vcoms.wildapricot.org · Web viewUnderstanding slope as a proportional relationship, a rate of change, and as a measure, degrees from the horizontal. Procedural fluency (computing)

Filling Your Mathematics Leadership Tool KitMarch 21, 2016

Southwest Higher Education Center

“Our goal is not to increase the amount of talk in our classrooms, but to increase the amount of high quality talk in our classrooms—

the productive mathematical talk.”

2009, Classroom Discussions: Using Math Talk to Help Students Learn

Framing Questions for this Session

How can purposeful questions move students to math talk that promotes reasoning and sense making for deep understanding?

What are the five mathematics talk moves that support more purposeful questioning? How can mathematics specialist and teacher leaders support teachers in being purposeful

in their questioning?

This outreach conferencefor mathematics specialist and teacher leaders is made possible with financial support from the Virginia Council of Mathematics Specialist, logistical support by Virginia Tech at the Southwest Center for Higher Education, and ongoing support from the Virginia Mathematics and Science Coalition.

1 | Compiled by Vickie Inge for the VACMS 2015

Session 2A: 1:00 – 3:00 P.M.

Teaching for Understanding: Discourse and Purposeful Questioning

Vickie Inge [email protected] Lambert [email protected]

mailto:[email protected]

mailto:[email protected]

Strands of Mathematical Proficiency for LearningThe five strands provide a framework for discussing the knowledge, skills, abilities, and beliefs that constitute mathematical proficiency. The five strands are interconnected and must all work together for students to be mathematically proficient. Teaching practices must reflect these interrelated components.1

STRANDS Examples of what the strand includes or meansConceptual understandingrefers to the comprehension of mathematical concepts, operations, and relations; it is the functional grasp of mathematical ideas, it enables students to learn new ideas by connecting to ideas they already know.

Understanding the mean as a balance point and as a fair share.

Making connections among concrete, pictorial, and symbolic (algorithmic) processes.

Understanding slope as a proportional relationship, a rate of change, and as a measure, degrees from the horizontal.

Procedural fluency (computing) – is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Knowing a procedure for calculating or solving that is efficient, accurate, and appropriate.

Computing mentally, with paper and pencil, and with technology as appropriate for the situation.

Knowing how to model algorithms with pictorial or concrete representations.

Being able to find a correct solution in a reasonable amount of time.

Strategic competence ( applying) – is the ability to formulate, represent, and solve mathematical problems.

Expressing or communicating a mathematical problem when given a problem in contextual situations

Solving routine and non-routine problems. Representing a problem in words, symbols, graphs,

tables, and pictures as appropriate. Being able to find a solution.

1 Kirkpatrick, J. & Swafford, J. (Eds.) (2001). Helping children learn mathematics. Washington, D.C.: National Academies Press. Retrieved from http://www.nap.edu/catalog/10434/helping-children-learn-mathematics.


http://www.nap.edu/catalog/10434/helping-children-learn-mathematics

Adaptive reasoning – refers to the capacity for logical thought, reflection, explanation, and justification.

Being able to explain one’s thinking in a way that someone else understands.

Being able to justify and explain why you think your response or solution is correct.

Productive disposition (engaging) - is habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy.

Seeing mathematics as important. Believing mathematics can make sense if one

works hard and sticks with it, able to persevere. Believing that you can learn mathematics even if

you have to work hard and sometimes make mistakes.


Mathematics Practices(Principles to Actions page #)

Brief Indicators – may not reflect all the ideas in the section.

Skill Level

Novice Apprentice Effective Proficient

Establish mathematics goals to focus learning.(pages 12-16)

• Clearly state what it is students are to learn and understand about mathematics as the result of instruction.

• Be situated within learning progressions. • Frame the decisions that teachers make

during a lesson. Implement tasks that promote reasoning and problem solving.(pages 17-24)

• Allow students to explore mathematical ideas or use procedures in ways that are connected to understanding concepts.

• Build on students’ current understanding and experiences.

• Have multiple entry points.• Allow for varied solution strategies.

Use and connectmathematical representations(pages 24-29)

• Be introduced, discussed, and connected.• Be used to focus students’ attention on the

structure of mathematical ideas by examining essential features.

