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We often refer to ground rules as norms, which are based on expectations (Yackel and Cobb, 1996). In a face to face environment, we spend the first weeks setting these norms for the hallway, the carpet area, and the playground. Teachers even set norms for reading and writing workshops.
This fall most educators will be establishing norms for online meetings. We do this because we know that it invites a sense of community, belonging, and purpose. That means that we need to take the time to establish these norms, or expectations, for learning math as well.
When I taught 3rd grade, I made it a point to always included activities during the first two weeks of school that were specific to setting up the culture and expectations for my math workshop, but I didn’t find out until I had already been teaching for 6 years that I wasn't going deep enough when thinking about building a sustainable math community. I was focused only on helping my students understand what the workshop looked like and sounded like but that year, one of my graduate professors introduced me to the work of researchers Yackel and Cobb who put forth the idea that there are in fact distinct norms for math with a very specific name - they’re called sociomathematical norms.
What is a sociomathematical norm?
It’s okay if you’ve never heard of these before - like I said I had been teaching for several years without ever having a conversation about them.
These are not the same as general social norms because they go beyond simply suggesting that children be kind and patient with one another.
Sociomathematical norms are the normative criteria by which students within classroom communities create and justify their mathematical work. Examples include negotiating the criteria for what counts as a different, efficient, or sophisticated mathematical solution and the criteria for what counts as an acceptable mathematical explanation (Stephan 2014).
Let’s talk about another example. For the past few years, a really popular general norm has been that “mistakes help our brains grow”. The sociomathematical equivalent of this norm would add another layer by stating exactly how teachers and students should respond when mistakes happen. Taking Action (2017) gives a wonderfully clear example of how to communicate this - simply say “share mistakes” (p.159).
This sets the groundwork for understanding that mistakes are “acceptable” and that they are going to happen and then when they do, here’s how we will respond. Having this “when x, then y” approach helps to make things clear for everyone which will ease some of the anxiety children will most likely be feeling at the start of the year.
They help define the why and how of math class and prepare us for understanding and interpreting the learning that is to come during the year. They also explicitly define what a child should expect from themselves, their classmates and their teacher while engaging in and discussing math tasks and concepts.
We have to make time to create sociomathematical norms.
Step #1 - Know your Beliefs
In the next week, the first step teachers can take toward building an online Kids Math Talk community that includes sociomathematical norms is to think deeply about your beliefs and answers to the following questions - What do you believe about the teaching and learning of mathematics? What is your definition of mathematical discourse? What criteria do you believe counts as a “sophisticated math solution” for the grade level you are teaching? What kind of culture do you want to create for your online learning community?
Head to my website, kidsmathtalk.com/podcast for a download of these questions to ask yourself. It is also a good idea to make sure you have dealt with your own feelings about this past school year too. Head to Episode 3 if you need some reflection prompts for this.
Step #2 - Ease into the school year
Step #2 involves us easing in the school year. We must remember that children have spent months outside of a familiar learning environment. They need the chance to become familiar again with interacting with peers and teachers. Talk with your admin team in your district to see what resources are being provided to help children begin to process the trauma they might have from this past school year and how to help them transition back into learning. Children need to know that teachers are there for them and giving them time and space to sort out their feelings builds trust.
Parents, ask for these resources as well, and continue to have conversations with your child about how they are feeling about school and their current learning environment.
Teachers- when speaking about subject areas, we also have to remember that children might be entering this school year with negative feelings toward math. Creating a productive online math community with students is going to take time. We can help create positive math experiences with children by completing activities like those from Jo Boaler’s site, youcubed.com. This is an amazing resource for back to school and has a variety of videos and activities that promote a growth mindset and other productive beliefs. It’s so easy to use, and the website even lets you save a playlist so that you can plan an entire week at once and have it ready to go.
I also recently found a blog post about some downloadable “getting to know you” templates that you can use with Google Jamboard, like Two Truths and a Fib, and Guess Who?, that I’ll link in the show notes for you.
A few weeks ago I was reading an article from the Boston Globe. The focus was on the findings of MIT and Harvard education researchers who suggest that, “tak[ing] steps to strengthen bonds between teachers and students, are more imperative than ever when in-person interactions are limited. The recommendation [is] that schools should focus on teacher-student relationships and make the curriculum as relevant as possible” (Martin, N. 2020).
Another activity you can implement to start learning more about your student’s identities is the drawing activity mentioned in Episode 2 of this podcast. This will help you create lessons later on that are more relevant for your students.
Step #3 - Establishing Sociomathematical Norms
This brings up to Step #3 for teachers, which is to have a direct conversation about sociomathematical norms with your students. Hopefully your class will be ready between the 2nd and 4th weeks of school, once you have had a few face to face or live sessions with your students. When starting to create norms, it’s important that each member of the class is involved so that each member knows they are an important part of the class community. Encourage children to use their experiences from the first week of this school year to help them think about the norms they would like for the rest of the school year.
