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.
the radical rational... 