum 4 weeks later, as each topic is approx. 8 weeks long) then in the mid-year practice exam, then in the end of year exam.

I wanted to take the opportunity to share how I actually choose which questions to put on these weekly tests (or ‘Progress Checks’ (PC) as they’re called in my classes).

Each week I run the PC, students self mark in class immediately after, then I collect up the PCs. I keep them overnight and return them to students the next day (for two of my classes, the third class waits for 3 days due to timetabling) and in the meantime I enter the marks into my gradebook. When I return the PCs to students (I do this once they’ve settled into some question work), I carry around a little notebook and have a mini-conference with each student, the questions I ask are generally

“How do you feel you went?”

‘What did you get wrong?”

“What mistake did you make?”

“How much prep did you do for this Progress Check?”

And finally

“Which question numbers did you get wrong”.

From that, I collate the following.

(For any student who doesn’t demonstrate that they prepared for the PC, they get a detention, which I also note on this sheet).

I then take a photo of this and store it with the progress check itself, like so.

Then, when it comes time to write the next week’s PC, I feed in the questions that were answered incorrectly (variations thereof) as well as new content, in addition to other concepts from the previous 3 weeks that I think also important to touch on again.

I was really excited by the excel approach, but I’m still very attached to the adaptive approach that I’m using. Perhaps the optimum would lie somewhere in-between, using both a more-complex structure than ‘the last 3 weeks’ (such as is offered by the excel spreadsheet), plus some element of adaptability to the questions and concepts that students are clearly struggling with.

We know that ‘Memory is the residue of thought’ (Daniel Willingham) and that in order for our students to learn they must actively think about the content to be learnt. This allows this content to occupy their working memory for long enough, and become anchored to sufficient elements in their long term memory, to trigger a change in long term memory, one of the well respected definitions of ‘learning’ (Paul Kirschner).

One of the arenas of teaching in which this can be most challenging is that of feedback delivery to students. Dylan Wiliam sums it up well in the following quote (Which I came across thanks to Alfie Kohn).

1/2: When kids receive grades AND comments, 1st thing they look at is the grade; 2nd thing they look at is…someone else’s grade -D William

Note: The original quote is “When students receive both scores and comments, the first thing they look at is their score, and the second thing they look at is…someone else’s score”, and can be found here (beware the paywall).

The challenge is, then, how do we give feedback to our students in a way that encourages them to actively think about their mistakes, and helps them to do better next time?

In the following I’ll share how I give feedback to students in two contexts. The first is on low stakes assessments that I carry out in my own classroom, the second is on major assessment pieces that contribute towards their final unit mark.

Assessment Feedback on weekly Progress Checks.

Before we dive in I’ll just paint a picture of how my weekly ‘Progress Checks’ fit into my teaching and learning cycle, and how each of these elements is informed by education theory.

At the start of each week students are provided with a list of ‘weekly questions’. They know that the teaching during the week will teach them how to answer these questions. Questions are to be aligned with what we want students to be able to do (curriculum and exams) (Backwards Design). Students are provided with worked solutions to all questions at the time of question distribution (The worked example effect). The only homework at this stage of the cycle is for students to ensure that they can do the weekly questions.

Progress Checks’ (mini tests, max 15 minutes) are held weekly (Testing Effect). Progress checks include content from the previous three weeks. This means that students see the main concepts from each week for a month (Distributed Practice). These PCs are low-stakes for year 11 students (contribute 10% to their final overall mark) and are simply used to inform teachers and students of student progress in year 12 (where assessment protocols are more specifically defined).

Edit: Here’s a new post on how I use student responses to these PCs to construct the next PCs.

When designing the progress checks I had two main goals: 1) Ensure that students extract as much learning as possible from these weekly tests, 2) Make sure that marking them didn’t take up hours of my time. The following process is what I came up with.

Straight after the PC I get students to clear their desks, I hand them a red pen, and I do a think-alound for the whole PC and get them to mark their own papers. This is great because it’s immediate feedback and self marking (See Dylan Wiliam’s black box paper), and it allows me to model the thinking of a (relative) expert, and to be really clear about what students will and won’t receive marks for. Following this, for any student who didn’t attain 100% on the progress check, they choose one question that they got incorrect and do a reflection on it based on 4 questions: 1) What was the q?, 2) Which concept did this address?, 3) What did you get wrong?, 4) What will you do next time?

