Author Archives: Deb Porcarelli
Having discussions with students is how most teaching is done. Classroom discourse in a mathematics classroom, for example, means having whole-class discussions around mathematics in such a way that students get to express their conceptual math understanding through reasoning, debate, and an exchange of ideas. Leading and engaging students in this form of instructional arrangement is a great way to help them informally assess their mathematical thinking. Knowing how to reason, think spatially, think critically, and problem solve for understanding can be promoted through mathematical discourse.
Shifting to a mindset that embraces the ways in which twenty-first century students have to engage fully with mathematics is what teachers are being asked to do. I encourage teachers to take time to read books, articles, and have conversations about how to engage in and use discourse in the classroom with colleagues. It will better prepare you for facilitating good math discussions with students. I just finished reading a newly published white paper by Gladis Kersaint titled “Selecting and Sequencing Student Solutions.” In it, she shares great tools for planning and engaging students in productive mathematics discussions. Here are three questions she shares that you may want to use to ask yourself ahead of having the discussions with your student:
- What is the intent of the discourse we will engage in?
- What are the class norms for mathematical discourse?
- What understanding do I want my students to develop?
Once you know have answered those questions then you can focus on what Kersaint explains are the five practices that are helpful in promoting good discussions. They are:
- Anticipating – how do you envision the discussion to go
- Monitoring – how did the students do in their prior work
- Selecting – let selected students know they will be asked questions during the discussion
- Sequencing – in what order you ask questions
- Connecting – synthesize the discussion at its conclusion
Asking yourself these important questions before engaging students in mathematical discourse will help you to focus on your math class goals. With your goals in mind, you can plan out how to follow the discourse practices. Discourse that is planned and facilitated well allows students to express their thoughts and reasoning behind their mathematical thinking. I would be happy to know how you “talk math” in your classroom.
Teachers help students acquire knowledge and become competent in all subject areas. After teachers have met the requirements for having and using a teaching credential, it seems one expectation is for them to be a “high-quality” teacher. How does a person become a “high-quality” teacher? Teacher quality has been consistently identified as the most important… Continue Reading
Theologian, philosopher, poet, and social critic Soren Kierkegaard lived from 1813-1855. He philosophized how one should live as a “single individual,” giving priority to concrete human reality over abstract thinking and highlighting the importance of personal choice and commitment. Here are two quotes and some thoughts that were shared with me by Richard Thiessen, the… Continue Reading
“Olympic Spirit strives to inspire and motivate the youth of the world to be the best they can be through educational and entertaining interactive challenges.” The Winter Olympic Games have ended but I am still thinking about what the spirit of the competition means to the athletes. It is much like what education and what… Continue Reading
From arithmetic to calculus, I see mathematics everywhere around Pyeongchang during the winter Olympic games. I’m also thinking about all of the math through the lens of CCSSM’s Mathematical Practice 4: Model with Mathematics. It says, “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the… Continue Reading
This is the third and final of my Teachable Points of View (TPOV) posts. To read the first two, click here to ready number one, and here to read number two. Teachers need ongoing quality professional learning opportunities. I am motivated to see teachers grow and learn, and to have the AIMS Center for Math… Continue Reading
This is the second of my Teachable Points of View (TPOV) posts. As a member of Learning Forward Academy’s class of 2019, we have been asked to write and share three of our TPOVs. It has been a great exercise to write about and share the ideas that are at the core of my… Continue Reading
I hope you enjoy this and the following two blog posts. I plan to share three of my own Teachable Points of View (TPOV) in these posts. As a member of Learning Forward’s Academy class of 2019, we have been asked to write and share three of our TPOVs. It has been a great exercise… Continue Reading
When I started writing this, I was on a plane headed to Indiana. I was going to spend a day working with a small group of primary teachers, sharing AIMS hands-on math tasks with them. I’ve prepared countless workshops, but every time I head out to do another, I get excited. Each time I anticipate… Continue Reading
Welcome to 2018! Have you written new professional goals for this year? If you are a teacher, I bet your goals may ultimately be linked to increasing student achievement. As an educator, my ultimate goal is for all students to achieve everything possible within their academic grasp. That means I need to reevaluate and revise… Continue Reading