Category Archives: always sometimes never

All Student Response Cards #made4math Monday

Standard

In reading Embedded Formative Assessment (Wiliam, 2011), there have been several practical techniques presented in each chapter.  While discussing chapter 4, @druinok suggested creating response cards this summer, based on the technique All Students Respond.

  I had seen a set made by an elementary teacher in my leadership network.  She had several cards labeled with letters, hole-punched and attached to a 3 inch ring that could be opened and placed around the metal frame on student desks. She explained students always had access to them.

I kept thinking about how to accomplish the same idea for my classroom.  I had a package of name badge holders I had picked up at our Mighty Dollar in town, but never found a use for them.  Basically, I put this example together quickly, to have something for #made4math today. Its not innovative, but for anyone who does not have a “clicker system” or devices to use with Poll-Everywhere, etc., its an option that I believe could prove as a useful tool.

My idea is to have a single card, with all responses.  I would need to ‘train’ students how to hold their cards allowing me to see their response clearly.  Mine is double sided, this could easily be accomplished with cardstock printed, then laminated if you didnt have the badge holders.  Each student could clip one into a pocket of their INB and have them on hand when its time to use them.  Or they could be clipped either to a hanging ribbon or the side of a magnetic cabinet, even placed in a basket if you only had one classroom set.

image

The first side includes a favorite of mine…always, sometimes, never…color coding green, yellow, red, respectively.  The student places their hand, so only the response they choose is visible and located at the top of the card when they hold it up for me to see.  I didn’t have the color circle stickers here at home, but I believe they may help in the visual for me to see.  By keeping responses color coded, I can quickly scan the room to see where students are, then make a decision as to what type of question follows or if we should procceed with discussion of why they responded as they did…supporting their claims with mathematical evidence, of course.

Notice, the QUESTION response.  A student may have a question or require some clarification, this choice doesn’t allow them to opt out, but provides a way to say, I need some help.

image

On the back side, there are simply color-coded (different from other side) multiple choice responses, again to allow a quick scan before deciding how to proceed.  If multiple answers are chosen, begin by asking students to give possible reasons why a student may have chosen A or D-the other answer, if I chose A, could I figure out how someone else would have chosen D?  I also like to ask, noone chose B or C, what is a possible reason why someone would not have chosen  ___?

image

image

image

Like I said, I plan to use color circle stickers which allow me to see student responsesmfrom across the room.  I am debating on howmto do true/false.  Would
Read the rest of this entry

Evaluating Statements About Length and Area

Standard

This lesson can be found http://www.map.mathshell.org same as title of the post.

image

This is one of six cards students discussed within small groups today. A student stated, “this is going to be a thinking day,” as they began removing the clips to start reviewing their cards. Most students would quickly come up with an always, sometimes or never true. However, to create their own examples or counterexamples to either justify or refute the statements was a struggle for some of them. Several groups had similar statements for this particular card. It was when a student asked, “do they have to be triangles?” that a turning point came for some.

image

Within our share out as a whole group, a student shared examples of reducing area, same perimeter and less perimeter. A question they wondered…can you reduce the area but increase the perimeter?

I really enjoy days like this, students are giving me the information, I am their scribe and I am slowly learning to let them determine if they agree or disagree with each others’ claims. I’m not even sure where the key is, that way I am actively having to listen to their arguments to determine if I agree or not. (Shout out to Max @Math Forum, I am listening to my students, not listening for the answer!) I go through the cards myself prior to the day of the lesson, just like I require them to do. But I am still closed minded in my own thinking at times. Why would you limit the example above to only triangles? Because that is what shape was presented on the card. However, does it state triangles only? Nope.

A task like this may drive some teachers crazy. Once you start considering different shapes, you begin to see what works for one, may not work for another. I had students cutting scrap paper, tracing patty paper, measuring side lengths…without me telling them to do it.

The classic question, a square and circle have equal perimeters, which has the larger area? I will do my best to share more reflections as we wind up tomorrow, if we wind up tomorrow…depending on their questions, discussions, claims and supporting evidence.

Always, Sometimes, Never – #75FACTS

Standard

I’ll be honest, I’ve only truly dug-in to reading the first 6 FACTS of Keeley & Tobey’s book over the past 2 weeks.  Through KLN – Kentucky Leadership Network, I’ve explored several others over the past year.  But I’ve gotten very drawn in to processing the descriptions, suggestions given on the first 6 (by the way, they are listed alphabetically, didn’t know that until someone pointed it out in twitter chat).

This past week, of these 6, I’ve attempted some form of Agree/Disagree (#1), Always Sometimes Never (#3) and Comments Only Marking (#6) in my classroom.  I’ll share more later on A/D and Comments.

Last year, I began experimenting with the Formative Assessment Lessons from the MARS site.  Sorting Equations and  Identities lesson asked students to sort mathematical statements into categories – always true, sometimes true, never true.  Part of the task was to justify their choices.  After using this lesson, I realized students really struggled with these statements.  In fact, they hated them – moaning/groaning each time one would pop up.  Which said to me – they were having to think.  I began embedding them in lessons/notes – class discusses/questions – especially in assessments.  By the end of the year, students were “not afraid” to face ASN questions as before.

This week, I gave geometry students 15 statements about quadrilaterals/polygons, in which they had to answer ASN.  When they arrived in class the following day, I had areas of the room designated A, S, N.

Depending on the FACT, it may help to explain to students why you are using the new strategy.  Part of this discussion was that when someone makes a statement, it may seem true, but we should check it out to determine if in face it always applies, sometimes applies or never applies (page 57).  Through the activity, students were able to share counterexamples if they disagreed with another student’s statement.  Great discussion (even a few semi-heated arguements) occured!

Mathematical Practice – #3 Construct viable arguments and critiques the reasoning of others.

Were students engaged?  Definitely – from the time they walked in, they saw the A, S, N posted and KNEW what was coming.  Most were engaged during the activity.  At least those who didn’t want to think – had to at least choose an area to move to in the discussion.  I used my “name cards” to call on students to ensure everyone needed to be ready to share their justifications.

Were you confident/excited about using the FACT? Yes.  I’ve found a new love for always, sometimes and never statements – though I remember detesting them a particular college geometry course – now I realize what a great learning tool they can be.

How did use of the FACT affect the student-to-student or student-teacher dynamic?  I tried to allow students to share their own counterexamples – but when one was stuck, I would question – referring back to properties we had investigated, drawing figures on the board, presenting a what if… if needed.

Was the information gained from the FACT useful to you?  I realized some students still confused a few of the rhombus, rectangle, square statements.  Mostly, that students often only considered the “obvious” – but this activity was great because others were able to share their “what about…” with their classmates.

Would you have gotten the same information without using the FACT?  In the past, I would have likely made the same realizations but only after giving the unit assessment.  This FACT helped clear up some misconceptions during the learning process rather than at the “end of the learning.”

What added value did the FACT bring to teaching and learning?  Students had to think about their thinking, jusitfy their reasoning, could be critiqued by classmates’ thinking – great opportunities for discussion / sharing!

Did using the FACT cause you to do something differently or think differently about teaching and learning?  During the task, I was able to use student comments as a springboard for whole class discussion, pointing out examples that made it true and examples that made it false (great piece of learning to impact understanding of counterexamples).

Would you use this FACT again? Yes.

Are there modifications you could make to this FACT to improve its usefulness?  This FACT lends itself well to written work, whole class & small group discussions.  Follow up is key – probing students and guiding them to consider other examples – if not shared by classmates first.  Even after arriving at what seems to be class consensus, ask again – challenge their thinking – don’t settle for the first correct responses – ask why – let them justify their reasoning.