Open Ended Questioning

In our Math department meeting yesterday we talked about what how warm-ups are a great opportunity to introduce common-core thinking and the eight standards for mathematical practice.

In our school, students must begin working as soon as they enter the class – whether the bell has rung or not.  Ideally, a good warm-up should have three qualities:

1)      All students can do it.  This means it needs to be review, to some extent, or otherwise accessible.

2)      Content related. In my class that means my warm up needs to involve math, although it doesn’t necessarily have to be about what we’re studying now.

3)      Open ended.  Since students come in the room at different times, preferably it should be something that everyone can have a response on after a short time, but also can be explored more fully.

 The biggest challenge is making sure our warm-ups open ended.  For comparison:

 Closed question: “Graph the equation 𝑦=(2/3)𝑥+3 on a coordinate plane.”

 Open question: “Write down everything you know about 𝑦=(2/3)𝑥+3  and be prepared to compare your thinking with a partner.”

With the first question, a student who is behind might simply say, “I don’t know how to do that,” and give up, while an accelerated student would be done in under a minute.

But with the second question, even a student who lacks confidence in math could say something like, “2/3 is in front of the x.  We are adding a 3.  There are two letters.”  And an accelerated student would have many, many things to say.

“Write everything you know about (blank)” is a great open ended structure.  Others are error analysis (spot the error and correct it), compare reasoning (give an example and ask students to explain how we got there), or a really fun one, give the answer and have the students come up with the questions.

Right now, my warm-ups are focused on getting the students prepared for their CAHSEE, so I probably won’t get a chance to incorporate these open-ended warm-ups into my class until mid-March.  I’ll use the time until then coming up with a “bank” of open ended questions.


Survey Says…

I began my algebra remediation classes today.  I’ve taught this in the past, and truth be told, I really like it.  The classes are very small so I can give each student the individualized, personalized attention they need.  The first year I was responsible for remediation I tried to teach it like a regular class with units and quizzes.  But I’ve since realized that the small class size means that I can customize what I do for each student.

This year, I decided to start with a survey.  I based mine on Mathy McMatherson’s.  I got some interesting results.

Question 1:  What makes math hard?

I don’t like negative numbers at all, they confuse me a lot.

Math is hard to me because it has a lot of stuff to learn and it’s too much thinking.

It’s not math that I don’t like it’s the way some teachers teach it.  Some go too fast or some go too slow or some rely on the book too much.

I find it challenging because I don’t comprehend math fast.  Like I need it taught step by step.

Something that makes math class hard is the way they teach it, because sometimes they go too fast and teach the same thing like 5 different ways and that’s where it gets confusing.

Question 2:  Do you think intelligence is fixed or can change with effort?

I think it’s just something determined because they listen and get it maybe they love math or something.

I believe that it’s in the middle because if math is all you do maybe it will click; maybe you’d go from F to B or an A.  But then the more I think about it some people are just good with numbers and some aren’t.

I honestly think that everyone is smart. Some people just don’t want to try.  There are a lot of people that can put the effort out there and try.  Me, I just don’t do anything.

Question 3: What do you want from this class?

I want to get better at math by learning better study habits.  Maybe less worksheets and more notes.

I want more activities.  I want to pass with a B at least.  I want to understand what is being taught.

To stay focused on what I am doing and take everything more seriously.

Try my best to all my work that they give me.

I would like for everyone to feel comfortable around everybody in the class.  We could also do like group work and have people introduce themselves to everybody.

They are very self aware and know their own strengths and weaknesses.  They know what they have to do, but they don’t know how to do it.  They also realized they were lost in previous classes, but were powerless to change it (for example, they know they couldn’t slow the class down).

We’ve been doing goal-setting in our Small Learning Community and while I had my Geometry class set goals for the semester today, I wanted to hold off with this group.  These survey results give me a great jumping-off point.


I created a new activity for my Geometry students to help them review transformations I’m calling the Transformation Go Round.  I was inspired by Irina Kimyagarov’s lesson, but I adapted it to my classroom’s level, which was a little more basic.

I made six stations labeled A-F.  For each station, I glued a blank graph and the station instructions to a sheet of 12×18 construction paper.  I placed these around the room.

The students divided into six groups. They move around the room, going from station to station.  At the station, they draw the figure on the graph paper (with specific color highlighter, to make it clearer what drawing went with what step), and then list the final coordinates on their sheet.

The first step is to graph the given coordinates and connect the dots to make a polygon. Then they do a rotation, reflection, translation, another rotation, and finally, another translation. Since their starting point is the previous group’s result, they need to check the previous group’s work before they start on each station.

One thing I would have changed is the grouping.  I let the students make their own groups, in order to get more buy-in from them.  But it meant some self-grouped with other low performers and were a bit lost.  Irina Kimyagarov stated that she did heterogeneous grouping and I think that was the key point I missed.  Another thing is that the activity took a bit longer than I had originally predicted, because the students needed to review (using their notebooks!!) the core concepts.

Looking Forward; Looking Back

Today is the first school day of 2014!  We are heading toward the end of the semester.  Two weeks of review, then Midterms/Finals.

I’ve been doing Interactive Student Notebooks, as detailed by Math = Love and Everybody is a Genius .  I started these the second month of school.

What I like about ISNs is that I have to really think about what it is I want my students to take away from each lesson.  The format requires me to chunk concepts down.  I like that it gives students something different to do in class (cut, color, and paste) and engages everyone.  It has slowed down my teaching so my pacing is more in line with where my students are at.

What I’ve seen is that students who do well on Notebook check also tend to do well in class.  My number of failing students has declined as well, with the failing students either those who came in low skilled (i.e., were in my remediation class last year) or who are attendance issues.

The downside is that it seems to work better for Geometry than Algebra 1.  I’m not sure why this is.  It may be that my Algebra 1 students are more varied in ability and knowledge.  It may be that my Algebra 1 is a double block.  It may be that I am not varying the type of practice enough.

Which brings me to my next concern:  Even with my Geometry students, they still struggle with higher-level problems that require creative thinking.  The plus side is that they are getting the basics, but the minus is that their thinking is stopping there.

In my POD (my math teacher group) we have decided to address this by concentrating our review for the finals on higher-level tasks.  This we will do for the next two weeks.  The idea is that now that they have the basics, we can build on that knowledge to deepen their understanding.