Tag: strategies

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“When I feel stuck in math, I can ____” (Lesson Sketch)

April 2020 Update. Distance learning versions now available: Stuck Strategies: Data and Reflection and Stuck Strategies: Complete Bundle

I am starting a new class, with a new group of students soon. I’m excited. And nervous. And all the conflicting things that change makes me feel.

There are many things to figure out in any new teaching situation. But this is also when I am most-glad for old-favorite classics. My new class and I are starting with an old favorite lesson  about productive struggle in math class.

I particularly like this one to start with a new group.

It’s powerful to start by saying “Yep, we all feel stuck sometimes. “

It’s even more powerful to start the year by saying “But ‘stuck’ isn’t the end of the story”

Feeling Stuck in Math Class? Reread the question Look at a previous question Re-read the directions draw a picture or diagram check your work think about it differently check your notes check the book work with a peer ask for help ... Keep trying!

Originally published Feb. 2018, updated spring 2020

These hint cards floated across my teacher-media radar. And I was intrigued.

I see too many students hit a roadblock and stare at it helplessly, unsure of how to get around it, and that’s the end of that study session/class/learning until someone comes around to get them unstuck.

I liked the idea of a resource that they could access when they hit those roadblocks, that wasn’t just waiting for me.

I work hard to convince my students that it’s great to ask questions, so I wanted to be sure I didn’t discourage that, just to broaden the options to include resources and strategies that they have or can implement themselves.

(Because self-directed learning, but also, homework.)

((And ultimately, for my students, a high stakes test when I’m not around to help.))

Also, I didn’t want to make a different set of cards for each lesson.

(Because in the reality of my prep time, I couldn’t be sure they’d actually happen every week, and I needed something reliable if students were going to use it.)

So, the idea rattled around in my head for weeks until it was ready to come out.

What emerged: have a discussion about strategies, and combine it with a math lesson so students don’t revolt about losing math time.  (Because, #reasonstoloveadultlearners, they would be upset to miss out of math time)

So, after the introductions and the homework policies and the other start of the term business, we brainstorm responses to the stem “When I feel stuck in math, I can ____”.

Some of my students were far better than others at this, and one class ran out of ideas after ‘keep trying’ and ‘ask for help’.  This says much about the struggles of that particular group of students.

But it also says, come prepared, teacher, with some ideas of your own.

Once we had a list, we collected data about my students’ current habits. (I had my students come to the board and make tally marks, you could use a printable ballot, hands, four corners etc.)

Then we analyzed our results. One class made bar graphs, one wrote statements with ratios. Since that first time, I’ve done percents and a few other math skills.

And, now their strategies (and the bar graphs) are on the wall, right next to my white board. A reminder – I hope! – for the rest of the trimester.

A full version of my lesson is  available on Teachers Pay Teachers

The lesson plan includes the plan (with standards and procedures), extension ideas, multiple data collection variations, and student handouts for fractions, ratios, percents, and bar graphs.

Free! I’ve also shared our answers as a printable handout that could be added to a binder/notebook

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Interleaving

Tonight, my students are working on math. I’m working on interleaving.

It makes sense as a strategy, I buy the research.

And, it’s sometimes hard to actually do. (For me and my students)

So, I’m teaching my students about it tonight, for the sake of accountability.  (And, so that they are less inclined to grumble when I mix topics, because interleaving is hard)

 

The plan:

Warm up: We’re reading about interleaving as a strategy they can do  (It’s an excerpt from this guide on retrievalpractice.org)

(edited to add: The general consensus on reading this one was “My head would hurt…“)

Activity: Converting with Celsius/Fahrenheit temperature formulas. We’ve been working on formulas and expressions, so this feels continuous….until the activity slips in some graphs.

Follow Up: Instead of more temperature formulas, their practice and homework options are more temperatures (Negative numbers on a thermometer, using charts to calculate windchills) Or, more graphs. Or some different formulas. Or a review from last week.  Also, reminders that interleaving helps their brains.