Here are some examples of student self-marked progress checks and accompanying PC reflections from the same students (both from my Y11 physics class). Note: Photos of reflections are submitted via email and I use Gmail filters to auto-file these emails by class.

Note how this student was made aware of consequential of follow through marks on question 1.

Here’s the PC reflection from this same student (based upon question 2).

Here’s another students’ self-marked Progress Check.

And the associated reflection.

Students are recognised and congratulated by the whole class if they get 100% on their progress checks, as well as one student from each class winning the ‘Best PC Reflection of the Week’ award. This allows me to project their reflection onto the board and point out what was good about it, highlighting an ideal example to the rest of the class, celebrating students’ successes, rewarding students for effort, and framing mistakes as learning opportunities.

I think that this process achieves my main two goals pretty well. Clearly these PCs form an integral learning opportunity, and in sum it only takes me about 7 minutes per class per week to enter PC marks into my gradebook.

Assessment Feedback on Mandated Assessment Tasks.

There are times when, as a teacher, we need to knuckle down and mark a bunch of work. For me this is the case on school assessed coursework (SACs), which contribute to my students’ end of year study scores. I was faced with the challenge of making feedback for such a test as beneficial to my students’ learning as the PC feedback process is, here’s what I worked out.

On test day, students receive their test in a plastic sheet and unstapled.

At the start of the test, students are told to put their name at the top of every sheet.

At the end of the test I take all of the papers straight to the photocopier and, before marking, photocopy the unmarked papers.

I mark the originals (Though the photocopying takes some time I think that in the end this process makes marking faster because, a) I can group all page 1s together (etc) and mark one page at a time (this is better for moderation too) and b) because I write minimal written feedback because I know what’s coming next…)

In the next lesson I hand out students’ photocopied versions and I go through the solutions with the whole class. This means that students are still marking their own papers and still concentrating on all the answers.

Once they’ve marked their own papers I hand them back their marked original (without a final mark on it, just totals at the bottom of each page), they identify any discrepancies between my marking and their marking, then we discuss and come to an agreement. This also prompts me to be more explicit about my marking scheme as I’m being held to account by the students.

In Closing

I’ve already asked students for feedback on the progress checks through whole class surveys. The consensus is that they really appreciate them and they like the modelling of the solutions and self-marking also. One good thing is that putting together this post prompted me to contact my students and ask for feedback on the self-marking process of their photocopied mandated assessment task. I’ll finish this post with a few comments that students said they’d be happy for me to share. It also provides some great feedback to me for next time .

I’d love any reflections that readers have on the efficacy of these processes and how they could potentially be improved.

From the keyboards of some of my students (3 males, 3 females, 5 from Y12, one from Y11).

Edit:

A fellow maths teacher from another school in Melbourne, Wendy, tried out this method with a couple of modifications. I thought that the modifications were really creative, and I think they offer another approach that could work really well. Here’s what Wendy said.

Hey Ollie,

I used your strategy today with photocopying students’ sacs and having them self correct. The kids responded so well!

Beyond them asking lots of questions and being highly engaged, those that I got feedback from were really positive saying how it made them look at their work more closely than they would if I just gave them an already corrected test, understood how the marking scheme worked (and seeing a perfect solution) and they liked that they could see why they got the mark they did and had ‘prewarning’ of their mark.

Thanks heaps for sharing the approach.

A couple of small changes I made were

I stapled the test originally then just cut the corner, copied them and then restapled. It was very quick and could be done after the test without having to put each test in a plastic pocket

I gave the students one copy of the solutions between two. Almost all kids scored above 50% and most around the 70% mark, and I didn’t want them to have to sit through solutions they already had.

if you have thoughts/comments on these changes I’d love to hear them.

Thanks again!

References

Find references to all theories cited (in brackets) here.

Seeing as my students have to endure my presence, instructions, and bad jokes for 3 hours and 45 minutes each week, I figure the least I can do is give them an opportunity to tell me how I can make this task a little easier for them. In my first year of teaching I knocked together the below form. I’ve used it for a year now and it’s been really helpful to date. In particular, it’s helped me to bring more celebration into my classroom, with many students over the past year indicating that they want their successes to be celebrated more (usually with lollies!).

