8 Moves to Harness the Power of
Mathematical Discourse
Which "teacher move" do you think is the most powerful
for generating mathematical thinking and discourse?
Below are 8 strategies that you can use right away in your classroom to promote deeper thinking and richer discourse for ALL students – and for my own entertainment, I thought it would be fun to use some well-known (and lesser known) sayings as a way to categorize and remember each of the eight strategies.
- A Goal Without a Plan is Just a Wish
- Be Careful What You Ask For Because You Just Might Get It
- The More the Merrier
- Good Things Come to Those Who Wait
RBF – No, Let's Call It "RMF": Resting Math Face- A Few Fries Short of a Happy Meal
- The Mind Needs More Space Than the Body
- Keep the Home Fires Burning
INTRIGUED? Keep Reading....
1. A Goal Without a Plan is Just a Wish
As you prepare your lessons, plan for a variety of possible paths and possible misconceptions that your students will have. Design the tasks so that rich student-to-student discourse and productive struggle are inevitable. Plan for specific questions ahead of time – before you are standing in front of students. Some of the questions that you plan will get used, others will not.
2. Be Careful What You Ask For Because You Just Might Get It
As you plan those questions (see #1 above), plan to use a lot of open questions, rather than closed questions. If you ask a closed question, you will get a closed response. When you ask open questions, students have room to think and explain and expand their ideas. You will learn more about your students' thinking and they will make more mathematical connections and will develop their mathematical vocabulary. Win-Win!
3. The More the Merrier
In our classrooms, we must become more intentional to include more student voices. Honestly, we (teachers) talk WAY too much in our classrooms. Our students should be doing much of the mathematical talking, not us. Our job is to facilitate their discussions by asking questions that focus them to ideas that they may not stumble upon without us. We need to encourage student-to-student mathematical discourse – a lot of it! We have to increase student voice in the classroom. Let's teach our students to rely on one another as sources of information rather than the teacher always being the only one with the answers and good ideas. We don't intentionally do it, but we steal students' opportunities to learn pretty regularly in a typical classroom. Want an easy first step for changing this pattern? Try this: Pose a question (an OPEN question as mentioned in #2 above). Have students think about their own ideas (we'll talk more about this one in #4). Then have students rehearse their ideas with a partner – I like to use Peanut Butter Jelly Partners.
After a minute or so of partner discussion, ask the question again and ask a student to share his/her response out to the whole group. The student-to-student talk takes less than 2 minutes and the benefits are worth every 120 seconds of it! Think about it: Every student had a chance to share and listen to ideas as they talked with a partner. In a traditional ask and respond classroom, if 8 questions are asked, only 8 students talked about their ideas - which means most students in my class had zero opportunities to process the information, formulate a response, and talk about math. By adding a simple turn-n-talk teacher move, EVERY student interacts with EVERY question... AND... because students have rehearsed their ideas with a partner, student responses are more refined and classroom discussions are much richer and deeper.
4. Good Things Come to Those Who Wait
In 1986, an article by Mary Budd Rowe came out in The Journal of Teacher Education on the topic of Wait Time. I was in college at the time and one of my classes required us to subscribe to the Journal as our textbook. I have a clear memory of reading that article during the second year of my teacher prep program. I'm not sure why, but I saved that volume even after I graduated. In 1986, I didn't fully understand the power of Wait Time, but during my third year of teaching (after a disastrous second year), it would become one of the most powerful tools in my teaching arsenal. That year, I established my "teacher wall" which I have had in every classroom since that year. My teacher wall was a place on the back wall where I looked most often during instruction (it was not an out-of-sight/out-of-mind spot next to my desk). Each school year, I decided on a skill I wanted to professionally develop then I posted a sign to remind me to practice that skill every day. For three years straight, my sign said "WAIT TIME". In year three, I revised it to specifically include both Wait Time I and Wait Time II.
So what exactly is Wait Time I and II? In short, it's one of the most powerful tools you'll possess as a teacher. It's an easy concept to explain – but honestly, it takes practice to perfect in the classroom.
