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Welcome to Episode 9- the second part of a series about moves that parents and educators can take to help create a Kids Math Talk community all year long. If you haven’t listened to Episode 8 yet, then pause here and head to that episode for a background about sociomathematical norms.
More and more districts are announcing a virtual start to the school year, which means that teachers all over the country are flooding social media sites with various well intentioned resources for what an online community should look like and sound like and expectations for engagement.
It is so tempting to just want to download and post or print one of these, right? It's already created for us and would be something that we can check off of our to-do list. But before presenting anything to children, we need to first think about the goal and also the impact that something will have on children.
The ultimate goal behind our actions is to build positive math identities, whether we are face to face or virtual.
So in the midst of reinforcing sociomathematical norms, we must also think about how to design instruction that includes equitable participation and elicits active engagement, regardless of whether children are learning face to face or virtually.
In Episode 9, we discuss how to increase active engagement in any learning environment.
Children have a lot to say, but sometimes they have trouble getting the conversation started. This can be true for any topic or area but it seems especially true for math.
And as stated in Talk Moves (Chapin et al., 2013),
Some students have not engaged in intellectual discussion before and may find it stressful to talk in front of their classmates. [C]hildren who have been taught that they should take an observer’s role in intellectual discussions may find it very challenging or even upsetting to take an active role in a classroom discussion” (Chapin, S. et al 2013, p. 9).
On top of this unfamiliarity, we must remember that many children will be dealing with trauma because of the complete change in how the world is functioning right now.
Patience is going to be key.
Patience does not mean to passively endure. It means to be farsighted enough to trust the end result of a process.
-Rumi
This quote, by the 13th century poet Rumi, applies to our learning today. Our end result, which is creating an environment where children feel comfortable and are willing to actively engage, is not going to happen over night.
We also need to have clarity in the process so that we all can envision the same result. But while we all might think that we already have same idea when we talk about active engagement, this concept is often extremely ambiguous-
For example, what descriptions, or observable indicators, enter your mind when you think of active engagement in learning?
Most likely whatever you are thinking is not going to be the same as what another adult is holding in their mind.
While one person might think about “eyes on the speaker”, another person might associate engagement with “working on a problem or writing a story” instead of sitting and staring at a blank piece of paper. Yet another individual might view engagement as responding with cues indicating agreement or disagreement. Some parents indicate that active engagement to them is not texting or playing a game during a conversation.
And on top of these, some people might alter what they consider to be an indicator or engagement depending on who they are observing.
This variation exists because we have not taken the time to identify a collective definition about engagement itself. Thus, our opinions which are formed in part by our own identities, backgrounds, and beliefs, are dominating and creating our own personal interpretations around what signals active engagement.
We have to start being more specific with what we mean by engagement if we truly want to create equitable learning structures for children, which means we need to deepen our own understanding of the concept. The fact is that the process of engagement is complex, having three separate dimensions.
Let’s use the popular text, The Distance Learning Playbook Grades K-12 (2020), as a guide for this understanding, as the authors have created a helpful frame for analyzing the dimensions of engagement we as adults can emphasize in any learning environment.
INCREASING COGNITIVE ENGAGEMENT
The first dimension, cognitive engagement, includes the degree to which a child monitors their own progress, solves problems, and sets goals when given the opportunities. This dimension essentially is talking about the effort a child exerts when learning.
When starting the school year, some might believe that children need “easy” tasks and lots of remedial work because they supposedly missed instruction or did not retain the learning.Giving in to these unproductive beliefs will actually decrease cognitive engagement. We need to expose children to rich and challenging tasks that provide multiple ways to approach and solve; tasks that are different, and exciting for children and help them make new connections about the world around them..
But we still need to be intentional here. “If we simply just ask students to talk, without thinking carefully about our purposes, we may end up with irrelevant, hard-to-manage talk that serves no clear academic purpose”. That’s where Math talk moves come into play. These are “tools to help reach instructional goals” and more cognitive engagement and are grouped into four categories.
