Increasing Student Participation

Student discussion and input can greatly impact learning in a positive way. The issue is that there are always students who are more vocal and have higher status. A few student will throw their hand up every time a question is asked to the class. Meanwhile, there are students who are constantly concerned that their question or answer is wrong. A major question we have to answer is: How do we get all our students to provide their input?

The article I read, “Increasing Student Participation” from The Teaching Center, which is part of the University of Washington in St. Louis. The article gave several ideas, but the ones I found noteworthy, along with some of my own ideas, are the following:

  • Set up ideal physical setup for discussion
  • Set expectations
  • Establish environment of caring and respect
  • Have class schedule set up for time for discussion
  • Respond positively to student ideas

Set Up Ideal Physical Set-Up

According to the article, there are many things that a teacher can do for the class to prepare them to participate in discussions. One thing is just the way the classroom is set up. The article suggests creating a U shape with the desks, which helps, since the students are facing each other and not just the teacher.

Set Expectations

Also, set expectations for how much each student should participate. If the intent is to have every student contribute, let them know that every one of them has to contribute. One option is to have participation be part of the grade, but if we do our job as educators, getting students to contribute to a discussion should not have to be something that we have to force them to do, but eventually something that they will do on their own with our support.

Establish Environment of Caring and Respect

One idea that the article did not address but I’d like to is establishing an environment of respect and caring. If we as teachers make it clear that every student’s input is valued, no matter their status in the class, then students will respect what other students are saying and not degrade them for it. As a result, students will not be afraid to speak their minds as much as they would otherwise.

Have Class Schedule Set Up for Time for Discussion

One way to promote discussion in a classroom is by allowing plenty of time for it in the proper way. If a teacher only asks for questions and students’ thoughts at the end of a lecture, they may not remember what they thought throughout the lecture. On the other hand, if a teacher stops after every fifteen minutes of a lesson and asks a question to the students and asks for their questions and comments, the students may better remember what they just learned. Also, asking a question and taking responses immediately is not always the most effective way for students to formulate ideas and give a response. Giving students 10-15 seconds to think allows everyone to come up with an idea before anyone else responds. Mixing up discussion methods can make it so every student can give a response. Moving from partner groups to small groups to large groups to a whole class discussion can make it so every student feels comfortable sharing at some level.

Respond Positively to Student Ideas

For students that lack confidence, pointing out their good ideas is very important. Even if their answer is not totally correct, pointing out what is correct or paraphrasing so it is correct can give them a confidence boost and think of their response as valuable. As stated in the last section, having students submit responses online or in some other private way and responding positively to that will give them the confidence to participate more in partner groups, where positive feedback will give them the confidence to participate in small groups, and so on.

The article “Increasing Student Participation” gave some intriguing ideas for how to get more students involved in discussions. I think that this is a very important subject to bring up, because all through my education, there were always people who would contribute every day and people that wouldn’t contribute at all. Sharing ideas can be a great learning experience for everyone. Hopefully we can use these ideas to have all our students contribute in meaningful ways.

http://teachingcenter.wustl.edu/resources/teaching-methods/participation/increasing-student-participation/

What are some best practices for teaching high school mathematics?

By Kevin Reins

This week I read the responses of a two part series in Ed Week by Larry Ferlazzo. The question of the week was, “What are some best practices for teaching high school mathematics?” This intrigued me as I was preparing the 18th revision of my secondary mathematics methods course here at USD.

“…there are a zillion different instructional strategies and practices that math teachers can use in high school.”

The focus of part 1 was on these ‘instructional strategies and practices,’

  • teach to big ideas (see image above), it allows students to have interconnected schema
  • focus on the processes and connections between different processes
  • use instructional routines (see Why instructional routines?)
  • keep a record of conversations when you orchestrate full group discussions
  • be selective and cautious in your use of technology
  • incorporate high leverage long-term strategies
    • -David Wees
  • embrace mistakes, normalizing mistakes, safe space for discussion and correction, utilize error analysis
  • formal error analysis through test corrections
    • -Jillian Henry
  •  provide relevance and contexts for the mathematics
  • engage students in a variety of practices and strategies
  • provide scaffolds for those who need the extra support when working with challenging content
  • plan intentionally and deliberately so your instruction is impactful, consistent, and effective
  • develop a community of learners where group participation and interaction is expected
  • employ student-centered teaching and learning
  • provide opportunities for students to develop and strengthen their skills of mathematical communication (including vocabulary)
  • make the development of a variety of problem-solving techniques a priority
  • eliminate the blank paper; require students to write (1) determine a strategy that could be used to solve the problem, (2) write a question that you have about the problem, (3) record everything you know about the content related to the problem.
  • develop their ability to ask good questions during problem solving phases, Entry (getting started), Moving (when stuck), Reflection (thinking about thinking), and Extension (deeper thinking).
  • utilize graphic organizers to help them employ processes independently
    • -Tammy Jones & Leslie Texas
  •  What works at elementary or middle level works for high school
  • pose interesting problems or set the stage for students to pose interesting questions/problems about the situation
  • encourage investigations, experiments, collaboration, and discourse as students explore problems
  • expect representations or models for the problems being investigated
  • engage students in discourse, creating mathematical arguments and critiquing the reasoning of others
  • proving their work with both formal and informal proofs 
    • Anne Collins