This has been great, but as I’ve moved into my role as head of senior maths this year it’s prompted me to think more strategically about student feedback, and the role it can play in my own, and my team’s professional development.

No feedback form is going to tell a teacher, or a team leader, everything they need to know in terms of ‘Where am I going? How am I going? Where to next?’, but I’ve been feeling more and more as thought these forms do have a key role to play in helping teachers to spot gaps, and motivating and inspiring us to improve our praxis.

I was really happy with the willingness of my team to roll out the above form (Obviously with ‘Ollie’ changed to their individual names) in their own classes, and the insights gained were very illuminating. But coupling these feedback forms with my own observations provided and even bigger insight for me. It surprised me just how differently student (novices when it comes to principles of instruction) and I (a relative expert) view what happens in a classroom.

From this it’s became more apparent to me that if I want student feedback to more effectively drive my own professional development, I need to start asking better and more targeted questions that will allow me to see exactly where my teaching is excelling, and where I’m falling short.

So, here’s a first draft of the new feedback questions (which I’ll eventually turn into a google form). I’ve based it off the Sutton Trust’s article What makes great teaching? Review of the underpinning research, headed up by Robert Coe. I’ve used the first four out of the six “common components suggested by research that teachers should consider when assessing teaching quality.” (p. 2). These are the components rated as having ‘strong’ or ‘moderate’ evidence of impact on student outcomes, and they’re also the components with observable outcomes in the classroom (5 and 6 are ‘Teacher Beliefs’ and ‘Professional Behaviours’, which encapsulate practices like reflecting on praxis and collaborating with colleagues).

For each of the following I’ll get students to rate the sentence from 1, strongly disagree, to 5, strongly agree, in the hope that this will give me a better idea of how students interpret the various components of my teaching and teacher disposition.

I’ll also add a question at the end along the lines of ‘Is there anything else you’d like to add?’.

I’ve numbered the Qs to make it easy for people to make comments about them on twitter. This is a working document and today is the second day of our 2 week Easter break. I’m keen to perfect this as much as possible prior to Term 2. Please have a read and I’d love your thoughts and feedback : )

Edit: A copy of the live form can now be viewed at: http://tiny.cc/copyscstudentfeedback

Four (of the 6) components of great teaching (Coe et al., 2014).

Questions.

1. (Pedagogical) content knowledge (Strong evidence of impact on student outcomes)

Student friendly language: Knowledge of the subject and how to teach it.

The most effective teachers have deep knowledge of the subjects they teach, and when teachers’ knowledge falls below a certain level it is a significant impediment to students’ learning. As well as a strong understanding of the material being taught, teachers must also understand the ways students think about the content, be able to evaluate the thinking behind students’ own methods, and identify students’ common misconceptions.

1.1 This teacher has a deep understanding of the maths that they teach you. They really ‘know their stuff’.

1.2 This teacher has a good understanding of how students learn. They really ‘know how to teach’.

If you have any comments on this teacher’s knowledge of the content and how to teach it, please write them below.

2. Quality of instruction (Strong evidence of impact on student outcomes)

Student friendly language: Quality of instruction

Includes elements such as effective questioning and use of assessment by teachers. Specific practices, like reviewing previous learning, providing model responses for students, giving adequate time for practice to embed skills securely and progressively introducing new learning (scaffolding) are also elements of high quality instruction.

2.1 This teacher clearly communicates to students what they need to be able to do, and how to do it.

2.2 This teacher asks good questions of the class. Their questions test our understanding and help us to better understand too.

2.3 This teacher gives us enough time to practice in class.

2.4 The different parts of this teacher’s lessons are clear. Students know what they should be doing at different times throughout this teacher’s lessons.

2.5 The way that this teacher assesses us helps both us and them to know where we’re at, what we do and don’t know, and what we need to work more on.

2.6 This teacher spends enough time revisiting previous content in class that we don’t forget it.

If you have any comments on the quality of this teacher’s instruction, please write them below.

3. Classroom climate (Moderate evidence of impact on student outcomes)

Student friendly language: Classroom Atmosphere and Student Relations

Covers quality of interactions between teachers and students, and teacher expectations: the need to create a classroom that is constantly demanding more, but still recognising students’ self-worth. It also involves attributing student success to effort rather than ability and valuing resilience to failure (grit).

