*The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.*

*─*

*National Governors Association Center for Best Practices and*

Council of Chief State School Officers

Council of Chief State School Officers

These past few weeks I have had a chance to interact with hundreds of colleagues at our NCSM Regional Workshop in Chicago, to the NCTM Regional meeting that followed (you can download the pdf of that message here), to the Solution Tree CCSS Math Workshop in San Jose and on to many friends at our pre-Session for the

*Learning Forward*conference in Boston.
And there was a common theme throughout that was galvanized by a long time friend and colleague of mine from Stevenson HSD 125, Neal Roys. He asked me: "

*Do you think it is possible to meet the expectations of Instruction for the CCSS from the front of the Classroom?"*
Without blinking, I said NO. No, it is not.

And this is a tension for many teachers of mathematics Every one of us. We must re-think, how instruction is designed. At all grade levels K-16. Take a closer look at part of the quote from above:

*student practitioners of the discipline of mathematics***increasingly ought to engage with the subject matter**as they grow...

I am convinced that K-12 mathemtics teachers cannot effectively check for student understanding and actively engage students, from the front of the classroom. That Era is over.

As

*you focus deliberate attention to the CCSS Mathematical Practices, the challenge is to envision the tasks used, the questions asked in the classroom, and the discourse in which students participate in a way that advances students’ abilities to engage in the Mathematical Practices. And this best occurs during small group student discourse with formative checks for student understanding by you, the teacher - as you monitor the small group student discussions and work.*
This requires dollops and dollops of peer to peer communication.

Continuous opportunities for students to work together and do mathematics together.

As a starter, I am urging you to take a look at your time distribution in class. Is at least 65% of the time spent on peer to peer discussions and work and prompts from you, and less than 35% on leading from the front of the room - using whole group discourse one raised student hand at a time?

As a starter, I am urging you to take a look at your time distribution in class. Is at least 65% of the time spent on peer to peer discussions and work and prompts from you, and less than 35% on leading from the front of the room - using whole group discourse one raised student hand at a time?

The CCSS for Mathematics explicitly call for for
building conceptual understanding.

*Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. (p. 8)*

You
promote conceptual understanding when you explicitly make, or ask students to
make, connections among ideas, facts, and procedures (Hiebert and Grouws,
2007). My colleagues and I suggest the following actions help students’ make these connections:

1. Challenge students to think and to make sense of what they are doing to solve mathematics problems;

2. Pose questions that stimulate students’ thinking, asking them to justify their conclusions, strategies and procedures to one another;

3. Have students evaluate and explain the work of other students, and compare and contrast different solution methods for the same problem.

4. Ask students to represent the same ideas in multiple ways, e.g., symbolically, pictorially, or to demonstrate a concept using manipulatives.

(Use of multiple representations, Kanold, Briars, and Fennell, 2011, p. 28)

(Use of multiple representations, Kanold, Briars, and Fennell, 2011, p. 28)

**abandon the front of the classroom**(especially as students get older) and re-think how to check for

*student understanding*(now called formative assessment) as they engage students in meaningful discourse.

Is it still

*possible*to effectively engage students from the front of the classroom?**Yes, but it must be done with great skill.**In future blogs I will write about how to do so. I will also address how to effectively manage small group discourse in a way that is efficient for all grade levels.
For now though, if you are a reader of this blog, check yourself on the 65% rule. Where are the most significant conversations taking place in your room? If it is peer to peer, than you are on the CCSS path!

Mr. Kanold, I attended NCTM Chicago where you made the point about the 65-35 split in front of the room teaching time. I totally agree with your information here. My issue is that 50% or more of my students have very low motivation and claim to be "helpless" when it comes to math. Have them work in pairs or threes is often a real struggle since they often complain about not being able to start a problem. Any suggestions?? Places on the web or books where I can find ideas how to combat this?? Thanks for your awesome blog!!

ReplyDeleteJoe Pfalzer

I definitely agree that we need more peer to peer discussion. It has been an interesting year trying to get students to talk to each other about math; and more than this, to rely on each other for accurate information. At the beginning of the year, students were still waiting for me to “save them” at the end of what was supposed to be a question that the students answered amongst themselves. Or in the least, they were looking for confirmation that their work was accurate. For a while I did help them, but only as long as they took part in the discussion. Now I can read when they are ready and hand it off to the students without an angry response or a frustrated look that says, “I am shutting down.” Fortunately if I push them too hard and too fast they are very vocal about it and I keep leading until they feel they are ready to take the reins. I think that the block scheduling has helped me in this learning process. I still think I need a list of questions/replies ready in my hands as I walk around the room (For example when the students ask, “Is this correct?” I can respond with, “Why don’t you show me why you think it is correct.”). In the same way I would like to have a list ready for responses during whole group discourse (For example, when a student responds with an answer I could direct the response to another student and ask, “How do you think she/he got that answer?” and then to another student I could say, “So, do you think they are correct?”). That being said, this takes the students time to adjust to as well. I think as the years go by and the students become more accustomed to the CCSS that it will be an easier adjustment.

ReplyDeleteYes, and I am in agreement with your writing. I have my custom writing service login. Do you have your own? By the way, it is really impressive writing. Thanks and keep posting things like this.

ReplyDelete