This week we’ve been off from school for fall break – a road trip down south to visit Winter the Dolphin in Clearwater and a few days of warm sunshine on the beach has me somewhat re-energized. I’ll be honest, my book is still at school. The directions for this week were to use one of the FACTS #1-10 but I haven’t been in class to do this. (Sorry) Before leaving school last week, I chose FACT #24 I used to think…, but now I know… as a left-hand page assignment for my Geometry students’ INB.
#24 I used to think… Now, I know…
Eight Standards for Mathematical Practices
Practice 1 Make sense of problems and persevere in solving them. This FACT allowed students to reflect on their learning, an opportunity to share what they used to think and what they now know after working with the concept. Students responded to this prompt after exploring in small group investigations, pair-share processing, independent practice and finally whole class discussions/questions over Triangle Congruence. I used to think… but now I know gave students the chance to make sense of the ideas they have been working with in class.
Facts and Teaching Goals
The goal of the lesson sequence was to allow students to recognize and determine which side-angle combos were appropriate and would guarantee triangle congruencies and finally applying those ideas with informal proofs. By allowing them to respond in writing, I was made aware of their initial misconceptions – but also able to see they had in fact realized on their own how to prove trianlges congruent with a limited amount of given information.
I learned that the AAA and HL were the two students had struggled with most but they wrote about how the activities / discussion helped them realize specifically what was needed with each combo. Another common error they pointed out in their reflections were that order of the included sides/angles did matter with situations of AAS and ASA.
Planning to Use and Implement Facts
One reason I chose this FACT was because I am looking to implement more literacy strategies into my instruction. This FACT provided students with the opportunity to reflect on their learning in written format – a different type of processing that just talking/telling what they’ve learned. By the time the prompt was given, students had explored in small groups, shared verbally with a partner, practiced individually. The writing component seemed to complete the various types of literacy strategies. By giving students a chance to respond to this prompt, I was able to see in-depth their full understanding of the intended concepts.
Were your students engaged? Yes, I was very pleased observing students as they wrote their responses. Most students took their time to share insightful reflections. There were a few who tried to skim by with very vague responses, I gave them written feedback and asked they resubmit their responses. Based on their new responses, I expect those few will give their best effort first time around next time given this prompt.
Were you confident and excited about using the FACT? I felt it was a good opporutnity to have students share their learning in writing. I was not as excited about the FACT until after I actually started reading their responses…
How did use of the FACT affect the student-to-student or student-teacher dynamic? Student to teacher – I felt they were honest in their responses – and most were insightful – I was encouraged to use this FACT again because it allowed me to see into their thinking.
Was the information gained from the FACT useful to you? Yes, however, I don’t think I will change my approach to the lesson in the future – students were able to adjust their thinking because of the lesson format. The FACT let me see this as a successful sequence – what a good formative assessment strategy should do!
Would you have gotten the same information without using the FACT? I’m not sure I would have given students the opportunity to reflect had I not used the FACT.
What added value did the FACT bring to teaching and learning? Based on student responses – I believe most appreciated having the opportunity to think about their learning – it “tied up loose ends” for them in the end.
Did using the FACT cause you to do something differently or think differently about teaching and learning? It made me realize I’ve failed to provide students with good opportunities to refelct on their learning between lessons / practice and before “official assessment” occurs. This is something I plan to implement more for my students! It was quick, little/no prep and offered me the chance to really see what students thought about their learning.
Would you use this FACT again? Yes.
Are there modifications you could make to this FACT to improve its usefulness? I believe next time I will plan more time for students to share out their responses – maybe within a pair-share then as a whole class, possibly using the ‘Around the Clock’ appointment cards idea from Global Math Department.
Using Data from FACTs
Most students realized that AAA could only guarantee similarity amond the triangles. There were several misunderstandings about HL I was not aware of until after I read student reflections. I will be more puposeful in defining the included parts in the various combos, for example I shared examples with students and asked how AAS and ASA are alike / different because this was one that a few still had struggle with. During this discussion / sharing – it was obvious some a-ha! moments occurred.