(Independent practice always has options in my class. It’s my favorite way to differentiate.)

 

I like the lesson. I think it will be good for everyone’s brains/learning.

(Also, the previously-planned negative temperatures and wind chills feel a a little too appropriate for the first SUPER COLD night of the year)

 

But, truth: it’s one night. 

And, things don’t really change in my practice until I find ways to systematize them.  :\

I do spiral reviews  so that’s a start.

And, I have a set of milk crates full of review materials, so the stuff is available. That helps.

And, I have plans, a first-steps goals (read: will you be my accountability buddy?)  Once a unit, in each class, for the rest of this year, their homework options will include one random review topic from a previous unit.

But, I’m going to need a spreadsheet or something if I’m going to scale that (I love charts, they fix so many things).

But also, I could use some more ideas.

My more conscientious students said they couldn’t imagine leaving a worksheet half done to switch to something else, so they were going to need some mixed up worksheets if I wanted them to try this. (Oof, more materials to design.)

 

 

 

 

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Back. Also, Lesson Sketch: Learning Strategies

So, that happened.

If, we define ‘that’ to mean life, a slight case of overwhelm, and an unplanned 5 month break.

 

But, it’s summer. I’ve been to the ocean, I’m off from teaching, and I now have the bandwidth to come back to this.

And, with my newly cleared head, I’m thinking about one of my favorite lessons.

 

Lesson Sketch: Learning Strategies

Why: 

I preach and plead for my adult students to study outside of class (see , por ejemplo: homework, more homework and planning for homework)

But —  I know the research: most students don’t use particularly efficient strategies to study. I think this doubly applies to my adults who didn’t have great success in the school the first time. And, they have even less time to waste on inefficient studying, this time around.

So, I’ve added preaching and pleading to study effectively. 

Also, this is one of a set of first class of the term exercises I use to ease people into doing math and being a student again. (Other examples: Stuck Strategies, Retrieval Practice)

 

What: Introducing research-backed strategies for effective learning + simple data and analysis.

The Learning Scientists have summarized lots of cognitive research to highlight 6 strategies. I rarely have enough students or time that it makes sense to do all 6, but they’re there if you do. For my class, I generally prioritize: Spaced Practice,  Interleaving, Retrieval Practice and Elaboration. 

 

How: 

I introduce the topic. I might talk about how scientists do experiments to see what works (I might add that if I had known you could do experiments about learning, not just chemistry or physics, I might have liked science better in high school)  I might talk about making the best use of our time, or about shaking things up/experimenting with new techniques, I might remind them how frustrating it is to forget what they’ve learned.

 

Then, I split the class into groups, and assign each group a strategy. One time I gave out these posters, more recently it’s been the bookmarks, because less is more. If tech wasn’t a headache, I’d try the videos. The group is in charge of working together until everyone understands the strategy.  (This can take some coaching) Then we jigsaw, and they teach it to their peers. (More coaching)

 

Once everyone understands the strategies, we take a poll:

Do you already do this?

Will you try it this term?

 

Then I have students analyze the data for the strategy they started with. Depending on the class and the time of year, they might find the percent, ratio and/or fraction of the class who gave each answer.  If I have more time, we might make graphs of the results. In a way less time pressured world, we might make a bulletin board display with the strategies and our data and study tips for other students at school.

 

Results:

Spaced practice is a hit. (at least in theory) Whether it happens or not, in the day to day of busy lives, they get this idea. In the great division between tortoises and hares, many of my students are tortoises. Slow and steady sounds good.

Interleaving, on the other hand,  is a hard sell. It just sounds so much harder and more confusing, and math is hard and confusing enough, thankyouverymuch.  (Although I make them do interleaved practice every week and they tell me it helps, so maybe someday…)

 

Next Steps:

Truth… this is the first class of the term and by the second we’re off and running, and it’s hard to get back to this. But, yeah, one-off’s are not all that helpful.

So, I’m currently pondering ways to fit a follow up in.  I’d love to collect a post- round of data later in the term to see if anyone is actually rying them out.

