Math Talk Moves

Today in my internship I observed a math lesson, with the focus on multiplying double-digit numbers. The teacher decided ahead of time that she wanted to teach a specific strategy to the students to help them solve this otherwise,“daunting skill,” in a clean and efficient way. I will call this strategy, “Box multiplication,” for my own and your clarification/benefit. The strategy stems off of place value, which just happened to be a previously acquired skill the students had just succeeded with the week before. It requires students to break the double-digit numbers down into two values: the tens whole value and the ones whole value (i.e . 42 becomes 40 and 2). The multiplication sentence is then re-written around a box with one inner box for each value being multiplied.

Example:

This was a strategy that was unfamiliar to the students, therefore today's lesson was spent really breaking down the strategy and it’s steps, and allowingthe students to practice it’s implementation many times. The focus was less on mathematical thinking and more onthe doing. I found three forms of Talk Moves, as discussed by Chapin, to be demonstrated in the lesson: revoicing, prompting for further participation, and asking students to apply their own reasoning to someone else’s reasoning. The first form of Talk Move that was used by the teacher was revoicing. This form of restatement was used most frequently in the lesson. In this context, the teacher affirmed and organized what the student said by re-stating the response with an undertone of clarification. (i.e. “You told me this (pointing to number) was worth ninety.” – student affirmed) I felt this Talk Move was very effective within this lesson, as it resulted in students’ having to confirm and affirm what their answer was. It also provided a source of repetition which aides in retention of new concepts for the student being revoiced as well as their peers. Students demonstrated their responses with the use of whiteboards while verbally responding to the teacher’s questions. The teacher also involved prompting students to engage in further participation. This was demonstrated by asking the students to provide additional information to what their peer had just said (i.e. completing the next step and then asking if the student agreed or disagreed with the answer a peer provided). Through this Talk Move I saw two different outcomes. The students struggled with being able to expand on their peer’s answer, and were often caught off guard by the teacher’s prompt. I felt that this was a result of the students not following along or answering the teacher’s question for themselves when their peer was called on to provide a response. On the other hand, I felt including this Talk Move repeatedly helped keep the students engaged and attended to the multiplication problem, even when they were not the one called on to start it. The more the teacher includes this form of extension into their lessons the moreeffective it will be in fostering deeper mathematical thinking and discussion. The last Talk Move prevalent in this lesson was the teacher’s attempts to get the students to apply their own reasoning to someone else’s reasoning. A great demonstration of this Talk Move was seen at the beginning of the lesson when a student was asked to explain why there were only two boxes used when setting up a two digit multiplied by a one digit math fact. The teacher then asked another student to use what his peer had just said to figure out how many boxesthey will need for math sentences with two digit numbers multiplied by another two digit number. This Talk Move was very successful within this context, and resulted in a class vote requiring students to agree or disagree with their peer’s reasoning. This required students to not only process the reasoning their peer presented, but also determine if they felt that reasoning to be true or not. Higher-level thinking was definitely occurring during this moment!

Upon reflection of this lesson I felt that while this specific learning opportunity had a lot of positive outcomes, there werealso some connections and thinking that could have really been enhanced by additional Talk Moves and questioning. Throughout the lesson I took note of a lot of, “What,” questionsbeing addressed to the student. These types of convergent questions only require one type of response, and the teacher is asking them to gain a specific correct answer. I thought through the use of more divergent questioning, students would engage in deeper mathematical thinking and solidify the strategy they were learning. Answering what 60 X 3 is requires a simpler type of thinking versus explaining why when the problemsays 65 X 3 we use 60 as a factor yet still multiply it by 3. When a student adds an extra zero or one to the end of their answer, instead of telling them that it is incorrect, I would ask them why they chose to add that zero, and clarify their reasoning so they may better understand the path they took resulting in the error. Having the students talk about their thinking out loud aides in retention and often helps the student self-correct and monitor where the error occurred. The teacher could really utilize restating and revoicing when having students explain their steps and reasoning for errors. Hearing their response or reasoning in a different way (by the teacher or peer) may help the student better understand what they were trying to express OR help them acknowledge errors and move in the direction of correcting them. Thislesson could really be transformed into an opportunity for students to, “talk out,” the multiplication problems they encounter. Hearing their own ideas expanded on through the words of someone else may present different ways to think about a problem, helping them solve a similar problem later faster and more efficiently! An additional activity could be for students to share their work and steps taken to solve the problems with a partner. This would be done after they solved the problem on their whiteboards (as what was done in today’s lesson). Once again, saying the steps out loud and explaining their work to someone else will ideally foster deeper retention and understanding of the strategy. Often these forms of interactions and discussions need to be formally or informally facilitated by the teacher, especially in math where there is a history of silent solving and written expression. Wait time would be a valuable component to include with these open-ended questions and discussion. Students require time to thinkthrough what they did, what they encountered and to be able to express what was written verbally. Often students feel rushed to answer a question quickly when in front of their peers. This pressure may result in error, leaving the student feeling more confused than before. Giving the students sufficient time allows them to dive in to their working memory and bring to the surface ideas and perspective used while solving the problem. I feel my CT already does an incredible job giving the students plenty of time to gather their thoughts and express themselves. Including some of TalkMoves and questioning prompts I discussed above would really compliment my CT’s already positive and interactive style in the classroom.

All our students can be math wizards when engaged in higher-level mathematical thinking!

Students are asked to put on their thinking caps when restating or re voicing their peer's responses and reasoning. WARNING: This may cause shock and astonishment when done for the first time!