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!

Stepping into Teaching...A Classroom Worth Sharing

Inside the strong brick walls of this local school paints a simplistic picture of white hallways, old carpet, and a modest display of student work and, “Beginning of school,” displays. The hallways seem to go on forever, yet around each turn are classrooms full of new beginnings and tomorrow’s success. I see faces of diversity filling the seats while teachers, whose faces seem all too familiar to me, fill their minds with knowledge. The Resource room I am in this semester, is a classroom that separates students from their peers during reading, writing, and math, while also keeping the students connected, being just a few doors down from their general education classrooms. It is classroom that I see students excited to come to; and it is a classroom that focuses on instruction and learning rather than the flashiness of bulletin boards, themes, and posters. This pullout classroom has to be more. More than what the students can get in their general education rooms, and more instruction that can close the learning gap our students come in to these hallways with.

I have been in my internship going into the third week, and I can already see the struggles the students have in math. Math instruction is at the end of the day, and this reality in it’s own comes with elements the students must overcome (exhaustion, anxiousness, annoyance, etc.). This combined with innate difficulties towards mathematics makes for a long hour and fifteen minutes! The teacher tries to keep spirits up by reminding students of their number one job while in the classroom: to try! This message was written on the board after a pre-test that left two students in tears, a handful of empty test papers, and students giving up before they even get started on the lesson. This message has been up ever since, and it is a reference point that is used throughout all subjects and activities. I admire my teacher’s message, and will work hard to use it this semester in my lessons as well as in my own classes!

These, “Texas Math,” books are displayed proudly behind my teacher’s desk. They were intimidating at first sight, but after looking through the twenty plus books, supplemental materials, assessments, and games, I realized that this math curriculum being used offers many of the elements we are taught to include in our instruction of children with disabilities and differences. Differentiation is a big part of each lesson in this collection, as well as adaptations for students with language differences. My teacher has adapted the material itself, and only uses what works for her students. For example, after the negative experience most of the students had with the first pre-test given, she decided that she would no longer give a formal pre-test and only assess the students prior knowledge through informal observations during the lesson. Each lesson begins with a review of key concepts and skills that the students need, and she adjusts her instruction according to the students’ success or limitations during this time. This was an excellent example of making the curriculum work for a group of students. It was refreshing to see this first hand, and I am also looking forward to seeing how it continues to work throughout the semester.

In addition to the worksheets and activities presented in the curriculum being used, the students are given opportunities to explore mathematics using manipulatives. These are on an open shelf and are located in a kid-friendly area, which encourages the students to take advantage of them whenever they need. Inquiry-based activities are designed to use these manipulatives, and I enjoyed seeing students use them and include them in their strategies. From observing the students using these colorful cubes and squares, I also saw how their use prompted discussion as well as facilitate, “Ah Hah,” moments from the teacher and students. I would really like to see them used more consistently during the students’ warm-up activities, which I think would be a great opportunity for the students to explore and respond to word problems and other skills using ONLY the manipulatives. I think that would be getting the students to think on a different level than worksheets and other pencil activities do. I am wondering what other types of manipulatives can be used and applied to skills in math that are not computational and problem solving. I would be interested to explore those options more.

Vocabulary is very important to this Resource teacher! She does vocabulary warm-ups every day, which include a fun cheer or basketball dribbling of the words being used during the unit. I feel this is incredibly important for students with learning disabilities, as vocabulary can really strengthen your understanding of math. A student does not need to worry about knowing what the word problem or directions are asking, just how and why they are going to solve it. These vocabulary cards are included in the Texas Math curriculum she uses and when I saw them I fell in love with them and knew I had to post them! On the front is the vocabulary word in English and in Spanish. On the back is a picture describing the word and it’s definition. If it is read or taped for the student their use is appealing to multiple senses, and will help the student store the new knowledge faster! Not to mention, with the diversity present in our schools in Texas, the pairing of pictures with the definitions differentiates for our students in an effective way! I have to admit that the idea of a vocabulary focus in math is a fairly new idea for me, but I am seeing how important it is, and I am excited to be equipped with an easy teaching strategy to help our students succeed.

Small group instruction is a big part of my teacher’s resource room, and she utilizes this area of the classroom to provide scaffolding to students who are struggling. She identifies these students at the end of the lesson, and while the rest of the students move on to independent work, she pulls a few students to this table and provides additional instruction until she feels they are ready to be independent. This is an excellent example of flexibility and progress monitoring, both of which are critical elements of math instruction. With the use of paraprofessionals, and her trusty student intern, she is allowed this flexibility and can easily give students the attention they need. Within small group instruction the use of white boards are used to help the student demonstrate their work quickly, and provides the teacher with a fast and efficient way to check their work. It is easy for mistakes to be corrected, and they can make a quick visual organizer for the student to take back to their seats with them. The students love using white boards, and I like how it provides them a break from the standard paper and worksheets they are used to. White boards can be also be used during lectures for the students to copy down the teacher’s examples and follow along with. A place value lesson I observed really came alive using the white boards!

My teacher believes in celebrating the students’ victories, both big and small. She has a section on the wall where students can draw pictures of any type of victory they had recently and display it for everyone to celebrate. I really appreciate this vision because it not only makes the students acknowledge that victories come in all different shapes and sizes, but it also gives the students, who may not be used to having their work displayed on classroom walls, the opportunity to be proud of something for everyone to see. As I already told her, I plan on stealing this idea and applying it in whatever position I take on as a future educator.

Response to Reading Week 1

1. It gives the students the opportunity to use what they already know and how they learn well to solve the problem themselves. It also teaches them strategies (that they developed themselves) to use in the future.

2. I feel that my experiences with Math will make me a stronger and more effective teacher for my students. I can take the good and the bad experiences I had to facilitate an environment that will either encourage my students to have similar experiences or prevent them from having hard ones.

3. Time spent letting the kids discover and explore their knowledge will lead to more retention and require less repeated instruction in the future. While it is important to teach certain concepts explicitly, students will more likely retain basic facts and operations if learned in way that is meaningful to them (not being talked at). If we give our students the tools and strategies to continue to grow as a learner we are setting them up to be successful students and people.

4. It is not a good idea to ever tell a student something is, "easy." We also do not want to be too quick to jump in and give them too much information that prevents them from solving the problem on their own. A better way is ask them questions that will lead to their own discovery of the answer. These questions may help them organize their thoughts and give them the push they needed to solve the problem.

5. The article tasks focused on activating the students prior knowledge and utilizing their strengths (what they did know) to solve the word problems. The tasks also forced the students to make sense of the problems before solving them. In the marbles problem, the teacher guided the student through the problem (without providing hints and prompts) by asking him questions that responded in answers that allowed him to make sense of what the problem was asking him. He did the work with strategies and ideas he already knew and were comfortable with.