Parents, this applies to you too, as using these moves can help you communicate more effectively with your child at home (Chapin et al., 2009, p. 6-7).
With that being said, start slow to move fast later - if you are new to the idea of talk moves and try to implement all four categories at the same time, it is going to be overwhelming for you and confusing for children.
Category #1: “Say more” prompts
The first category, as organized by the text Classroom Discussions (2009) is called “say more” prompts. These are generally used by the adult and have the goal of getting children comfortable with sharing out loud and “sends a signal that [we as adults] want more than just a correct answer” because we truly care about children’s thinking. Some of the prompts to try out after a child gives a yes or no answer or after an answer needs more unpacking include:
-Can you say more about that?
-Can you expand on that?
-Can you give an example?
Revoicing
The second type of prompt in this category, Revoicing, invites greater clarity.
Two key pieces to remember here are that revoicing is not just repeating. You as the adult are rephrasing what a child has said and then asking that child “to verify whether or not the revoicing is correct” (Chapin et al., 2009, p. 15). It signals that a part of learning is figuring out how to “regroup and clarify” your own thinking (Chapin et al., 2009, p. 14).
Some possible examples of revoicing include:
-Ok, let me see if I understand…
-If I’m hearing you correctly, then I think you’re saying…
-So are you saying that…
Research states that “if [children] know that the teacher and their classmates will hold them accountable for making themselves clear, many of them will make great efforts to do the best they can to be clear and comprehensible” (Chapin et al., 2009, p.9).
And effort is the focus of this dimension. Planning for and implementing Math Talk moves creates equitable participation that leads to greater cognitive engagement.
Parents- Again, these prompts are not just for the classroom. These can be used to help you communicate with and better understand your own child. It might feel a little artificial at first, but the more you use these prompts, the more natural they will feel for you and your child.
Teachers- The beginning of the school year is an excellent time to try out these prompts with children while introducing a high-yield routine, such as Which One Doesn’t Belong or Picture Talks.
Remember that these high-yield routines don’t always have to have a mathematical concept as the base. Children need to feel safe and valued in order to become vulnerable enough to share their thoughts out loud and developing pictures for these routines that build on children's funds of knowledge in other subject areas is one way to create this safety and lower children’s anxiety.
I want to note here that while we might think that the prompts of “I agree/disagree” would be the place to start, children need to first be comfortable with their own thoughts and expressing those before thinking about the reasoning of others. Research suggests starting to increase engagement by emphasizing category #1 with the Say More and Revoicing strategies with children.
We will talk about other categories of Math Talk moves in later episodes of the podcast.
INCREASING EMOTIONAL ENGAGEMENT
The second dimension, emotional engagement, is influenced by the relationships that a child has with their peers and the adults that are a part of the learning environment. Whether we emphasize them or not, these factors “contribute to a student’s ability to learn and their sense of belonging” (Fisher, D. et al., 2020, p. 102). Learning environments that foster this emotional engagement affirm identities and build confidence, resulting in children who are willing to engage in discussions, pose questions and seek help when needed.
Wait Time
One math talk tool that is essential to think about when planning for equitable participation and active engagement is that of... wait time. Was that pause a little awkward for you? Don’t worry, it was a little awkward for me too - it’s awkward for most people, which is why we have to work so hard to implement it well.
It gets uncomfortable to sit through the silence and have one pair or even 25 pairs of eyes staring at you and it’s in our nature to be tempted to fill the silence with our own thoughts and voice. It’s imperative that we don’t though.
Thinking is the rehearsal for discourse- In order to increase emotional engagement throughout a lesson, we have to give children time and space to think about how to cognitively engage with the task, with their peers, and with adults.
You might be thinking that this is not a new strategy - and you’re right- teachers in particular have been using the idea of wait time for decades. But just because something has been implemented does not mean that it is equitable or that it will increase engagement.