• Support students’ ability to justify and explain their reasoning.

Facilitate meaningful mathematical discourse(pages 29 – 35)

• Build on and honor students’ thinking.• Let students share ideas, clarify

understandings, and develop convincing arguments.

• Engage students in analyzing and comparing student approaches.

• Advance the math learning of the whole class.


Structuring Mathematical Discourse (In the section on Facilitate meaningful mathematical discourse)(page 30)

1. Anticipating student response prior to the lesson

2. Monitoring students’ work on and engagement with the tasks

3. Selecting specific student representations and strategies for discussion and analysis.

4. Sequencing the various student approaches for analysis and comparison.

5. Connecting student approaches to key math ideas and relationships.

Pose purposeful questions(page 35 – 41)

• Reveal students’ current understandings. • Encourage students to explain, elaborate, or

clarify their thinking. • Make the targeted mathematical ideas more

visible and accessible for student examination and discussion.

Build procedural fluency from conceptual understanding.(pages 42-48)

• Build on a foundation of conceptual understanding.

• Over time (months, years), result in known facts and generalized methods for solving problems.

• Enable students to flexibly choose among methods to solve contextual and mathematical problems.

Elicit and use evidence of student thinking(pages 53-56)

• Provide a window into students’ thinking.• Help the teacher determine the extent to

which students are reaching the math learning goals.

• Be used to make instructional decisions during the lesson and to prepare for subsequent lessons.


Question Sort■ Open the envelop on your table and work as table groups to

sort the questions into exactly 4 non-overlapping groups or sets.

■ Analyze the type of “brain engagement,” thinking, each set og questions brings out in a student and develop a word or phrase that could be used to categorize the type of questions in each set.

■ Develop 1 additional question for each category.

In what ways might the division of fractions be related to the division of whole numbers?

How is the relationship between a collection of dogs’ noses and legs related to the relationship between a collection of bunnies’ noses and ears?

How might you prove that 51 is not a reasonable estimate for the correct solution to that problem?

What does the median indicate for a set of data?

Can you show and explain more about how you used a table to find the answer to the ducks and cows task?

What is the formula for finding the area of a rectangle? Help me understand how you found 29 x 12 using 30 x 12.


When you write an equation, what does the equal sign tell you?

As you drew that number line, what decisions did you make so that you can represent fourths on it?

How does that array relate to multiplication and division?

How do you know that the sum of two odd numbers will always be even?

Why does plan A in the Smartphone Plans task start out cheaper but become more expensive in the long run?

The Case of Elizabeth Brovey and the Calling Plans 2 Task Principles to Actions Professional Learning Toolkit Website with Resourceshttp://www.nctm.org/ptatoolkit

CALLING PLANS

Part 1Long-distance Company A charges a base rate of $5 per month, plus 4 cents per minute that you are on the phone. Long-distance Company B charges a base rate of only $2 per month, but they charge 10 cents per minute used.

How much time per month would you have to talk on the phone before subscribing to Company A would save you money?

Part 2Create a phone plan, Company C, that costs the same as Companies A and B at 50 minutes but has a lower monthly fee than either of the plans.


Recording Sheet for Calling Plan 2, Case of Ms. Bovery Video: Clip 1

Type of Question Description Evidence from Video

Gather information about and reveal students’ current understandings. Checking for a method, leading students through a method

Wants a direct answer, usually right or wrong

Rehearses known facts or procedures Students recall/state facts, definitions,

formulas, etc.

Probe thinking and encourage students to explain, elaborate, or clarify their thinking. Getting students to explain their thinking.

Explains, elaborates, or clarifies student thinking including articulating the steps in solution methods or the completion of a task.

Enables students to elaborate their thinking for their benefit and the class.

Make the mathematics more visible and accessible for student examination and discussion and connect mathematical structures.

Students discuss mathematical structures and make connections among mathematical ideas and relationships.

Points to relationships among mathematical ideas and mathematics and other areas of study or context.

Encourage reflection and justification to reveal deeper understanding including making generalizations and developing arguments.

Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.

Extends the situation under discussion, where similar ideas may be used.


D ee p er

U n d er st a n di n g

What can you say about the pattern of questions? What do you notice about the student actions?

