Joshua Sawyer currently serves as the 7-12 Math Coach for Camden County Schools in Camden, NC. He has served as an AP Statistics teacher, AP Reader/Table Leader, adjunct instructor, and tutor. He is featured in AP Classroom as an AP Daily instructor for AP Statistics, and was selected as a member of the NCTM/ASA Joint Committee on K-12 Curriculum on Statistics and Probability Education. In December 2019, Joshua released his first musical single, "Chillin Chillin". He can be reached on twitter at @MrSawyerMath.
I have often found myself guilty as a teacher of making the statement “my students should know this, because I know I taught it.” But, did my students learn it? By definition, teaching is showing or explaining to someone how to do something. In contrast, learning comes not only by being taught, but also through experience and study (Oxford Dictionaries). To ensure that students learn, I found that I had to offer experiences to engage with the content. I had to create spaces for students not only to sit and hear what I had to say, but use their own insight and vantage points to discover their “Eureka!” moments.
Getting Students Thinking and Talking
As a teacher, my philosophy was always focused on “thoughts and communication”. That is, to provide students with two major opportunities: activities that require critical and analytical thought, along with avenues to express those thoughts to others. I find it valuable not to simply give students a set of procedures and rules, but to also provide a rationale behind the rules. The development of conceptual understanding can lend itself to promoting procedural fluency (West and Cameron, 2013).
For example, the calculation of a sample mean is a fairly straightforward process where one adds all data values from the sample followed by dividing by the number of data points. This is a basic skill within statistics, and one that most students are able to do. However, by discussing the formula for the mean itself, students can begin to see the value (no pun intended) of each data point. Students can begin to recognize the effects of outliers, discuss what happens as entire data sets are transformed, and even see connections between typical values and measures of spread. By offering students an opportunity to delve into the conceptual nature of the topics, it can help solidify their ability to perform the rote calculations.
Strategies for Getting Students Thinking and Talking
Along with routine problems that reinforce fluency of skills, students should be provided with tasks that promote deeper conceptual understanding, along with chances to extend thinking to novel scenarios. According to longtime statistics professor and former AP Chief Reader Allan Rossman, to become effective in teaching statistics, one must ask good questions. “I suspect that we teachers spend too much of our most precious commodity time on creating presentations for students to hear and writing exposition for them to read. I think we serve our students’ learning much better by investing our time into crafting good questions that lead students to develop and deepen their understanding of what we want them to learn.”
2. Amplify student voices
Provide students with opportunities to provide voice or video evidence of thinking and learning. Video creation and collaborative apps such as Flipgrid, Youtube, Animoto, and iMovie can empower student voice. Video responses can provide student benefits over written responses, such as opportunities for individual creativity, elevating voices of students who may not be strong writers, and helping to create a more real understanding and appreciation of how statistics affect our world.
Getting Teachers Thinking and Talking
As an educator, I find this equally true. As teachers bound to a curricular structure, we often reach a place where our daily actions are not grounded in innovation and discovery, but simply making sure we fulfill the checklist of topics required for our course. Even when we become comfortable with our curriculum, we often go to tried and true instructional strategies, not because they are necessarily the best, but because we are comfortable with those techniques. Professional support systems, whether learning groups, coaches, or educational forums, can help provide a more conceptual understanding of our practice, as well as a means of reflection.
Strategies for Getting Teachers Thinking and Talking
1. Ask good questions
Self-reflection plays a role in effective teaching. As educators, we can improve our practice by intentionally asking questions that challenge us to identify areas within our practice that we can adjust to effectuate cha