Building Mathematical Comprehension, Chapter 4

     Chapter 4 is about using the strategy of asking questions before, during, and after problem solving tasks. I thought an interesting point Sammons brings forth is encouraging questioning even when the questions do not have answers. It is more important to find the right question than the right answer.

     She applied the Question Answer Relationships to mathematics. 

• Right there questions can be answered using the textbook glossary, math word wall, or the word problem. Examples: What does sum mean? How many cookies were eaten? 
• Think and Search questions can be answered using schema or prior knowledge and the problem solving task. Examples: What situations do you use divisions in? What information do I need to solve the problem?
• On my own questions are answered using the student's knowledge. Examples: When do I use division in my life? What strategies can I use to solve this problem? 

     Sammons suggests introducing strategies in small group strategy sessions where teachers can explicitly teach and model by thinking aloud while using the questioning strategy. Then students are given the opportunity to apply and discuss the strategy while the teacher provides immediate feedback. It ends with the charge to apply the strategy to their mathematics work. She also suggests a mini lesson where students brainstorm generic questions stems to use when applying the questioning strategy before, during, and after problem solving. Then you can revisit the chart throughout the year and add to the questioning stems as students become proficient in the ones already posted. 

     Some tools that were suggested for use with the questioning strategy are as follows.

• Wonder Wall-Students write their questions before, during, and after problem solving on sticky notes and sign. Then they add it to the wonder wall. The teacher takes time to review and discuss the questions throughout the problem solving process. It helps to students to work through the problems and may inspire questions of their own. I am thinking about designating a space on one of my walls for this activity and incorporating it as part of our daily routine at the beginning of the school year at least until students become proficient. I use Brenda DeBorde's TEKSing Towards STAAR spiraled practice at the beginning of class. It consists of three different questions about three different concepts. I'll designate one of the problems for students to share their questions about. 
• Question Journal-Students are given a sheet with four columns-Question, Before, During, or After?, Predicted Answer, and Final Answer. It is a tool that gives teachers insight about the student's thinking throughout the problems solving process. I would introduce and practice this in class and then make this apart of their homework assignment as a way to monitor their thinking when they are working on their own. 
• Question Web-Students can use the question web two ways. The first way the a specific question is put in the middle of the web and students/class record possible answers around the web. Then once the final conclusion is reached, it is recorded at the bottom of the paper. They can also be used to generate questions about a mathematical concept such as fractions or multiplication. Students record the concept in the middle of the web and then record questions about the concept around the web. This can be done whole group with students recording their questions on stickies, signing their name, and place it around the web. 
• Math Stretches-Two math stretches are suggested. The first one is questions for understanding. Students  are given a concept and must brainstorm a question that will help other students understand the concept better. This one can be done as a whole class chart like question web, written on a sticky, signed, and then discussed as a class during the math huddle conversation. The second stretch is the what's the question stretch. Students are given a generic problem solving situation that does not have a question. Then they brainstorm a question, record it on the sticky, sign their name, and add it to the chart. Then the questions are discussed. Students should write a question that is not already on the chart. 

     Students should be taught to think about the questions that are helpful during the problem solving process. They gave an example of a graphic organizer that students could use to think through the questions and record their answers. The chapter ends with suggestions for using children's literature. On book that was suggested was Counting on Frank by Rod Clement. Frank is obsessed with measurement in his life. It was suggested that you could have the students brainstorm the questions that lead him to the measurement tasks he takes on in the story.