Implementing equitable wait time that will increase emotional engagement involves waiting at least four to five seconds “at three crucial points - after a question has been asked, while a child is answering, and then again for another 4 to 5 second interval after the student responds to the question” (Chapin et al., 2009, p. 19).
Research shows, however, that the average teacher only waits between .7 and 1.4 seconds after asking a question before either calling on a child who already has their hand raised, or answering the question themselves.
Which amount of time would you rather have in order to gather your thoughts - 15 seconds or 4.2 seconds?
More wait time allows “more students [to become] able and willing to join in [because] time is provided for them to create something that they feel comfortable about sharing.” (Stein et al., p. 72). It also allows us as adults to think about which talk move to use in order to move the conversation forward.
The wait time also indicates to all children that it is okay to take your time, that your words are important, and that your thinking is valued. We can indicate to children that the silence is thinking time, with a prompt such as, “Take your time” or “We will wait for you.”
Encouraging children to have a pencil and paper or whiteboard next to them to brainstorm if needed during this wait time might help children feel more confident about the thoughts that are forming in their minds and their “ability to engage in intellectual discussions” (Chapin et al., 2009, p. 132).
All of these extended wait time check points focus on increasing emotional engagement and help affirm children's identities as doers of mathematics and of being capable members of the community.
There is so much important work being done in this silence - let’s embrace it.
If you happen to be teaching virtually, it is even more important to implement wait time because “one of the risks with distance learning is that teachers [will] replicate all of [their] talk online or even increase the amount of talk so that they can fill the space” (Fisher et al., 2020, p. 132). Again, be willing to embrace the silence.
Having concrete manipulatives available for children, or even online manipulatives like those from Brainingcamp are another support that can be made available to encourage active engagement. Remember that if you leave a review on Apple Podcast you will be automatically entered to win a variety of prizes, including one of 3 12-month subscriptions of a classroom license to Brainingcamp!
And speaking of prizes, before we continue, I want to congratulate to our first winner- listener Rkg228 who writes - Education Gold! This is something that’s so necessary and needed. I’m not a math person but I can only imagine where I would be if my educators had implemented some of the tools discussed. The key to being able to develop new and original ideas starts with firm understanding. Lives are going to be changed from using the suggestions discussed on this podcast. Wow! Thank you so much Rkg228 for the review! Email me at kidsmathtalk@gmail.com to claim your prize.
Now let’s transition BACK TO INCREASING ENGAGEMENT
Something else that can be implemented to increase emotional engagement is classroom jobs. When I was teaching, I admit that I was never a really big fan of these. My students did have jobs, but I never put as much emphasis on these as other teachers. It’s because I just thought of these jobs as something extra to think about. The cute graphics, badges, and charts created to accompany the classroom job titles always made me lose sight of the why.
But a social media post by one of my fellow coaches in my district is what inspired me to think differently. She posted about classroom jobs, not with the goal of something that is cute or fun, but with the goal of community. These jobs are important because they help us attain the goal of emotional engagement. They send the message that each child is a valued member of the community and that everyone has a role in creating and maintaining that community.
Jobs also help build confidence and depending on how they are implemented, can build connections between peers. If you have been thinking about not incorporating classroom jobs because you will be teaching online or because you are still figuring out seating arrangements with new face to face guidelines, reconsider while thinking about ways to build community and emotional engagement.
The jobs wouldn’t need to be implemented on the first day, or even the first week. You as the teacher will need to talk with children about what the job entails and model the responsibilities for them. I recently spoke to a teacher in my district who had the suggestion of including a game show host as one of the jobs for the high-yield instructional routines mentioned earlier. Eventually children could even be the ones creating their own graphics or problems that can be used for these routines. Together we are better and I thank them both for stretching my thinking in this area!