- WAIT TIME I: After asking a question, pause and expect students to think about the question before any discussion begins. I consistently remind students that I am not looking for hands or discussion in the first 5 seconds after I ask a question. I remind them (and myself) by putting my finger to my head to signal 5 seconds of think time. I then cue them to discuss their ideas with a partner or to raise a hand to share. In my classroom, these 5 little seconds improved the quality of the answers that students gave ten-fold, and I noticed that I had a larger pool of student hands from which to call and a wider variety of students who were willing to share. Now that's a powerful 5 seconds! By my second year of practicing this teacher move, I was pretty good at it. As I was sharing the idea with some colleagues, I realized that I had completely ignored Wait Time II, so during that third year of working to improve my use of Wait Time, I took steps to intentionally include Wait Time II.
- WAIT TIME II: Every time a student gives an answer, pause. You may want to silently count 1-2-3-4-5 to help you remember – I used to use my fingers hidden behind my back to count down. Do not nod in agreement or make one of those typical "teacher faces" that indicates the answer was not what you had hoped. Instead, just wait... for just 3-5 short seconds allowing everyone in the room to process the answer given by their classmate and to begin deciding on their own if they agree, disagree, or even understand the response given.
RBF – No, Let's Call It "RMF": Resting Math Face
If you Google RBF, you will likely get images of a scowling Anna Kendrick or Kristen Stewart or perhaps an article touting that science has proven that RBF is real. RMF, on the other hand, has no photos of contemptuous megastars, but I assure you, Resting Math Face is very real and very powerful in the classroom - and having it is a GOOD thing!
Do your students seem to stop short of the perfect complete answer? In many cases, it's because we have sent them the message that they have said enough when we do not maintain our Resting Math Face and allow facial expressions and body language to slip out too soon. Consider this common scenario: You ask a question. You remember to use Wait Time (hooray!). You call on a student. The student begins with an answer that you just know is going to be perfect by how it starts off. You begin nodding and smiling to encourage the student to keep going. And the student suddenly stops talking. Wait! She started off so strong and it seemed she would have so much to say. Why should she continue? You have already given her the praise she was seeking for a good answer by nodding and smiling. Now let's say a student does not start off with what you know will be a perfect response, so you crinkle your nose and tilt your head ever so slightly. Oops! The student knows his answer has started off on the wrong track by your expression and body language. So he stops talking - which means he stops thinking and processing. He has shut down (perhaps for the rest of the class period). The best way to encourage students to keep going and to expand their ideas is by maintaining a Resting Math Face (RMF). Let's say the answer calls for a simple number as the response. The student says, "12". While maintaining your RMF, you ask, "How do you know the answer is 12?" The student stumbles and falters thinking that she must have answered incorrectly since you did not immediately nod and praise her correct response, so she changes her answer to "11". Using the same tone and continuing to maintain your RMF, ask, "How do you know the answer is 11?" This forces the student to consider why that answer is correct. Yep, it'll be awkward at first because we have conditioned our students through the years to look for teacher cues, but they'll soon catch on that they need to fully explain because they'll be initially met with the teacher's Resting Math Face every time.
6. A Few Fries Short of a Happy Meal
Okay, forgive me for the quirky little title of #6, but, according to my children, I use these types of sayings more than I am aware😏. When asking students questions, it's true that we are often a few questions short of getting to their deeper understanding (or their misunderstandings) because we don't use questioning to push their explanations (and their thinking) farther. When students answer, we should push/probe/challenge their ideas. Part of our job is to help our students develop their ability to engage in mathematical discourse. To do this, we need to encourage them to explain/elaborate/clarify their thinking. Remember the "teacher wall" I mentioned earlier? The sign I had hanging on my wall in more recent years said "How do you know?" – I wanted to remind myself to ask students (often) to explain their thinking. Students will become so accustomed to every answer they give being followed by the question "How do you know?" that they will automatically begin giving an answer AND a reason as part of their initial response.
Love my new laptop sticker designed by my daughter Erin
7. The Mind Needs More Space Than the Body
I heard this saying somewhere and it has stuck with me, especially when I'm working with students. As we ask students to talk to each other about their ideas, it is critical that we give them time and space with their partner/group to play with those ideas. We will gain great insight into our students' thinking and understanding as we listen to their discussions – but it is important that we do not hover or interject our own ideas as we walk around from group to group. [An alternate title for this one could be "A Watched Pot Never Boils"]. Just listen. Take notes. Let the students grapple with the learning. Let them talk and really listen to each other's ideas. Give them space to reason, question, debate, and yes, even to stumble and struggle a bit. Then use what you heard as you walked around listening to their mathematical ideas to orchestrate productive math discussions.