Recording Sheet for Calling Plan 2, Case of Ms. Bovery Video: Clip

As you watch the second video this time, pay attention to the questions the teacher asks. Make notes on specific evidence of your noticing.

To what extent do the questions encourage students to explain, elaborate, or clarify their thinking?

To what extent do the questions make mathematics more visible and accessible for student examination and discussion?

How are the questions similar to or different from the questions asked in video clip 1?

Other things you notice about the teachers questioning:


Classroom Discourse and the Types of Questioning

The new NCTM publication, Principles to Actions: Ensuring Mathematical Success for All, reminds us how important classroom discourse is to help students at all levels make sense of mathematics and advance the mathematical understanding of all students. Also, mathematical discourse is a powerful tool for real time formative assessment; that is as a "window" into students' thinking, their understandings and their misunderstandings. However, the value of the ideas and information shared during partner, small group, and whole group classroom discussions is heavily dependent on the type of questions posed and the pattern of questioning the teacher uses.

Teachers have various reasons for asking questions such as the following.

Assess knowledge and learning. Encourage students to extend their thinking and make predictions. Prompt students to clarify, expand, and support their claims. Encourage students to question their thought process or reasoning. Apply class concepts to real-world scenarios.

When teachers are consciously aware of the types of questions and the frequency of each type they are able to evaluate the impact of the classroom instruction on student learning. When posing too many lower-level types of questions they can adjust their questioning and ask more higher-level types of questions. Teachers who create specific questions during planning a lesson have higher-level thought provoking questions ready to use, without having to come up with the questions on-the-fly. Different researches use various terms to designate the the types of questions, but for the purposes of this work the four types are identified as the following.

Gathering information Probing thinking

Making the mathematics visible Encouraging reflection and

justification

Patterns of Questioning

Not only does the type of question posed impact students' reasoning and sense making, but the pattern of questioning also has an influence on student learning. There are three primary patterns of questioning in a mathematics classroom. They are initiate-evaluate-response (IRE), funneling, and focusing.

INITIATE-RESPONSE-EVALUATE (IRE): Like pingpong, a recall question “tossed” out to students for a quick and factual response. Teacher asks a question to quickly gather factual information with a specific response in mind. A student responds and then the teacher evaluates the response.

– Student has limited opportunity to think.– Teacher has no access to whether or how students are making

sense of the mathematics.


FUNNELING: Pattern of questions that lead to a desired procedure or conclusion.

The teacher has decided on a path for discussion to follow, leading student(s) along the path. Higher level questions may be part of this pattern. However, student responses that stray from the teacher’s goal will be given limited attention. This may not allow students to make their own connections or build understanding.

Teacher engages in cognitive activity Student merely answering questions – often without seeing connections

FOCUSING : Pattern of questions that press students to advance their understanding.

Teacher attends to what the students are thinking, pressing them to communicate more clearly, and expecting them to reflect on their thoughts and those of their classmates. Focusing questions requires the teacher to listen to student responses and probe or ask another question based on what students are

thinking rather than how the teacher would solve the problem. The teacher plans questions and outlines key points that should become apparent during the lesson . This permits the teacher to analyze and understand better what the students are thinking and presses students to communicate their thinking more effectively and to reflect on their thoughts.

Allows teacher to learn about student thinking Requires students to articulate their thinking Supports students making connections

Overview of the Relationship Between Question Types and Patterns of Questioning

Pattern of Questioning Question Type Description Examples

Ass

essi

ng

Stud

ent R

ecal

l In

itiat

e-R

espo

nd-

Eva

luat

e

Gathering Information:

Checking for a method, leading students through a method.

Wants a direct answer, usually right or wrong

Rehearses known facts or procedures

Students recall/state facts, definitions, formulas, etc.

When you write an equation, what does the equal sign tell you?

What is the formula for finding the area of a rectangle?

What does the median indicate for a set of data?

Ass

essi

ng S

tude

nt

Thi

nkin

g

Probing Thinking:

Getting students to explain their thinking

Explains, elaborates, or clarifies student thinking including articulating the steps in solution methods or the completion of a task.

Enables students to elaborate their thinking for their benefit and the class.