Behavioral Engagement
The third dimension, behavioral engagement, is usually the dimension that adults are alluding to when discussing engagement. That’s because this dimension is highly observable, such as “eyes on the speaker” or “raise hand to speak”, which can often be translated as a student knowing “how to do school.” While all three engagement dimensions discussed today are related, placing an emphasis on behavioral engagement is not going to help children learn or build a more positive identity.
In my opinion, the majority of the pre-made online expectations posters currently floating around the internet focus solely on behavioral expectations that are intended to encourage. In some cases though, not conforming to these expectations will have negative consequences for children. Expectations such as logging in on time, keeping the video on, and dressing for success - all which might be completely outside of a child’s control-, can actually result in losing points because these expectations are unfortunately connected to a school’s or district’s definition of learning and success. Grading on such factors conforms to and maintains the status quo that marginalizes the underprivileged.
To be clear, these factors are about maintaining power- they have nothing to do with what a child may or may not have learned or is capable of learning, nor are they connected with success.
Teachers - I urge you to rethink any practice that emphasizes an extremely narrow, classist, or Eurocentric interpretation of engagement. If you, your school, or your district is debating about online expectations, such as whether or not to expect children to have the camera on, consider providing information about the different dimensions of engagement. Having a camera on or off is not an indication of learning. With the three dimensional breakdown of engagement we have just talked about, we now know that this camera debate is about behaviors, it’s about control and power, and not about cognitive or emotional engagement which are large factors in learning.
Instead of requiring children to have their cameras on, children can have a picture of themselves posted, maybe even a cartoon version of themselves, such as a Bitmoji character. If you find yourself needing more tools for advocacy, there are many articles and blog posts making the argument for choice about video. Another helpful piece of information to make your case is an infographic about Using Video to Assess Student Attention in Virtual Class Meetings by Dr. Torrey Trust, Associate Professor of Learning Technology at the University of Massachusetts, Amherst.
Parents - If you notice that the majority of the class norms or expectations for your child fall under the behavioral dimension and/or if your child will be graded on such behaviors, speak out about it. This is not building more equitable spaces and will not create environments that build positive identities.
We need to let go of focusing on whether or not we can see and focus on that child’s learning.
For instance, if a child is not talking during class, it is going to be more difficult to indicate what that child is learning, so we can implement a move such as the “one of three” technique.
With this intervention, The teacher speaks privately with the child that is not participating during live sessions. The teacher then encourages that child to actively engage during upcoming lessons with the choice of: “volunteering a comment during a whole-class discussion, responding when called on at random to do so, or ask a question during a whole-class discussion” (Chapin et al., 2013, p. 77). The teacher can also take the step to talk during a small group meeting about which comment the child would like to share. If in an online environment, a teacher might send a private chat message, video response or audio response to indicate what they hope the child shares with the whole class during the next live session. Implementing this one of three technique aligns with the sociomathematical philosophy of speaking out at some point, which honors a child’s time and space.
The last thing that we want to do in these first weeks of school is to trigger anxiety or fear because we know that when fear takes over, the brain enters a survival mode and learning is not going to happen.
As I close I want to leave you with this to think about:
If what we believe about teaching, learning, and engagement do not align with the free and pre-made posters circulating on the internet, if we truly can’t articulate how these posters and acronyms promote equity, access, inclusion, and positive identity building - then we shouldn’t be using them with children, even if it is more convenient for us.
Our beliefs, words, and actions must all revolve around planning for and implementing equitable participation structures that increase active engagement for sustainable Kids Math Talk.
Episode Sources:
Chapin, S. H., O'Connor, M. C., & Anderson, N. C. (2013). Talk moves: A teacher's guide for using classroom discussions in math, grades K-6. Math Solutions.
------------------------------------------------------------------- (2009). Classroom discussions using math talk to help students learn: Grades K-6. Sausalito: Math Solutions.
Fisher, D., Frey, N., and Hattie, J. (2020). The Distance Learning Playbook Grades K-12. Corwin.