8. Keep the Home Fires Burning
This one may be last on my list, but it is perhaps the most important one! If we hope to create powerful mathematical discourse in our classrooms, we MUST begin by establishing a supportive learning environment. And once established, we must continuously "stoke" the fire to keep it burning. I find that the best way to get the fire started is by being genuinely curious about students' ideas. We sometimes get so wrapped up in the "right" answer and the specific procedure that we fail to listen to what our students know and what they are ready to learn next. There are many ways to foster a supportive learning environment. Want a few more ideas to help stoke the fires? Try these:
- Promote student-to-student discourse every day
- Encourage students to be mathematically curious
- Help students focus and form new ideas by asking questions that probe thinking
- Model a growth mindset
So... which "teacher move" do you think is the most powerful for generating mathematical thinking and discourse? And more importantly, which move(s) can you begin cultivating right away to increase mathematical discourse?
As you prepare your lessons, plan for a variety of possible paths and possible misconceptions that your students will have. Design the tasks so that rich student-to-student discourse and productive struggle are inevitable. Plan for specific questions ahead of time – before you are standing in front of students. Some of the questions that you plan will get used, others will not. As you plan those questions (see #1 above), plan to use a lot of open questions, rather than closed questions. If you ask a closed question, you will get a closed response. When you ask open questions, students have room to think and explain and expand their ideas. You will learn more about your students' thinking and they will make more mathematical connections and will develop their mathematical vocabulary. Win-Win!
In our classrooms, we must become more intentional to include more student voices. Honestly, we (teachers) talk WAY too much in our classrooms. Our students should be doing much of the mathematical talking, not us. Our job is to facilitate their discussions by asking questions that focus them to ideas that they may not stumble upon without us. We need to encourage student-to-student mathematical discourse – a lot of it! We have to increase student voice in the classroom. Let's teach our students to rely on one another as sources of information rather than the teacher always being the only one with the answers and good ideas. We don't intentionally do it, but we steal students' opportunities to learn pretty regularly in a typical classroom. Want an easy first step for changing this pattern? Try this: Pose a question (an OPEN question as mentioned in #2 above). Have students think about their own ideas (we'll talk more about this one in #4). Then have students rehearse their ideas with a partner – I like to use Peanut Butter Jelly Partners.
4. Good Things Come to Those Who Wait
In 1986, an article by Mary Budd Rowe came out in The Journal of Teacher Education on the topic of Wait Time. I was in college at the time and one of my classes required us to subscribe to the Journal as our textbook. I have a clear memory of reading that article during the second year of my teacher prep program. I'm not sure why, but I saved that volume even after I graduated. In 1986, I didn't fully understand the power of Wait Time, but during my third year of teaching (after a disastrous second year), it would become one of the most powerful tools in my teaching arsenal. That year, I established my "teacher wall" which I have had in every classroom since that year. My teacher wall was a place on the back wall where I looked most often during instruction (it was not an out-of-sight/out-of-mind spot next to my desk). Each school year, I decided on a skill I wanted to professionally develop then I posted a sign to remind me to practice that skill every day. For three years straight, my sign said "WAIT TIME". In year three, I revised it to specifically include both Wait Time I and Wait Time II.
So what exactly is Wait Time I and II? In short, it's one of the most powerful tools you'll possess as a teacher. It's an easy concept to explain – but honestly, it takes practice to perfect in the classroom.
- WAIT TIME I: After asking a question, pause and expect students to think about the question before any discussion begins. I consistently remind students that I am not looking for hands or discussion in the first 5 seconds after I ask a question. I remind them (and myself) by putting my finger to my head to signal 5 seconds of think time. I then cue them to discuss their ideas with a partner or to raise a hand to share. In my classroom, these 5 little seconds improved the quality of the answers that students gave ten-fold, and I noticed that I had a larger pool of student hands from which to call and a wider variety of students who were willing to share. Now that's a powerful 5 seconds! By my second year of practicing this teacher move, I was pretty good at it. As I was sharing the idea with some colleagues, I realized that I had completely ignored Wait Time II, so during that third year of working to improve my use of Wait Time, I took steps to intentionally include Wait Time II.
