Author Archives: Deb Porcarelli
When I was in school, I was never asked what I knew, what I thought about, or how I processed mathematical information. I’m happy that this is different today and that valuing mathematical communication in today’s classrooms is recognized as important. Better known as mathematical discourse, whole-class discussions where students talk about mathematics can reveal their understanding of concepts. We owe it to our students to be curious and inquisitive about what they know or don’t know about their mathematics. Are you having conversations with your students about math?
Educators have the opportunity and privilege of teaching students how to participate in meaningful mathematical discourse. How do we begin? The opportunity for discourse starts by presenting students with, and engaging them in, rich mathematical tasks. Rich math tasks focus students’ attention on mathematical ideas and allow for the development/use of the mathematical habits of mind. Rich math tasks are not memorized procedures and facts, but engaging and powerful experiences. Teachers are no longer simply the transmitters of knowledge.
I suggest you set a goal for engaging your students in discourse, then formulate a plan to accomplish your goal. Questions keep students engaged and prompt them to think more deeply while the discourse happens organically. As part of your plan, I recommend that you craft a list of readily available questions to ask students in any situation. Here are some suggested questions:
- Can you convince the rest of us that your answer makes sense?
- Is this a reasonable answer?
- How did you think about the problem?
- What is another way you could have solved this problem?
- How did you reach that conclusion?
- How did you organize your information? Your thinking?
- Which skills or concepts did you use?
- What were the mathematical ideas in this problem?
Plan time to reflect on how the mathematical discussions have gone in your classroom. Check on the progress your students have made. Think about the student learning that is occurring. Revisit and revise your questions based on your reflections. I would like to hear your ideas about mathematical discourse in your class(es).
I hope that you have had the chance to personally experience an AIMS professional learning opportunity. We AIMS facilitators have multiple goals as we lead workshops. We provide classroom teachers an opportunity to increase and/or strengthen their own content knowledge, explore their teaching practices, and we strive to help teachers find ways to improve their… Continue Reading
The AIMS Center for Math and Science Education is happy to be in a cooperating partnership with H.O.P.E. for K-8 Education (Hosting Ongoing Professional Experiences), an educational non-profit organization in Garden City, Michigan. H.O.P.E. for K-8 Education is also in collaboration with Schoolcraft College, a comprehensive community-based college located in Livonia, Michigan, with a satellite… Continue Reading
Learning by teaching, Edgar Dale was an American educationist who developed the Cone of Experience, which is a conical display of what brain research shows. We remember 10% of what we hear, 10-15% of what we see, 15-20% of what we both see and hear, and 20-40% of what we discuss. We remember 40-80%… Continue Reading
My mathematics mentor, Dr. Dave Youngs, used to ask that very question. I think the question implied, was I a recreational mathematician? Was I on a journey of playing with mathematics for life? Yes, I am a lifelong mathematics learner. When I am facilitating workshops, I ask classroom teachers if they do recreational mathematics or… Continue Reading
Last week I made a trip to New England to visit my family. While I was there I took time to travel to Hillsboro, New Hampshire, to visit one of our AIMS facilitators, Stephanie Savoy. Stephanie teaches 5th grade at Hillsboro Elementary School and joined the AIMS Professional Learning cadre in April of 2016. She… Continue Reading
I am honored to work with dedicated, smart, and caring educators. Carmella Crawford, another AIMS Professional Learning Facilitator, is all of these and I would like to take this opportunity to introduce her to you. Carmella lives in Charleston, West Virginia, and has been an AIMS Facilitator for some time. She has taught all grades,… Continue Reading
In the mid-1980’s after becoming a teacher with my own classroom, finding a learning community to think and reflect with was difficult. I wonder what I might have changed, given the chance to work with colleagues, and how I could have been an even better educator. My thoughts wandered to that place again last week… Continue Reading
The benefits of being an AIMS Facilitator are many, but when I started I did not know that I would get to know so many amazing educators from around the United States. Paul Agranoff is another one of our AIMS Professional Learning Facilitators and he hails from Minnesota. His teaching career has been spent in… Continue Reading
I am writing to introduce you to another AIMS Professional Learning (PL) Division Facilitator. Sheldon Erickson has been a classroom teacher and an AIMS Workshop Facilitator in the Central Valley of California for many years. To celebrate the reopening of the newly remodeled AIMS Center for Math and Science Education in early 2016, I asked… Continue Reading