Review foundational knowledge about Online Interaction in K-12 Blended Teaching (Volume 1).
Math classrooms can thrive on interactions with and between students. Both in-person and online interactions and feedback provide students with ways to share and support their insights, give and receive feedback, and present both written and oral opinions and positions on math inference in a polite and evidence-based manner.
In math, it's important for students to express their ideas using correct terminology and vocabulary. They don't get an opportunity to do that very much. When it's spoken, we tend to let them get away with saying things incorrectly or we correct it for them. But when it's written and it's permanent and you can see it, they tend to edit more. They think, “I'm writing this, I'd better make sure it sounds good and I'm using the right words.” If you want to try something, a discussion board is a really good and easy place to start. Perhaps in the last 10 minutes of class, you ask students to answer a discussion and respond.
Reflection Questions: How can you use online discussions to enhance students' participation and interaction?
Manipulating, observing, exploring, measuring, calculating, analyzing, and inferencing are at the heart of math classes. Conversations around these activities can help students to build critical thinking skills, express themselves, listen and civilly respond, and revise their opinions or understanding when needed.
There are many technologies that support online discussions. Here are a few of them and how they can be used in math. (You might want to become proficient with one technology before branching out to another one. Don’t try too many at once.)
Just like in-person discussions and interactions, online interactions can become stale if they do not include variety and contrast, inviting students to think deeply and/or creatively.
Here are some ideas that are relevant to a math classroom. Note that some of these discussions start in the online space and end in person, some start in person and end online, and some may even bounce back and forth between the two modalities.
Online Discussion Ideas
|Introduce new concepts/theorems/formulas etc.
2. In a full class explanation (with video backup) explain the new concept.
3. In different stations, have objectives, pencil and paper, and graphs available for students to manipulate, draw, observe or compare.
4. Ask students how they visualized or organized their thinking. Ask if they had a preferred method for thinking through the new concepts.
5. Ask students to reflect on the important information/quantities/numbers in the problem?
6. Have students post videos of their manipulations and explain their rationale as a new response to their initial discussion board post.
1. In an online discussion have students write an equation or equations to represent a problem or situation requiring the new concept. What math tools or models do the students think can be used to solve the problem?
7. Let students review others' responses, and ask them, do your peers' equation/approach make sense to you? Is there another equation/approach available? Which model/approach is more efficient and effective to solve this problem—their initial attempt or their revised attempt?
1. In person review the concepts/theorems/formulas students just learned, and ask students if one value is changed in this problem, how this could affect the situation and solution?
2. Demonstrate to students either in person or online some other ways to solve the problem.
3. In an online discussion board, post a similar question to each group, and have students write their solution as the first post.
4. As a second post, have students review others' first responses, and have students consider responses such as the following: Does your peer's solution make sense to you? Do these different solutions express the same or different ideas? Explain any connections to your original post. Can such different solutions both be correct? If you think your peer's solution is wrong, why do you think this solution is wrong?
|Apply the concepts/theorems/formulas
|1. Review the concepts/theorems/formulas again and ask students to come up with a similar problem as they have solved previously.
2. Ask students to write their problem in a discussion board as the first post.
3. Assign students to solve another peer's problem within their group.
4. Have the student who provided the initial post grade their peer's solution. Was their peer's solution and process what they expected? If not, what was expected? If it was to be expected, were there any other ways to solve the problem?
|Observe, predict and summarize math patterns
2. In person have students meet in a group different than the one they will communicate with online to compare: What patterns they saw in the given set of data? What those patterns might tell them? Whether they think they can reasonably predict what additional data might suggest?
5. Let the students reply their peer's assessment and summarize by answering, is there a summary or shorthand way of expressing these recurring patterns?
1. Provide a data set online that is accessible to all students. After a few minutes of reviewing the data set give students a brief amount of time to record their initial impressions in an online discussion.
3. In the discussion board have students write their predictions. Did they get these by counting or calculating?
4. Review their peer's predictions and assess them by answering if they are correct in all cases? If yes, why do they always work? If not, why? And do you have a question for their peer group?
|Identify common mistakes
|4. In person, use the data gathered from looking at student responses in the online discussion to create small groups for review or facilitate a whole-class review of misconceptions or problematic misunderstandings.