- WAIT TIME II: Every time a student gives an answer, pause. You may want to silently count 1-2-3-4-5 to help you remember – I used to use my fingers hidden behind my back to count down. Do not nod in agreement or make one of those typical "teacher faces" that indicates the answer was not what you had hoped. Instead, just wait... for just 3-5 short seconds allowing everyone in the room to process the answer given by their classmate and to begin deciding on their own if they agree, disagree, or even understand the response given.
If you Google RBF, you will likely get images of a scowling Anna Kendrick or Kristen Stewart or perhaps an article touting that science has proven that RBF is real. RMF, on the other hand, has no photos of contemptuous megastars, but I assure you, Resting Math Face is very real and very powerful in the classroom - and having it is a GOOD thing! Do your students seem to stop short of the perfect complete answer? In many cases, it's because we have sent them the message that they have said enough when we do not maintain our Resting Math Face and allow facial expressions and body language to slip out too soon. Consider this common scenario: You ask a question. You remember to use Wait Time (hooray!). You call on a student. The student begins with an answer that you just know is going to be perfect by how it starts off. You begin nodding and smiling to encourage the student to keep going. And the student suddenly stops talking. Wait! She started off so strong and it seemed she would have so much to say. Why should she continue? You have already given her the praise she was seeking for a good answer by nodding and smiling. Now let's say a student does not start off with what you know will be a perfect response, so you crinkle your nose and tilt your head ever so slightly. Oops! The student knows his answer has started off on the wrong track by your expression and body language. So he stops talking - which means he stops thinking and processing. He has shut down (perhaps for the rest of the class period). The best way to encourage students to keep going and to expand their ideas is by maintaining a Resting Math Face (RMF). Let's say the answer calls for a simple number as the response. The student says, "12". While maintaining your RMF, you ask, "How do you know the answer is 12?" The student stumbles and falters thinking that she must have answered incorrectly since you did not immediately nod and praise her correct response, so she changes her answer to "11". Using the same tone and continuing to maintain your RMF, ask, "How do you know the answer is 11?" This forces the student to consider why that answer is correct. Yep, it'll be awkward at first because we have conditioned our students through the years to look for teacher cues, but they'll soon catch on that they need to fully explain because they'll be initially met with the teacher's Resting Math Face every time.
Okay, forgive me for the quirky little title of #6, but, according to my children, I use these types of sayings more than I am aware😏. When asking students questions, it's true that we are often a few questions short of getting to their deeper understanding (or their misunderstandings) because we don't use questioning to push their explanations (and their thinking) farther. When students answer, we should push/probe/challenge their ideas. Part of our job is to help our students develop their ability to engage in mathematical discourse. To do this, we need to encourage them to explain/elaborate/clarify their thinking. Remember the "teacher wall" I mentioned earlier? The sign I had hanging on my wall in more recent years said "How do you know?" – I wanted to remind myself to ask students (often) to explain their thinking. Students will become so accustomed to every answer they give being followed by the question "How do you know?" that they will automatically begin giving an answer AND a reason as part of their initial response. |
| Love my new laptop sticker designed by my daughter Erin |
This one may be last on my list, but it is perhaps the most important one! If we hope to create powerful mathematical discourse in our classrooms, we MUST begin by establishing a supportive learning environment. And once established, we must continuously "stoke" the fire to keep it burning. I find that the best way to get the fire started is by being genuinely curious about students' ideas. We sometimes get so wrapped up in the "right" answer and the specific procedure that we fail to listen to what our students know and what they are ready to learn next. There are many ways to foster a supportive learning environment. Want a few more ideas to help stoke the fires? Try these:
- Promote student-to-student discourse every day
- Encourage students to be mathematically curious
- Help students focus and form new ideas by asking questions that probe thinking
- Model a growth mindset
So... which "teacher move" do you think is the most powerful for generating mathematical thinking and discourse? And more importantly, which move(s) can you begin cultivating right away to increase mathematical discourse?
