#MTBoS My Favorite: Open Questions & Level-Up Quiz

Goodness.  I think this is where I fall apart.  I have so many favorite things I’ve used in my classroom, at times I cannot focus and choose one.  I become distracted, thinking I have to use EVERYTHING.  I have to pause, think about the learners in the classroom and what will be best, most effective for them.

Our second week back after Christmas break was very productive.  I chose to combine 2 ideas and focused my energy with them.  One goal I had set was to use open questions.  (Older posts – first attempt, more good questions – about strategy from Small / Lin).  Rather than giving students more inequalities and asking them to graph.  I gave them a point and asked them to create an inequality whose graph would “capture” the point.  Students had to think differently in order to create their response rather than following a procedural step by step or copying a classmate’s work.

The other was an idea someone had tweeted that caught my attention and I wanted to see how it would work in my classroom…level-up quizzes.  Since the target involved graphing inequalities, I gave each student a paper with 4 empty graphs and space in margins to write inequalities and verify.  Here is a sample of the criteria I gave them:

I told students I wanted everyone to be at level 3 by the end of the week – Level 4 was using multiple measures to verify their responses.  If students were at 3 or 4 early in the week, I posed a challenge to them to create two inequalities that would both capture the point.

This task accomplished several things for me.  It was obvious where students got stuck, it allowed me to give feedback or have a conversation about the symbols, which direction to shade, helped point out when/why to use the = if the point was on the boundary line or not, could quickly address issues with graphing key points of the line.  It allowed students to move on without waiting on their peers.

There were a couple of students in each class who continued to struggle-mostly students who had chosen NOT to put any time/effort into practice the prior week or who had been absent, but the rest of students made gains and improvements with this skill.  By the end of the week, majority of students were at or above the level 3.

The big thing with verifying I saw was students using (0,0) to test in their inequality algebraically as opposed to the actual point we picked.  I feel this was due to us graphing inequalities the prior week.  This year, I opted to encourage evidence of their claim by having them test a point to determine direction of shading as opposed to just saying above/below.

With only 1 response for every student each day, I was not overwhelmed, but able to give feedback.  I made notes of most common errors and addressed them as a whole class prior to passing the quiz back.  For many, I simply wrote a number corresponding to the Level-Up criteria.  Students knew the first couple of tries “didn’t count” but were opportunities to learn and level up by the end of the week.

My concerns after reading about Rubrics in Embedding Formative Assessment –  have I made it more of a skill-ckeck list?  By presenting it as an open question, is that enough to allow for student thinking?  Thoughts on how to improve are welcome!

Thoughts on #75facts

As I read SimplifyRadicals #75facts post this morning, it really got me to thinking…about things I do and how I could use “Create the Problem” in my own classroom.

I’ve given students the answer before and asked them to write a scenario that could model the problem.  But reading her refelction and suggestions for modifications helped me realize a couple of ways I could improve the way I’ve done this in the past.

The FACT reminds me of ideas from More Good Questions, Marian Small & Amy Lin.  Give students the answer and they have to come up with the equation/problem.  Example, the slope is 2/3, what are 2 points that could give you this slope?

As suggested in the FACT#11 description, providing students with an open ended task takes their thinking to another level.  Student examples generate whether they know why a computation is performed rather than just knowing a procedure.  But this FACT actually asks them, not to find the computation/problem, but to give a scenario/context where this strategy could be used to solve the problem.

The key, as with many successful strategies, is sharing student ideas.  Not just allowing them to talk about their examples and how their story matches the solution, but the teacher asking the class for feedback on whether it is a match, if not, how could it be changed/made better (pg. 81)?

This reminds me of another FACT I’ve used in class before “2 stars and 1 wish.”  however, when I first saw this a couple of years ago, it was called 2 +’s and a delta…two positives and one thing I’d like to change.  Playing off of My Favorite No, I ask students “What do I know this student understands?  Give me 2 examples of what this student did well.”  By focusing on the correct parts first, especially if I’m using a student’s example (anonymously) – the student can see it wasn’t completely wrong.

Then for the delta (wish), I ask students not to point out the mistake, but to think of a question they could ask the student to help the student realize their mistake.  Sometimes, this is a tough task, depending on the mistake that was made, but by asking a question, students, again, are having to think on a different level.

In several of the Formative Assessment Lessons from the MARS site (Solving Linear Equations in Two Variables) – the lesson format actually allows students in small groups to evaluate different levels of student work.  On a slide in the projector resources for this lesson, Assessing Student Work, students are given these questions to guide their discussions:

You are the teacher and have to assess this work.

Correct the work and write comments on the accuracy and organization of each response.

•What do you like about this student’s work?

•What method did the student use?
Is it clear? Is it accurate?  Is it efficient?

•What errors did the student make?

•How might the work be improved?

My thinking, use the FACT #11 – Create a Problem as an exit slip.  Divide the responses into different levels.  On overhead, share different levels, both correct/incorrect, as well as different approaches, using the above questions as a guide for class discussion.  Then present students with solution(s) and ask them to create a problem.

Thanks to Simplifying Radicals for getting my brain to churning so early this morning!

 

INBs – A New Adventure – “Flip 4 Answers”

INBs – A New Adventure

All summer long I searched for ways to improve my literacy in math class – I learned so much chatting with my tweeps during our #lit4math book study.  It helped me redefine what literacy is / should be in math class – not just about reading.  And writing.  Not about creating something completely new – but improving what I already do to emphasize communication – discussing – giving students opportunities to make connections.