3.1 Students in this teacher’s class feel academically safe. That is, they don’t feel they’ll be picked on (by teacher or students) if they get something wrong.

3.2 Students in this teacher’s class feel socially safe. That is, this teacher promotes cooperation and support between students.

3.3 Even if I don’t get a top score, if I try my best I know that this teacher will appreciate my hard work.

3.4 This teacher cares about every student in their class

3.5 This teacher has high expectations of us and what we can achieve.

If you have any comments on the atmosphere of this teacher’s classroom, or their student relations, please write them below.

4. Classroom management (Moderate evidence of impact on student outcomes)

Student friendly language: Classroom Management

A teacher’s abilities to make efficient use of lesson time, to coordinate classroom resources and space, and to manage students’ behaviour with clear rules that are consistently enforced, are all relevant to maximising the learning that can take place. These environmental factors are necessary for good learning rather than its direct components.

4.1 This teacher manages the class’ behavior well so that we can maximize our time spent learning.

4.2 There are clear rules and consequences in this teacher’s class.

4.3 This teacher is consistent in applying their rules.

4.4 The rules and consequences in this teacher’s class are fair and reasonable, and they help to support our learning.

4.5 Students work hard in this teacher’s class.

If you have any comments on this teacher’s classroom management, please write them below.

Final Open-ended Questions

If you have any further comments or questions in relation to this teacher, please feel free to share them below.

My school is currently reviewing our PDR process. As the new head of senior maths this is a really crucial time for me to step up and try to bring some things to the table that will ensure that, as a team, the senior maths teachers are teaching in an evidence informed fashion.

I’m posting now, prior to submitting final ideas to our college, in order to share some thoughts and hopefully open up a discussion with others so that I can improve and optimise this process.

In partnership with my colleagues we’ve brought in a whole new instructional process this year at our senior college. At the moment we’re working on bedding it down, and having imput into the PDR process means ensuring that we’re all being asked by leadership to provide evidence for instructional practices that we actually think are going to contribute to student learning.

I’ve drafted the document below as a list of things that I myself would like to be measured against and I’m looking to take this to our maths team meeting soon to see if there’s anything that the team would like to add or subtract as we make our submission to leadership. (Hover over the top right of the doc to open in a new page).

I’d love any thoughts or comments on what I’ve put together thus far and how it can be improved.

Note: The ‘goals’ across the top come from our pre-existing PDR process. They’re non-negotiable so each of the elements I’ve included below will fit under those three goal headings (I’ll work out which goes where later, they’re each broad enough that alignment shouldn’t be an issue).

Note 2: SIM stands for ‘Sunshine Instructional Model’, we have a pre-established instructional model so I’ve just highlighted the main points that I think map really well onto that.

Any thoughts or comments appreciatively received : )

Ollie.

Edit, I have replaced the original version with the most recent version, as attached below.

Edit: This activity follows a broadly constructivist approach. Since running this activity last year, and in light of the evidence, my view on constructivist teaching methods has changed. If I were to use this activity again, I’d change the order. That is, I wouldn’t run it as a way to try to get students to discover the embedded concepts, instead I’d run it as a way to consolidate the knowledge of concepts previously taught via direct instruction.

At the recent Educational Changemakers 2016 conference (EC16) I came across the work of Shane Loader and the Empowering local learners project. After an engaging chat at the post-conference drinks, Shane was generous enough to share with me some of the top blogs that he follows as well as a link to the Empowering Local Learners (ELL) project that he’s currently working on. Whilst browsing the site I found a great lesson plan on surface area and volume that gave me an idea for my Methods Class. The activity: ‘What’s my function?’.

The previous few lessons had been on introducing the derivative function. Students were able to calculate the derivative of a polynomial both from first principals and ‘the rule’. The goal of this lesson was to scaffold students to make the link between the zeroes of a derivative function and the turning points of its parent/primitive function.

I split my (luxuriously small) class into two groups and gave each group one of the following instruction sheets.

Students were excited! They were straight onto Desmos to explore their functions

Then they jumped into asking their questions. Here’s how the discussion went…

The students were taking the activity really seriously, and being very competitive. Due their deep consideration of the questions they were going to ask, they were really taking their time, and we were fast coming up to the end of the period. With about 15-20 minutes to go I took advantage of my teacher privilege with the following change to the rules (I recorded the following in class).