If you are starting the year with online learning, you could pre-plan part of this conversation and have some quick polls ready to use with your class, or breakout rooms for discussion, depending on the age group you are working with. Another suggestion is to have students send you videos of themselves talking about the norms they would like included so that you can review these ahead of time to better organize the live discussion. Both of these strategies support the belief and created the norm that all voices are important.
However you decide to design the lesson, remember to keep the final list of norms concise and easy to remember, so aim for no more than 7 items. If you’re getting stuck with how to frame some of the language, an excellent reference guide is chapter 8 of the book Classroom Discussions (Chapin, 2009). A suggestion the authors give is to make sure that your norms embody three philosophies-
That every student is listening to what others say
That every student can hear what other say; and
That every student may participate by speaking out at some point (p. 12).
This makes me think that part of a class's discussion might mention whether or not to have cameras turned on during math and about which participation tools that are a part of many video conferencing platforms a class will use and why these tools matter.
Once your class has decided on norms, create a community poster of these and add on accountability by having students sign this. If you are in the classroom, hang this poster on the wall as a visual reminder of these norms. If you are in a virtual environment, you can type up the norms on a virtual whiteboard or slide, have each child sign online by typing their names on a virtual sticky note or another tool - or even upload their pictures-and then take a screenshot of this so that a timestamp is created. Make sure that you sign this too! In an online learning community, it will be important to reference these norms at the beginning and end of every session so that they simply become how you and your students operate.
It’s also important for children who might not be online often to also be involved with these norms. Consider reaching out to them via family email or a phone call to make sure that they also know that they are a valued member of your class community.
As authors Chapin, O’Connor, and Anderson state in their book, Classroom Discussions: Using math talk to help students learn (2009), “When a teacher succeeds in setting up a classroom in which students feel obligated to listen to each other, to make their own contributions clear and comprehensible, and to provide evidence for their claims, that teacher has set in place a very powerful context for student learning. The class as a whole develops an understanding about values held by mathematicians and scientists all over the world: precision, clarity, intellectual honesty, effort, and thoroughness” (Chapin, 2009, p. 9-10).
Creating these norms might be something that some teachers want to avoid because it’s going to take time, energy and honesty from everyone involved - At first it might feel overwhelming to think about all that is involved to reach this success, but just remember that this is a journey and we can take things one set at a time in order to create the most productive experience possible for children.
Sociomathematical norms are what the members of a learning community believe about the teaching and learning of mathematics. They highlight mathematical identities and define core values. Making the choice to jump into the first lesson of a math curriculum and to just not bother with community building activities because we’re trying to make up for lost time or because we’re operating under the false belief that “all we teach is math” is a mistake.
It’s a mistake because dismissing explicit norm creation doesn’t mean that norms won’t be created for your class. What it does mean, unfortunately, is that by not talking about productive values and beliefs, we will be allowing unproductive beliefs to dominate, including the idea that children’s thoughts, opinions, and backgrounds are separate from mathematics and do not matter.
Children need to know that they are truly valued, that their ideas are worthy and will be listened to and that their teachers will not ignore them.
Parental involvement is important
Parents - your continued involvement is important. Stay informed about the sociomathematical norms set in your child’s class by asking your child’s teacher to email you a picture of this class poster so you are aware of this agreement as well.
Help your child create a meaningful space in your home that is designated for learning without distraction.
You can also create a similar contract with your child and everyone in your home. Set guidelines about keeping a growth mindset, persevering through problems, or playing board games a set number of times each week or add on some others that come to your mind. Have everyone sign this after it is agreed upon and then post it in a prominent area, like on the refrigerator.
I’m going to stop here for now because this idea of sociomathematical norms is a lot to take in.
Part 2 of this series, which is Episode 9, continues our conversation about moves parents and educators need to take at the beginning of the school year to set the stage for Kids Math Talk all year long. I’ll see you there.
Episode Sources:
Huinker, D., & Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices in K-grade 5. National Council of Teachers of Mathematics.
Martin, N. (2020, July 15). Keep it simple. Discard what's nonessential. Spark joy. MIT and Harvard researchers recommend strategies for teaching this fall - The Boston Globe. Retrieved July 26, 2020, from https://www.bostonglobe.com/2020/07/15/metro/call-teacher-button-marie-kondo-ing-curriculum-harvard-mit-propose-ideas-better-remote-learning-amid-coronavirus/
Stephan M. (2014) Sociomathematical Norms in Mathematics Education. In: Lerman S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht.
Yackel, E., & Cobb, P. (1996). Sociomathematical norm, argumentation, and autonomy in mathematics, Journal for Research in Mathematics Education, 27(4), 458-477.
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