Teaching the Test

Teach the students, not the test.

I am quite certain that what I care most about teaching is that you, yes, you the one who never got above a C in math class, can learn anything, even math. Teaching the students.

Except that what my students care most about passing a test (HISET) that stands between them and big dreams (jobs and college and examples for their kids and a sense of pride at finally doing the thing they quit years ago) And, there’s something worthy in helping them reach those goals, and it is nice proof of my basic thesis when they do it …so, yeah, we do kind of teach the test, too.

In a perfect world it would be different, but in this world, I’ve made some peace with the idea that it’s possible to teach both.

 

I have not, however, settled on a favorite way to actually, effectively incorporate test practice into class, so I’m giving it some thought before the rush of the school year.

The challenges:

How to give enough to expose them to the breadth and challenge of the test, without sending them into overwhelm.

How to connect it to our current learning and prepare them for an exam that covers approximately 5 years of K12 math standards.  (Yes, really: 6th grade area to high school algebra)

How to fit it in an already over-stuffed curriculum.

 

Past attempts:

Give interested students practice tests to take home.  (This only really works with a subset of students who are pretty prepared and pretty self directed)

Slip questions from the practice tests in to my weekly review routine  (A keeper, I think, although probably not enough by itself)

Collect multiple questions relevant to our topic from across the stack of practice tests, make it part of the lesson (Super-laborious until we found an intern to help us organize, now only moderately laborious)

Review sessions, on those random end of term/all-the-interuptions days when you can’t teach anything new anyways.  (Not bad. Not brilliant, I don’t think, but not bad)

 

Additions for this fall:

Easy win: Bubble sheets. Apparently one student was totally thrown off by the answer sheet when she took the exam last year.  I put “use bubble sheets in class each trimester” on my goals list. *Check*

Question of the Day: One practice test question every week, slipped into the routine of the class.  I spent one distinctly not-fun afternoon sorting through tests and picking a couple dozen out. This is the exposure therapy theory of math teaching: see the test questions often enough and they’re less intimidating.

 

But, I’m still in search of structures for those random review days that make them something more than solo worksheet time. Especially, ones that don’t rely on speed, shouting out answers, or competition to make them game-y. My students have enough math anxiety already, thank you very much.

 

My favorites so far:

These 3 problems all have the same answer. What is it? Where ‘answer’ means: the same letter on the multiple choice format questions.  This let me mix in questions students were likely to get with stretch questions without inducing overwhelm. It worked particularly well in groups, where different people knew different questions and could check each other.

Test question sort When you’re being tested on 5 years worth of standards all at once, quickly identifying what math you need to use is crucial. And hard. So we say, lets not worry about the answers for a little while and focus on identifying what we’re being asked to do.  Also, my students are very, very familiar with card sorts.

 

But, really, I could use more ideas. My best googling turns up few ideas that suit my class 🙁

 

 

 

Lesson Sketch: Reading Algebra (Card Sort + Critical Thinking)

Topic: Reading Algebra (CCRS: A.SSE.1a)

Why:

Half of the battle with algebra (well, some significant fraction of the battle anyways, because half is always anxiety and focus and  grit and all the metacognitive things) is just reading algebra. The variables, the changes in notation and conventions, it looks so unfamiliar to new learners. And for those inclined to doubt their math abilities, a string of letters and a lack of familiar symbols is often a trigger to shut down.

So, a lesson to get used it to before we try to do anything with it.

What:

  1. A warm up: Sal Kahn answers a darn good question “Why all the Letters in Algebra”
  2. Some translation (aka direct instruction on the conventions)
  3. And, then the core of the lesson. A card sort. We matched cards with a x b to cards with ab, and b x b to b2, and we kept going a x b x b, and b 2, etc. etc.

(I love card sorts. I love how they prompt collaborative work, and aren’t worksheets, make things a tiny bit more tangible. I particularly love them for teaching equivalence. I wrote here about how playing Concentration is a go to activity for me)

Pro Tip: My new favorite way to make card sorts is using GoogleSlides. Subscribe to receive my tips.

  1. But, as much as I love card sorts, I’ve been thinking about how I could raise the bar, and ask students to do some deeper thinking (to mix directional metaphors)

So after we matched the cards, I distributed some critical thinking questions:  Which were hard? Which were easy? Why do certain cards go together? What do the symbols mean? Write your own examples (because, goals )

Results: It was the first math class after vacation, and all of us were having a slow time getting back to work/school, so something like three quarters of my class conveniently, um, overlooked, the question that asked them to write with words the first time through.

But, in the end, I had one of the best student comments I’ve seen in a while:

Student writing "Tho my mind was pudding we eased into learning. Was very nice"

Pudding brain. I totally get this metaphor.

Also, I take that as a victory.

(This if from my metacognitive exit tickets, read more here)

And, those extra questions? I added them in and prettied it up, and put it all on Teachers pay Teaches for the next person teaching their students to read algebra.

