**Make teaching more efficient and effective by using whole class discussions to meet diverse learners.**

Three Levels of Sense Making by Teruni Lamberg, Ph.D.

**What is a Whole Class Discussion?**

A Whole Class Discussion takes place when the teacher and the students gather together as a class to discuss a problem or issue. As a result, they make new mathematical connections.

An Example:

Several students conclude that the answer always comes after the equal sign. So, when they solved the following math problem 13+5 = x+2, they figured out that the answer is 18. However, some students figured out that x is 16. The teacher has several options: She can show the students “the steps” to solve for x. She could point out who is “right” or “wrong.” By doing so, the students might learn the procedure for solving for “x.” However, they may not understand what they are doing. Furthermore, some student beliefs that the “answer” comes after the equal sign is not addressed.

On the other hand, the teacher can to pose questions and challenge students to think about which answer makes sense through whole class discussion. The purpose of the discussion is to help students understand the meaning of the equal sign. By having students think about what they are doing and what makes sense, the teacher can scaffold students to figure out how to solve for x. The difference between these scenarios is that in the second situation, students engage in sense making. Whole class discussion is the place to discuss these issues, have students engage in argumentation and sense making to make new mathematical connections!

**Implications for teaching**

The Common Core Standards of Mathematical of Mathematical Practice 3 : Construct viable arguments and critique the reasoning of others.

According to this standard, mathematically proficient students are able to communicate their ideas to others by using concrete representations. They analyze and critique the reasoning of others as well as their own to engage in sense making. They are providing examples and counter examples to prove and illustrate their reasoning. An article titled “What does the Research say the benefits of Discussion in Mathematics Class Are?” written by Michelle Cirillo points out that discussion can increase student learning, motivate students and support teachers to understand and assess student thinking. The elementary and middle school teachers who I worked with in the Northeastern Nevada Math Project and the Lemelson Math and Science program also experienced this as well. Student achievement scores went up (e.g MAP testing). In addition, they reported an increase in student motivation as well as their own motivation to teach.

I interviewed fifth grade students (other students as well) and asked them how communication helps them learn math (see video clip 1.1 PDToolkit in Whole Class Mathematics Discussions). They made some interesting observations. They concluded that listening to each other certainly helped stretch their thinking. Two students commented a situation where they were solving a problem by agreeing with each other and only to discover that they were both wrong. (They giggled as they shared this story!) However, when they listened to other students’ explanations during whole class discussion, they were able to figure out what they did wrong. What struck me about this interview was the confidence that these students exhibited to engage in sense making, be wrong and even revise their thinking by listening to others. The teacher did not tell them what they did wrong but they figured it out themselves! Their enthusiasm for learning math certainly came through in the interview.

Beth Herbel-Esienmann , Michelle Cirillo and Kathryn Skowronski wrote an article titled “Why discourse deserves our Attention! ( Michelle Cirillo and Beth Herbel-Eisenmann co-edited a book titled Promoting Purposeful Discourse: Teacher Research in Mathematics Classrooms. (This book is based on their work in Secondary classrooms.)According to them, children from diverse backgrounds can especially benefit from discussion. Students learn math through their natural spoken language. Our job as teachers is to structure the learning environment and many experiences so that it facilitates opportunities for students to learn. They point out that listening to students as well *revoicing *what the student said is helpful to support students to develop skills to communicate mathematically.

**Designing a Classroom Environment to Optimize Discussion**

*Physical Space*

Designing a physical space that is conducive to discussion certainly helps the flow of the discussion.

The whole class discussion book (Chapter 2) provides some concrete ideas on how to build a classroom environment to support discussion. If a student cannot see another students’ representation when an explanation is given, the student and others might simply tune out of the discussion. Furthermore, it interrupts the flow of the discussion.

*Classroom Routines*

Building Classroom routines is the best way to get students used to talking (See chapter 3 of Whole Class discussion book). This includes routines for listening, sharing and critiquing their ideas. Building classroom routines takes time. Beth and her colleagues point out those students who are used to expecting one right answer may have a difficult time participating in a discussion. Building classroom routines and a classroom culture takes time. Consistent expectations are important for effective classroom routines to develop.

*Teachers’ Role*

The teacher plays a critical role in facilitating the discussion. Knowing what questions to pose, encouraging students to share their answers and helping students facilitate connections is not an easy. The whole Class discussion book (chapter 5) provides a framework to ask questions that build on each others’ thinking to facilitate deeper connections. This chapter discusses three levels of sense making and questions a teacher can ask. Margaret Smith and Mary Kay Stein in their book 5 Practices for Orchestrating Productive Mathematics Discussions point out the importance of *Selecting* what ideas and *Sequencing* which students will present in what order is important for helping make mathematical connections.

*Lesson Planning*

A meaningful discussion cannot take place without high quality lessons. Furthermore, having one good lesson is not good enough. Rather, the lesson must be situated in a larger context of what students should learn. Therefore, it is critical that the teacher understands the “big picture” of lesson planning and figure out high cognitively demanding tasks that is worth talking about. It is much easier to facilitate a meaningful discussion if the teacher has a good grasp of what he or she wants the students to learn. This is helpful when analyzing student work, and thinking to make decisions. Lesson planning involves as three levels. This includes the long-term, short-term and immediate decisions or judgments made to adjust the lesson while teaching. Assessing student learning and building it into the plans is important for support student learning. Lesson planning and Assessment are reflexively related.

*Structuring Instruction Time to Include Discussions*

Using instruction time effectively matters. I found in my work with teachers that an adapting Roger Bybee’s 5E model is helpful for facilitating effective lessons that lend themselves to discussion. (See chapter 4 of Whole Class discussions.)

Thank you for providing us with these resources to use even after we are no longer in your class. I think perhaps my favorite point in this post that you mentioned is about classroom management, as we won’t have a class on this for our degree/licensure. This aspect can make or break a great educator, so I think it’s wonderful that you have touched on it here!