1. Show students some problems that commonly have mistakes or that can be solved in a better way than what students commonly attempt.
2. In the online interaction, have students identify the mistakes in the problems or brainstorm better methods.
3. Ask students to respond to their peers' ideas relating them to their own.
The Big List of Class Discussion Strategies, compiled by Jennifer Gonzalez, is a longer list of ideas that could be adapted for online mathematical interactions, including Socratic seminars, gallery walks, affinity mapping, etc.
I really love having students discuss an idea online. They make a conjecture and then respond to other people. It's like, “Oh, I didn't think of that.” or, “I don't agree with you because of this.” and then they're arguing, but in a constructive way in the discussions. It's really great to read because some of them were right on and some of them were almost there and some of them weren't there at all. Then other students will tell them, and say, "oh yeah, you're right because if I do this..." They're exploring and testing each other's theories until they come to a consensus.
One of the features I really like in the math learning tool Desmos is that it will show students others' answers because students always want that validation, such as "Was I right?" " Am I thinking what others are thinking?" " Am I the only one thinking this?"
In your Blended Teaching Workbook create an online discussion for the lesson/content area that you are addressing with your problem of practice. How will you make it engaging for the students? How will you target your problem of practice?
If you haven't already opened and saved your workbook, you can access it here.
Not all online interaction has to take place in a discussion. It can take place in a shared Google Doc, in a real-time Zoom meeting, through blogs or social media, through visits to each other's websites, etc. Below are some examples of online interactions that do not require the use of the online discussion format.
One of the challenges is that some students don't like to talk. But when I give them an opportunity such as a discussion board, they wouldn't be quiet.
Another thing I love about blended teaching is that it opens up opportunity for student ownership. I can have the ones with higher ability help me and become tutors for kids who need support. And that makes review or tutoring more manageable for me.
Reflection Questions: Mrs. Stuart talks about three kinds of interactions. What are they and how could they benefit your classroom?
Interactions between students and the teacher are also important in a math class. Experienced blended teachers often report that their interactions with students online have strengthened relationships and contributed to student growth. Below are some ways that teachers can foster these interactions.
There are so many ways I can communicate with students online. With Canvas I can email students after a quiz to send a quick message to them. I have the option to email the students that have taken it and those that haven't. “Hey guys, you’ve got to get this taken by this time. If you need any help, reach out to me. I'm here for you.” When I communicate with students online they aren’t as afraid as when they are surrounded by peers in a classroom. There is more anonymity for them and it’s safer. My students think, “Oh, Mrs. Stuart is following me and cares!”
Discussions are nice because I can reply right away to a student when I see a misconception. I can read through each one and I can see, “Oh, this one's a little off. Think about this.” Or I can reply, “Yeah, great thinking!” Just being able to give that response to them individually has been really fun.
I've also utilized Canvas announcements. It's been really nice because some things have been math related and instructional but some have just been to connect with the students. I started doing Google forms and surveys asking things like, “What's your favorite activity?”
The students that I think the most about, and come to mind first, are those students that are blenders in the classroom. They're not the loud one or the misbehaving one. They’re the students that don't ever say anything and do their own things but wouldn't tell me if they didn't understand something, and I wouldn't necessarily notice because there are so many of them. But online, all of a sudden, everyone becomes equal. So then I can see when a student has a misperception that I can address, where I probably wouldn't have noticed before. Even if they're not reaching out to me, I can reach out and give them individual feedback.
I can think of several students where that's the case. They did something or said something or had some sort of misperception that I would not have noticed, otherwise. Sometimes someone used to do something for quite a while incorrectly, and I didn't notice. Or they have one little thing that's not correct, but if they fix that thing then everything else is fine, but they feel frustrated and stuck way back here when they're really not. It's easier to see evidence if that’s online.
The online space significantly increases opportunities for interaction between students and content, students and other students, and students and teachers. Students who never or rarely speak in class may find themselves suddenly communicating on a regular basis. The results of learning through a combination of content interactions, instructional interactions, and feedback can improve student outcomes, investment, and engagement with the subject matter. You don't have to start all at once. Just choose one interaction that looks promising to you—and begin.
This content is provided to you freely by BYU Open Learning Network.
Access it online or download it at https://open.byu.edu/k12blended_math/math_olint.