Student Engagement Strategies and Visual Thinking Routines are great ways to create a Ripple (getting all students thoughts heard)! Using these strategies can provide opportunities for students to think and talk about mathematics! As we model student engagement strategies and visual thinking routines during our sessions, we will add those strategies to this list. Additional strategies can be found on the Secondary Teaching Strategies website.
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Chalkboard (or Whiteboard) Splash
All students write or draw their reflection on the chalkboard, whiteboard, or poster. After all students have responded, debrief by asking students to find similarities, differences, and surprises. (Note: this is very similar to Jot Thoughts.)
Chalk Talk
Questions or prompts are written on the board or large sticky paper around the room. Students rotate in groups to the various prompts and write their thoughts, prior knowledge, or questions about the prompt without talking. As students rotate and others have already written a response, they can respond to or emphasize the ideas of others. We modeled Chalk Talk when we reviewed the 8 Mathematical Habits of Mind during the Engagement & Collaborative Groups session.
Confer, Compare, Clarify
Place students in pairs. In pairs, students confer (share one sentence summary of what they believe is the most important concept of the lesson), compare (reading each other’s notes and “borrow” ideas to improve their own), and clarify (record any questions they have). Students can then be regrouped into groups of four to discuss their clarify questions with others. We modeled a similar strategy when we had you develop your definition for "rigor", compare it to group members, and then revise your definition.
Converstation Starters/ Sentence Starters
Teacher posts sentence starters for students to use if they have difficulty working collaboratively. Sentence starters also model appropriate conversation for academic group work. Sample Math Talk Sentence Starters can be found here. We modeled this strategy by projecting the Math Talk Sentence Starters while groups analyzed the brainstorms of others following a Jot Thoughts activity.
Convince Yourself, a Friend, a Skeptic
Students think about an argument for three different audiences. They first justify the argument in a way that makes sense to them, then they explain their argument to a classmate. For their third audience, students explain why they know their argument is true for someone who disagrees with them.
Critique, Correct, & Clarify
The teacher presents a partial or flawed argument, explanation or solution and has students critique, correct, and clarify the argument. Students begin by individually critiquing the argument, then work in pairs or groups of three to refine their response.
Example and Non-Example
Given a concept, students write (student created) or sort (teacher provided) various examples and non-examples.
Expert Testimony
(I made up this strategy name, but it probably goes by many other names.)
Teacher moves throughout the room and actively listens while students work in pairs or small groups. Teacher makes note of student understandings or misunderstandings and preps specific students to share key points of their conversation with the whole group during the share out, thus creating "experts". We modeled a this strategy each time groups were asked to discuss ideas or work collaboratively.
Find Someone Who
Students mix about the room finding others who help them learn content or to students who have certain characteristics.
Graphic Organizers
Teacher-generated organizers used to scaffold to support student learning and help students make connections. We modeled this strategy frequently during math tasks, video clips, and reading activities.
Inside-Outside Circles
In concentric circles, students rotate to face new partners and then answer or discuss teacher questions.
Jigsaw
Students become an expert on certain topics, and teach the information to classmates in order to learn a great deal of information in a short amount of time. We modeled this strategy when we had each group become an expert on one of the Five Principles for Effective Questioning and then share that principle with the whole group.
Jot Thoughts
Students brainstorm in teams, each teammate simultaneously writes ideas, with each idea on a separate slip of paper or sticky note. When time’s up, the team processes their brainstormed ideas. We modeled Jot Thoughts when we brainstormed "What happens in elementary, middle, and high school math classes." during the Rigor session.
Mix-Pair-Share
The class "mixes" until the teacher calls "pair". Students find a new partner to discuss the teacher's question.
My Favorite No
The teacher provides a prompt and students write a response. The teacher collects the responses and quickly sorts them. The teacher then selects his/her favorite wrong answer and shares it with the class to critique, provide feedback, and identify mistakes. A video explanation of this strategy can be found here.
Notice & Wonder
This is a sense-making routine that can allow all students the opportunity to feel comfortable engaging. Students are presented with an image or situation and are asked to share what they notice and wonder about both math and non-math related aspects. Students should be encouraged to share verbally while teachers make a list of responses.
Numbered Heads Together
Students are placed in groups and count off. Members of the group work together to agree on an answer. The reacher randomly selects one number. The student with that number answers for the group. We shared this strategy during the Student Engagement & Collaborative Groups session as a possible solution to engaging all group members.
Numberless Word Problems
Students are presented with a scenario or problem situation that suggests operations, but with no numbers. For example, "Some dogs are in the park. Some dogs come into the park then some dogs leave the park." Students are asked to make sense of what is being described in the situation and explain which operations it could represent. Without numbers, the students are able to develop a better understanding of the underlying structure of the problem itself.
One Marker
Collabortive groups are given only one marker per team to record their work. Team members are expected to rotate use of the marker. Alternative: every group member has a different color marker; all colors must be present in final display, but only one person may write at a time. We did not model this strategy, but discussed it during the Student Engagement & Collaborative Groups session as a possible solution to engaging all group members.