As I ran across various posts on the Interactive Notebooks – I knew this was something I wanted to do.  At first I had the wrong perception – thinking the interaction was between student and teacher – I struggled, wondering how in the world would I find the time to “grade” and evaluate that many notebooks efficicently and effectively and keep them in students’ hands for continuous learning???

After reading – mostly from @mgolding – I realized I had it all wrong.   The interaction was between the students and their own notebooks – to provide them with opportunities to engage with the information I gave them.  I was overly excited when I saw @mgolding would be presenting at #TMC12 – then crushed to find out my session was at the same time. boo. and I would miss out.

Listening to conversations that came out of her session and reading more once I returned home only confirmed my decision to move forward with INBs.  My science colleague had decided to pursue this learning tool as well – so grateful to have an in-person to collaborate/share ideas with too!

During the first Global Math Department meeting, she brought calm to me – answering so many of my questions in her session that night – thank you, thank you, thank you @mgolding!!!

I have begun my venture with INBs.  I feel a bit stronger in one class than the other – but I have been upfront with my students – this is a learning experience for me as well.

Some things I’ve quickly learned:

1. I MUST keep my TOC up to date – its easy to get off track if I don’t!
2. I MUST do the INB along with students – having completed the pages myself – knowing exactly what I want to go on them;
3. I MUST practice any foldables / graphic organizers to make sure they’ll fit/work.  I may have a great idea in my head – in theory anyway- but I have to put it to the paper to see if it will acutally do what I need it to do!
4. I MUST think about what I want to accomplish with the LHP assignments.  This is the one I tend to struggle with some…thankfully I have lunch with my colleague and bounce ideas to get feedback.

Flip 4 Answers

I plan to blog my list of RHP ideas later, but for today, I want to share an idea that came from my students.  Its similar to something I saw @mgolding share at #TMC12.  She had used post-its to cover hints/work/solution to an assignment she left with a substittue teacher.

When asked to create a practice quiz, one of my students used an index card to cover their work – thus “Flip for answer.”  When  I shared the student’s example, I never dreamed others would follow.  Yesterday during our first cumulative test – I oberved several others started playing off the concept.

   

As I look at the sample below, a CWP (color with purpose) would be VERY easy to assign…I think on Monday – that may be a good warm-up – turn to page 12 and CWP…  positive or negative or zero or undefined, even identifying which letters model parallel & perpendicular.

 

Another idea I think I’ll lean toward using for my LHP assignments – is the use of “Open Questions” – an idea I got during a book chat last fall from More Good Questions Small/Lin.  The second part of RHP 12 was an example of this…give coordinates of two points: with zero slope, undefined slope, positive slope, perpendicular to the slope in part c.

I believe the INBs require me to be more organized in my example choices.  It helps students be more focused / organized as well.  Looking through INBs yesterday – those who were having some trouble with their INBs / not completing their LHP assignments – seem to be the same (few) students who were struggling to make the connections I need them to.  This confirms to me the choices I am making – since most are finding great success.

Open Questions: My First Attempt

I’ve been reading More Good Questions and am so excited about this book!  #sbarbook study Monday nights 9:30 est. on twitter  – the big ideas so far, have been defining open questions and parallel tasks and how easy it is to create them. 

@druinok that’s what I’m enjoying too – very low stress, but HUGE dividends! #sbarbook

@druinok @jmalpass totally agree!!! I think what I’ve gotten out of it the most is rich questions don’t have to be hard for the teacher to do 🙂

Such simple, quick changes – yet great opportunity for thinking at ALL levels!

Today, on a target quiz on slope/rate of change – I made my first planned attempt to use an open question. The last question (no discussion on the first 4 ?s) took us into a great in-depth discussion.  The question was this:

Slope is 4/5. 

Give me two points on the line.

A student asked…does it have a y-intercept?  My response, Does (voice inflection) it have a y-intercept?  When I asked students for responses – I called on this student because I wanted to talk more about his question.  Student stated – its not vertical, so it has to have a y-intercept – even if its (0, 0) – the y-intercept is zero.  Good point.

While students were working – I observed their various stratgies for getting their coordinates- THIS is the part I *LOVED*!!!!  There were graphs, tables of values, slope formulas, and other strange strategies I would have never been aware of – if I hadn’t given this question!  I attempted to call on students with different strategies for getting their solutions.  Even calling on a few I knew had incorrect answers to allow for discussion.  I didn’t have to correct them – other students were able to ask questions.** 

One student looked confused as she asked, “How can we have so many points, but the same slope?”  My answer, “How can we have so many points, but the same slope?”  Another replied – “the lines are different but they have the same slope – so it makes them parallel.”  A concept not included in the objective – but I think it will stick.  On the board graph – students were able to quickly identify points that were not giving the correct slope and able to explain – usually inverted coordinates.

About 1/3 of the class struggled with where to start on this question – but my feeling is as the year goes on and they are given more open questions, I’ll see a higher number successfully attempting it.  One student made a comment on her way out – how ‘seeing other ways really helped (her) to better understand slope and how it works’ –

How difficult was it to come up with the question?  Not at all.  Level of cognitive demand – much higher that #’s 1 – 4; Level of discussion – much more in-depth! 

This idea may be something most of you use in your classroom.  I consider myself a good teacher – but my thinking has shifted – when I’m looking at examples / assessments – my thought is, how can I make this an Open Question???  I will continue to share my experiences initiated through this book!

** When a student sees a mistake another student has made – I encourage them to  question by asking, “What question can you ask them about their work/answer,” rather than tell them what they did wrong.  It gives both students a chance to reflect.