 

 

Free Resource: I fancied up my tally sheets a bit (ahem, data collection tools) and I’m making them available for free in my TPT Store

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Challenge (aka Task) Cards

Challenge

A couple of my favorite lessons, recently, have been basically amp’ed up task cards.

I call them “challenges”, because it sounds more motivating than tasks, and make each challenge rather bigger than some of the (often-elementary-grades) card sets I see online.  Last night, 7 cards took my fastest group about an hour.  

I love how easy it makes differentiation, and how many different kinds of thinking we can get in one class.

For a lesson like this, where the cards are the class, I’m sequencing them so I can gradually increase the challenge and cover the content in an order that makes sense.

For a couple of topics, we’ve learned a topic without any stand and lecture moments, just cards and small groups and conversations when questions come up. (To be fair, I’m strategic about these topics – area of a quadrilateral is pretty gentle learning curve, I don’t know that I’d try that with introducing algebraic equations)

So, while I’m loving cards, I pulled together a few of my favorite stems (and a few examples)

  • Read and summarize

  • Look at a (completed) example problem, make observations about how it was solved

  • Complete guided notes  (I’ll break format to give them a card with the instructions + a copy of the notes to keep)

  • Vocab: matching words and definitions, or a card pointing to a quizlet set.vocab
  • Put the steps in order and/or match a description of a step to its mathematical representation

steps

  • Solve a few problems (usually a few cards in a class set with different kinds of problems) plus or minus a reflection question.

  • A mini-sort or search 

sort

 

  • How is ___ similar or different from ___ ?

  • Guess and googleguess google

 

  • A challenge to preview the next lesson

 

 

My sequencing mostly follows a pretty familiar pattern: some input-y cards (reading, examples etc.) some supported practice (sorting steps etc.), independent practice, then challenges or create your own. 

One of my secret-but-not-really objectives is that they’re learning skills for independent learning. Being able to look at and make sense of an example problem, or a paragraph of math book, or to make a guess and then check it, will serve them well when they get to college math homework.  

And, challenge cards do a good job of demonstrating that they can learn something without me standing at the board with the answers. (My adults, having gone through mostly-not-successful school already often have pretty traditional ideas about what math class should look like)

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Challenges

It’s May.

There’s a month left of school. We just went through a round of testing. And we’re all a little fried.

And so, I was sitting in my office a few classes ago, with a topic (functions),  no particular lesson plan inspiration, and a textbook with a nice series of activities that checked all the boxes (mixed question/task types, at the right level, moving smoothly up Blooms…) I’ll be honest,  “Class, please complete the exercises on pages __ to ___” was a tempting plan.

Except

It’s May. The students are fried, they’ve worked hard all year and focusing on a textbook for a big chunk of class now was just not going to work.  They’re good, they’d try, but who could blame them for losing interest?

But was a nice series of activities, and I’m fried enough myself that I didn’t want to waste a perfectly good set of learning materials.

 

Solution: Envelopes.  Scissors. Some re-framing.

 

I made copies and started cutting and sorting. Those vocab words? A tiny matching activity, in an envelope. A big #1 on the front.  That exercise identifying functions? Cut apart and stuck in an envelope, it’s a card sort. With a big #2 on the front. That other exercise? I just stuck it in an envelope. Add a graph, ask for a sentence, envelope, envelope.

With a few additions and some cutting and editing, I soon had a few copies each of six enveloped tasks. I called them challenges and handed out the envelopes with that big #1 on the front. I told my students when they had completed the first challenge, they could exchange it for #2.

And it worked.

The mystery of the envelopes, the challenge, the sense of accomplishment and progress as they exchanged one envelope for the next added enough interest that they worked hard and stayed engaged the whole class.

In May.

When we’re all fried.   (Did I mention that fact?)

 

I love that they worked hard and learned.

But, I also love that I got a new tool in my teacher-kit.

Cut it up, put it in envelopes, set up a challenge – that’s a transferable skill-set for the next time I’m contemplating “please complete the exercises on page…”