Pairs Compare
Pairs list multiple responses to a question and then compare their answers with another pair to create additional solutions. We modeled this strategy during the Student Engagement & Collaborative Groups session when we had groups of 2-3 list the pros and cons of various grouping strategies and then compare to another groups assigned the same topic.
Processing Cards
Students place cards on desk to notify teacher of their readiness (“Still Thinking”, “Ready to Share”). Can be used individually or in groups. We modeled this strategy during the Productive Struggle session. We asked groups to use the processing cards to indicate whether their group was ready to share or still working.
Quiz-Quiz-Trade
Using question cards, students quiz a partner, get quizzed by a partner, and then trade cards to repeat the process with a new partner.
Question Stems
Teachers and students can use question stems to vary question complexity. Example question stems using Bloom's Taxonomy can be found here.
Response Cards
The teacher shares a true/false statement or multiple choice question with the class. The students then hold up a card indicating their answer. Scanning the cards informs the teachers about the students’ thinking. The teacher can purposefully select students with the correct or incorrect answer to discuss their thinking. A template for True/False response cards can be found here. A template for Multiple Choice response cards can be found here. We modeled this strategy during the Questioning session by asking participants to share whether they thought statements were true or false.
Round Robin (Group) or Rally Robin (Pairs)
In teams, students take turns responding orally to a prompt. Teachers can choose to have student write each response on their own paper.
Roundtable
In teams, students each write a response on their own paper. Students then pass their papers clockwise so each teammate can add to the prior responses.
Same but Different
This is a sense-making routine that can allow all students the opportunity to feel comfortable engaging. Students are presented with two or more images or situations and are asked to share how they are similar or different, both mathematically and non-math related. Students should be encouraged to share verbally while teachers make a list of responses.
Send a Spy
While students are working in collaborative groups, allow one group member to eavesdrop on another group. We modeled this strategy during the Student Engagement & Collaborative Groups session by allowing struggling teams to eavesdrop on other teams (specific instructions on what to listen for/ask about were given).
Sometimes, Always, Never
The teacher presents a mathematical statement that students analyze to decide if it is always, sometimes, or never true. This strategy can be used as formative assessment to determine students' level of understanding and can be followed by requiring student justification of their thinking.
Stand Up-Hand Up-Pair Up
Students stand up, put their hand in the air, and quickly find a partner closest to them them who is not a teammate. Students share information with their new partner.
Summary Bar Graph
After students have completed the Biggest A-Ha or a One Word Summary, have students bring them to an area on a wall to create a bar graph with similar responses.We modeled this strategy during the Engagement & Collaborative Groups session by asking participants to justify opinions and graph their similar options on a wall bar graph.
Stronger & Clearer Each Time
Students work individually and then listen to the ideas of other class members. After gathering ideas from 2-3 classmates, students revise their original work. We modeled this strategy when we had you develop your definition for "rigor", hear the definitions written by group members, and then revise your definition.
Talking Chips
During a discussion, team mates place their chip or card in the center each time they talk. They cannot talk again until all team members have placed a chip.
Timed-Pair-Share
In pairs, students share with a partner for a predetermined time while the partner listens. Then the partners switch roles.
Think-Pair-Share
Students reflect individually to a prompt, turn to an assigned partner to discuss the prompt, and then the pair shares with a larger group or the whole class. We modeled this strategy frequently by asking participants to consider a prompt or task individually, then discuss it with a partner or group,and then share to the whole group.
Triangle, Circle, Square
Students write down new points that were made in the discussion (triangle), things still going around in their head (circle), and some that squared/agreed with their thinking (square). We modeled this strategy in our online session reflections following each session.
Vertical Surfaces
The teacher provides vertical spaces for groups of students to work collaboratively on a problem or task. Vertical surfaces provide less anonimity than sitting, errors can be quickly erased (less risk), the work is visible to all group members, work is visible to other groups, and the work is visible to the teacher for quick formative assessment. We used vertical surfaces frequently and shared our favorite non-permanent vertical option: Wipebooks.
Which One Doesn't Belong?
This is a sense-making routine that can allow all students the opportunity to feel comfortable engaging. Students are presented with four images, quantities, or numbers and asked to consider which one doesn't belong. An ideal WODB problem would allow for any of the four options to be a "correct" answer. Students are encouraged to justify many different ways to identy the one that doesn't belong. The website wodb.ca is a great source for sample problems.
Whip Around
Teacher poses a question and asks students to write at least 3 key points. Teacher then either randomly or sequentially calls on one student at a time to share one new item on his/her list. We modeled this strategy during our Rich Math Task session when each group or member of the group was asked to share a characteristic of a rich math task.
Wows and Wonders (sometimes called Biggest A-Ha!)
At the end of the lesson, students write down their biggest “A-Ha” on a sticky note or note card. Similarly, students may be asked to create and “IQ” card where they write down one insight (I) from the lesson and one question (Q) from the lesson. We prefer to identify "Wows" (things they learned) and "Wonders" (things they have questions about). We modeled this strategy during our Questioning session while asking participants to share their experiences facilitating their first task. We have also included a section for Wows and Wonders on the Task Checklist.
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