Here’s he chat that followed… (The team on the left knew their original fn was a cubic, and the other knew they were looking for a quartic).

It can be seen that the team on the left got the hint and jumped into asking for the zeroes of the derivative to find the turning point. The team on the right tried a similar thing, but only on their second turn, and they were playing copy-cat so didn’t quite know why they were asking the question. Results? Here’s what was produced…

By this time we were up against the end of the period so I took a photo of the fns to prompt discussion at the start of the following lesson.

In the following period, I asked one basic question of the team who drew the fn on the bottom right: “Why did the other team ask for the zeroes of your derivative function?”. A long discussion ensued but we managed to boil it down to the following spaced repetition card…

I guess I could have just told them that at the start, but that would have taken out the joy and excitement of making the connection themselves*. We’ll see if it helped it stick… term break starts tomorrow!

*Many readers will already be familiar with Paul Lockhart’s ‘A Mathematician’s Lament‘ on this point.

One of the most powerful lessons that’s emerging out of my current Masters project on multiplicative thinking is on the power of maths card games in the classroom.

The power of games jumped out to me for two particular reasons; one relating to spacing repetition, and the other relating to formative assessment.

It’s perhaps not surprising that playing games has proved a fun and engaging way to incorporate spaced repetition of traditionally laborious number facts (like doubles of the numbers to 10, complements of 10, and doubling strategies) into sessions with students. But what definitely came as a surprise to me was the notion of using student boredom as a formative assessment tool.

Students would come in at the start of our sessions and ask me, session after session ‘Sir, can we play double trouble bingo* again?’. I was shocked by how many times the students were authentically excited to play the same game. It took me a while to realise that what was happening was that they were still challenged by the maths on which the game was based, and as a result, were still keen to play. With all of the games there came a day when the students would suddenly say ‘this is boring’. Why such an abrupt change?

Original Image Source: Pixbay

The answer came when I serendipitously had a campfire-side chat with an early childhood educator and, whilst discussing learning through play, she spoke of the analogous situation in her learning space. “Yeah”, she said, “They’ll play with a toy and they’ll struggle with it, then they’ll solve it. They might solve it a few times, but then they’ll leave and go to another toy. That’s when we know they’re ready for us to make it a bit harder”… BINGO! What a revelation!!! (Well, for me anyway). Turns out we can trust students to know when they’re ready for the next challenge. #studentvoice!

As my masters project wraps up, and I think of taking some of the techniques and strategies out of the small group setting and into the classroom, I’m trying to brainstorm ways to bring the power of these games into the mix.

What I’ve shared below is the three games that I’ll be trialling with my VCAL numeracy class tomorrow. I’ve created a quick worksheet as a warm up to each of the games (and as an aid to help the students select the right game for them) and I’ve bought a bunch of packs of cards to get us started. The idea of the videos is not only to share with other teachers some of these games but also as a (non literacy-dependent) reference for students to check if they’re a bit hazy on the rules. I’ve got a whole heap of other games that also powerfully support multiplicative thinking and I hope to eventually compile them all into a nice concise resource. But for now, here’s a taste whilst I experiment with what actually works at the chalkface.

Big thanks to my buddy Holly for helping me with the vids!!!

A note on modelling and mathematical language: Holly and I have tried to model the kind of mathematical thinking (and talking) that we hope to promote in students. In addition to explaining our thinking out loud, doing our own calculations and keeping our own scores is a really important part of the game play to ensure that everyone learns as much as possible through playing.

*I’ll upload my ‘double trouble bingo’ slideshows soon.

Complements of 10 memory

Quickly recognising the complements of 10 (2 and 8, 7 and 3, 6 and 4, etc) is an imperative skill for students addition and subtraction abilities and is a key element of part-part-whole understanding (students recognising that numbers are made up of other numbers!). I developed this game by making a simple change to the age old ‘memory’ game that I used to play with cards as a kid. (ps: Another game to easily be modified to work with complements of 10 is the game of ‘snap’. Depends on how much you value your cards though as this game will definitely reduce their longevity).