Fall 2020 Update: I love this activty, but found it often wasn’t enough practice on it’s own…. so I made 8 different worksheets. #onaroll #differentiation.

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)

Goals: Student Written Problems

I’m a goals kind of person. I like them, find them helpful, function best when I’m clear on them. (Classic upholder, for any other Gretchen Rubin fans) So, the document that organizes all of my teaching is topped by a bullet pointed list of goals.

(Best goal ever: “Actually use sick time” That was actually helpful)

This fall, one says “incorporate student-written math tasks/problems/questions”

It’s an attempt to share agency, to give a confidence boost (you, yes, you, can write a math problem…), to switch up the formats (no worksheets!), to have open ended tasks.

 

So, this month I’ve tried two formats, with three topics, in two different classes.  (Because, upholder with goals)

 

Version 1: Passing Problems

The order of operations:

Introduce a model, a template, a pattern, a way to isolate a particular skill. (For us, expressions like 5+3×2 and (5+3)x2 that are different only in their parentheses)

               Students write similar problems on index cards.

Check and double check the cards, write answers on the back.

Collect, shuffle, redistribute cards

Do the problem, without writing the card. (Repeat, and repeat, and repeat this instruction. The impulse to write on the cards instead of the scrap paper is strong)

Check the answer

               Pass the card to the right, receive a new card.

Repeat.

 

Version 2:  Card Sort

The order of operations:

Introduce new material

Small groups complete pre-existing card sort

(This so far, is a classic mathacognitive lesson. I have a bin full of card-sort-like activities )

Students write their own pairs of cards to be sorted.

Once checked, the new cards are scrambled and displayed with our doc cam

The class repeats the process of reuniting the pairs with their own newly-written cards. (For my class, students are just writing on notebook paper which goes with which, you could have a whole class activity of physically moving and matching the pairs, or make copies for everyone to cut out and arrange)

 

Particularly with the passing problems, there was a fair amount of incredulous staring, with verbal and non-verbal versions of ‘you want me to write the problem?!?’

But, incredulity/confusion aside, everyone eventually wrote their own problems and solved some of their classmates’, so I’m declaring it a victory and looking for the next spot to have them write the problems.

 

Bonus: It inspired me to upgrade from my previous, handwritten, kind-of-rushed, oops-there’s-an-error cards to a new actually-typed-and-formatted set of my exponent card sort.

Further Bonus: I was on a roll, so I typed up my cards, then kept going until I had a whole pack of different exponent cards and instructions and templates and a lesson plan for student-written cards. They’re available on TeachersPayTeachers if you’re interested)

 

card sort cover

 

 

Go To: Concentration Cards

Go-to’s: My go to activities: flexible, easy to prep and explain, engaging for students and their brains.  (Inspired by one of those ‘so what do you do …’ conversations with another teacher)

Activity: Card game, matching pairs based on “Concentration” (aka Memory)

Theory:  We need a break from worksheets.  Mostly: I find my students struggle with equivalence and recognizing two items in different formats as the same value, concentration focuses them on these relationships.

Example: We’re easing in to a new term with a word problem review, so I made Concentration cards. Once half of each pair was an expression in English (5 less than 16, the sum of 2 and 7…), its pair was either a mathematical expression (16-5) or a final value (9).

Prep: 

Fold a piece of paper into small squares (8ths or 12ths work for me) to hand write or use a template to type (Next time I’m using a blank business card template – they’re a nice size and should print just fine without the fancy paper)

You want pairs of cards, blank on the back.  I like values that are equivalent but not equal, so an expression and an answer, a definition and vocab word etc. I find 10 – 15 pairs (20 to 30 cards) is a nice level of challenge.

Print and cut out a deck per student-group.

Pro tips/Learned it the hard way

Use card stock or dark-colored paper – I’ve had crafty students figure out how to read through my lighter paper versions.

Use a different color for each deck of cards so you don’t spend forever reuniting lost/scrambled/mis-placed cards.

 

In class:

Remind students how to play. (I’m always surprised that people don’t know or have forgotten this game)  

In short: The cards go face down on the table. Each student takes a turn trying to make a pair by turning over two cards and looking for a match. Winner is the player with the most pairs at the end.

Here are  full instructions

I like groups of 2 or 3. Any larger and there’s too much downtime.  Groups play until all of the cards have been paired or until a set time has elapsed.

Pro tips/Learned it the hard way

A reminder to return cards to their original places is valuable. There’s always one group that inadvertently ups the difficulty level by rearranging the cards.

Extension Possibilities

Students create a new pair or pairs of cards with their own examples.

 

Works for:

  • Vocab (word on one card, definition on the other)
  • Conversions (e.g. 1 foot = 12 inches)
  • Equivalent values (e.g. equivalent fractions, simplified and expanded expressions)
  • The math equivalent of sight words, those things you want them to recognize quickly (e.g. perfect squares)
  • Really, pretty much anything….