Part 2: Students must ‘engage in math problem-solving’ and not just ‘follow procedures.’

The acquisition of best practices for teaching high school mathematics is necessary for student academic success.

The focus of part 2 was on engaging students in problem-solving. The following was said by the experts interviewed,

  • you must have as your guiding philosophical principle the belief that all students can learn
  • you must provide opportunities for them to fall in love with learning
  • Standards for Mathematical Practices can serve as a guide for the ways students need to be engaged in mathematics
  • choose open-ended problems
  • focus more on the process rather than the correct answers
  • challenge them with mathematically rigorous tasks, choosing a Higher-Level Demand Task
  • learn how to anticipate student responses and misconceptions for tasks
  • ask students to find multiple strategies to the tasks you present
  • learn how to help students learn from mistakes
    • -Wendy Monroy, LA math coach
  • math learning should be developing conceptual understandings of the mathematics
  • focus on the conceptual relationships
  • create a synergy between the lower levels and higher levels of thinking through inquiry
  • create a social environment that promotes team work and collaboration
  • provide an open, secure environment that allows for mistakes as a part of the learning process
  •  use an inductive teaching approach (vs deductive)
  • reduce teacher talk time (increase productive mathematical discourse)
  • differentiate by content, product, and affect (Tomlinson)
  • use all types of assessment; visible thinking routines, “I use to think… Now I think…” (Harvard University’s Project Zero)
  • use a flexible fronts layout of the classroom which encourages more collaboration
    • -Jennifer Chang Wathall, educational consultant in concept-based mathematics/curriculum
  •  give challenging problems that build patience and persistence in their maturing problem solving skills
  • then spend ample time in joyful struggle
  • create rich mathematical dialogue that leaves the building
  • 12 challenging problems that 5 of which will appear on the final, and give them time in class to work on them (e.g., A point P, inside a square, was 3, 4, and 5 units away from three of the corners. Find the length of the side of the square.)
    • -Sunil Singh, author of Pi of Life: The Hidden Happiness of Mathematics
  • sufficient time to make sure that students know how to solve problems using different methods
  • look for opportunities for students to have multiple entry points or strategies for solving a problem
  • take time to discuss strategic choices
  • find flaws in short cuts and when certain methods won’t work
  • open their mind to new and different approaches
    • -Matthew Beyranevand, author of Teach Math Like This, Not Like That: Four Critical Areas to Improve Student Learning.

So after bolding all of the big ideas of the laundry list of instructional strategies and practices that were provided I compared it to the content that I normally would teach in my secondary mathematics methods course. The result was two ideas, one new, and one that could use a deeper focus. I would like to incorporate more ideas on how to utilize math mistakes in the classroom as learning opportunities. I also would like to explore instructional routines a bit more.

To think more deeply about embracing mistakes, normalizing mistakes, and creating a safe space for discussion and correction, I think it is important to start off knowing what some common math mistakes in high school are. I found Math Mistakes website that does just that. This should be a good start for a discussion on how to utilize some of these mistakes when they pop up as a learning opportunity.

With respect to instructional routines, I read Why instructional routines? It turns out I know what they are and how one should utilize tasks in teaching. One instructional routine that David Wees talks about is, Contemplate then Calculate, as a tool for learning how to use the 5 Practices for Orchestrating Productive Mathematical Discussions. The high level goals of Contemplate then Calculate are to support students in surfacing and naming mathematical structure, more broadly in pausing to think about the mathematics present in a task before attempting a solution strategy, and even more broadly in learning from other students’ different strategies for solving the same problem.

“Instructional [routines] are tasks enacted in classrooms that structure the relationship between the teacher and the students around content in ways that consistently maintain high expectations of student learning while adapting to the contingencies of particular instructional interactions.” Kazemi, E., Franke, M., & Lampert, M. (2009)

I’m looking forward to expanding my teaching and learning opportunities to include both instructional routines and normalizing mistakes.