Stop or Dare

This game builds on part-part-whole understanding and place value understanding (e.g., to add a 10 we just increase the number in the 10s column by 1) to help build students’ addition strategies. I can’t claim this game, I came across it through the people behind MrMooreMaths on youtube. This was one of the students’ faves and, as I mention in the video, it can be made more complex by subtracting or adding, or even adding or subtracting doubles to or from 200 (could do triples or quadruples too, the possibilities are endless).

Picking Percentages

Holly and I designed this one together a couple of days ago. I feel it’s a really powerful way to help students to link fractions to percentages and develop some proportional thinking (the fact that the percentage changes as the number of the cards in the round changes has the potential to be a real mind bender!). It’s only been played by 2 people in the world so far so I feel it’s got some tweaking to go. In particular I want to change the scoring system to more of a progressive adding one, this will help build the tension in the game. I’ll try it out in the classroom and we’ll see how we go. Again, this game could be made more complex by introducing more rounds such as 6, 8, 9 and 20 card rounds.

If you have any suggestions on how to improve these games, or any suggestions on other games I’d love for you to hit me up on twitter. @ollie_lovell : )

What others are playing. Some nuggets from twitter…

In late 2013 I set myself a challenge of getting conversational in Mandarin Chinese in one year. One of the biggest barriers to me reaching this goal was the pronunciation of the language, as it has many foreign sounds to a native English speaker.

Throughout my journey I came across a whole host of incredible resources, from the website Hacking Chinese to the Glossika approach, that really helped me to overcome this challenge. Over summer I sat down with my brother (who is now also learning Mandarin) to try to give him a bit of a crash course on what I had garnered from these resources. Please find a video of that lesson below with the associated document and links embedded below that. I hope that Mandarin learners of all stages find this a helpful article.

An additional tip that I didn’t mention in the video is the benefit of recording yourself and playing it back to check how you’re tracking with your pronunciation. I can’t recommend this approach highly enough. Good luck!

This post is one of a series detailing my current mathematics lesson rhythm and routine. This one outlines how I use spaced repetition software (SRS) at the start of my lessons to help students to remember key information. There is a video of me teaching with SRS at the bottom of this post.

Thinking back to my own time at school, I distinctly remember one challenge in particular. I remember feeling that studying mathematics in discrete topics (or units), made it really hard for me to remember the relevant concepts when it was time to revisit that branch of mathematics again, sometimes over a year later.

Through my post-schooling forays into language learning in particular, I have come across some research backing up those schoolboy intuitions.

What I was feeling was the effects of a cognitive phenomena called the ‘forgetting curve’ (Ebbinghaus, 1913). The forgetting curve (pictured below) is a graph that approximates the rate at which an individual will forget a given unit of information.

In the late 1800s, a German chap by the name of Hermann Ebbinghaus constructed the first forgetting curve by trying to memorise nonsense syllables (such as “WID” and “ZOF”) and then testing himself at regular intervals, rating his level of accuracy, then plotting these points out on a graph.

As can be seen in the picture of the forgetting curve, if we want to remember something, we need to be reminded about it at regular intervals*. The good news is that the more times we’re reminded about it, the longer the interval until we need to be reminded about it again!

*(The necessity of reviewing a unit of information at regular intervals is obviously dependent on what the unit of info is, and how it relates to your prior knowledge/how emotionally charged that memory is. For example, It’s highly unlikely you’ll ever forget your first kiss! Ebbinghaus’ original forgetting curve is, however, a great approximation for units of info like; words in a foreign language, or even terms such as ‘perimeter’ or ‘circumference’.)

Such a curve has important implications for teaching and learning. If we want a student to remember the basics of trigonometry when we come around to the topic again a year later (e.g., basic terminology, sum of the angles in a triangle, etc), we had better ensure that several times between now (time of teaching) and next year, they get reminders at key intervals.

The basic idea underlying this reminding-at-intervals is the spacing of repetition. We all know that it isn’t a good idea to cram your study, but a recent meta-analysis of studies, Carpenter, Cepeda, Rohrer, Kang and Paschler (2012) brought together research on the actual effectiveness of spacing repetition. The following excerpt details the results from just one of the studies that they cited in their meta-analysis.

(Carpenter et al., 2012, p. 371)

This is all well and good as a concept, but how can we do it in practice? There are literally hundreds of new words and concepts that a student is expected to grasp in a year, is it realistic for a teacher to keep track of each of these terms and ideas, and remind students of all of them at periodic intervals?

I’m hoping that the answer is yes.

In 2014 I set myself the challenge to learn Mandarin Chinese in a year. As I delved deeper and deeper into effective learning methods, I came across spaced repetition software (SRS). SRS is a program of digital flash cards (you can make them yourself, or download pre-made decks) that, based on self-ratings, uses an algorithm to calculate the optimum time to review each given unit of information. It is essentially plotting your forgetting curve and reminding you of that piece of information just before you forget!

This software has been notably used to great success by such polyglots as Scott Young (who learnt 4 languages to a very high standard in one year) and Benny Lewis (very famous polyglot). It definitely helped me, and with the help of the SRS program that I use, Anki, I was able to reach my goal and achieve a conversational level of Mandarin within a year. These days I use it to remember a whole host of things; from people’s names, to new english words, to the countries of the world. I currently have a little over 3000 digital flash cards in my review ‘circulation’ and to keep on top of all this info it only takes between 10 to 15 minutes of my time per day. Here’s a snapshot of my study statistics from the last month.

(my personal spaced repetition data from the past month)

I was really keen to bring this incredibly powerful tool into the classroom to try to help my students to overcome the memory challenges that I, myself, faced as a student. So I did!

Since I started teaching at the start of this year, I’ve been using an SRS program (Anki) in all of my classes. We use it at the start of every lesson and I call students’ names with the use of coloured pop-sticks, a method that I’ve written about previously.

The result?

It’s hard to comment on the long term effects as it’s still early days, but student feedback has been good, for example: On the end of Term 1 feedback form that I handed out to students, many of them made comments such as the following:

But hey, I thought that the most helpful thing would be to give readers some eyes into my classroom to see exactly how it plays out. With my students’ permission, I’m sharing below a clip from my VCAL (Victorian Certificate of Applied Learning) numeracy class. Just for a bit of context, VCAL is a program designed for students who are planning to explore post-secondary pathways into vocational training. I have students who want to be nurses, flight attendants, and many of them aspire to the a position in the military. What you see below is a classic beginning of lesson episode. One of the students (Sharnee) is in charge of the pop-sticks, pulling out student names, and the other students are sitting (with varying degrees of focus), considering what their answer would be, then answering if their name is called up. I’ve found that the students enjoy the routine and it adds a game show like feel to the start of the class. Hopefully this little clip gives you a bit of a glimpse into how Anki works, and how I feel it can help my students to overcome one of the challenges that I myself faced in school.

References:

Carpenter, S. K., Cepeda, N. J., Rohrer, D., Kang, S. H. K., & Pashler, H. (2012). Using Spacing to Enhance Diverse Forms of Learning: Review of Recent Research and Implications for Instruction. Educational Psychology Review, 24(3), 369–378. http://doi.org/10.1007/s10648-012-9205-z

Ebbinghaus, H. (1913). Memory: A contribution to experimental psychology, (3).

I’m super excited about sharing this ‘Problem Solving Spell’. I modelled it on the problem solving template outlined in Charles & Lester (1984, p. 20), a pic of which I’ve also included at the bottom of this post.

Please feel free to use as you see fit, I’ve included the text below the pic incase you’d like to format in some other way.

Text:

A Problem Solving Spell
In a test or in a lesson
Come across a tricky question
No need to worry, fret, or doubt
This solving spell will help you out

Read the question carefully
Which words or phrases might be key?
Do you understand ok?
Now write it in another way

List what you already know
This gives us hints of where to go
Draw a pic, or act it out
Visualise what it’s about

List your info in a table
Spot a pattern, if you’re able
We now are only half way through
The many tricks that you can use

Struggling to make progress?
Working backwards could be best
Make the question simpler
Or solve a problem similar

But sometimes there will come a time
You’ve thought, and thunk, and tried and tried
Eventually say, ‘what the heck!’
And have a crack at guess and check!

You’ve found an answer, good for you!
And showed your working right way through
Before you’re feeling too spellbound
CHECK THE ANSWER that you’ve found!!!

Basis for the ‘spell’ (Charles & Lester,1984, p. 20)

Reference:

Charles, R. I., & Lester Jr, F. K. (1984). An evaluation of a process-oriented instructional program in mathematical problem solving in grades 5 and 7.Journal for Research in Mathematics Education, 15-34.