As you drew that number line, what decisions did you make so that you can represent fourths on it?

Can you show and explain more about how you used a table to find the answer to the ducks and cows task?

Help me understand how you found 29 x 12 using 30 x 12.


Adv

anci

ng S

tude

nt U

nder

stan

ding

Focu

sing

Pat

tern

of Q

uest

ioni

ng

Making the MathematicsVisible

Students discuss mathematical structures and make connections among mathematical ideas and relationships.

Points to relationships among mathematical ideas and mathematics and other areas of study or context.

How does that array relate to multiplication and division?

In what ways might the division of fractions be related to the division of whole numbers?

How is the relationship between a collection of dogs’ noses and legs related to the relationship between a collection of bunnies’ noses and ears?

Encouraging Reflection and Justification

Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.

Extends the situation under discussion, where similar ideas may be used.

How might you prove that 51 is not a reasonable estimate for the correct solution to that problem?

How do you know that the sum of two odd numbers will always be even?

Why does plan A in the Smartphone Plans task start out cheaper but become more expensive in the long run?

Compiled using the work of Boaler and Humphries (2005) Connecting Mathematical Ideas: Middle School Cases to Support Teaching and Learning and NCTM (2014) Principles to Actions: Ensuring Mathematical Understanding for All Students.

Facilitating Meaningful Discourse First Step to Establishing a Discourse Rich Classroom

In Principles to Actions (NCTM, 2014) the authors bring out why it is important for teachers to set up a community and an expectation in their classrooms for students to share, explain, and defend their mathematical thinking and their mathematical work. How might a teacher move from a low usage and or quality level of discouse to a classroom that is buzzing with mathematical rich discussions? Using the idea of progression and possible steps in the progression to think about where the teachers and students are at the moment and then moving to a classroom with more high quality mathematics talk can be helpful in taking incremental steps that are manageble and sustainable.

For example, if students are not accoustomed to listening to understand or to explaining their thinking so that others understand the teacher will need to spend time building a community whose members are students and the teacher. Spend some time developing the ground rules for respectful talk and equitable participation. Everyone’s ideas are respected and it is OK to not have the correct answer or for one’s thinking to be incomplete because the community helps each other by listening carefully and asking respectful questions of each other.

A next step in the progression may be for the teacher to examine the 5 Talk Moves shown in Figure 1 and the three types of productive talk formats or ways of configuring classroom interaction for instruction as follows.


Whole Class Discussion – the teacher is not primarily engaged in delivering information or quizzing. Rather he or she is attempting to get students to share their thinking, explain the steps in their reasoning, and build on one another’s’ contribution. The teacher facilitates and guides quite actively, but does not focus on providing answers directly. Instead, the focus is on the students’ thinking.

Small Group Discussion - The teacher typically gives students a question to discuss among themselves, in groups of two to four. The teacher circulates as groups discuss and doesn’t control the discussions, but observes and interjects. This format may not be as effective because the teacher cannot be sure that the students are always on task, but small groups give more opportunity for more students to be sharing ideas.

Partner Talk - In this talk format, the teacher asks a question and then gives students a short time, perhaps a minute or two at the most, to put their thoughts into words with their nearest neighbor. This move is especially helpful for ELL students because it gives them opportunity to practice what they want to say, emerging from the partner talk ready to participate in the whole-group discussion.

Getting Started with the Students

Making a change in the normal classroom routine can, at first, is like puttng on a pair of new shoes. And, like new shoes, the new classroom routine may be a little uncomfortable at first but a commitment to work through the newness is important. To get started first a teacher needs to map out a plan for herself and her students. Introduce the talk moves in Figure 1 to students. Perhaps modeling how each of the talk moves looks and sounds in the class. Make a talk moves poster for the classroom as a reminder for the community.

The following list of ideas will help a teacher get started.

Explain your expectations Try only one ‘Move” at a time Model math talk for the students Establish and maintain a respectful, supportive environment Focus talk on the mathematics Provide for equitable participation Create a safe, learning environment where mistakes are opportunities and are not

unexpected along the way to learning

Figure 1. The 5 Talk Moves: Teacher Moves To Encourage Math Talk

Teacher Moves

Purpose Examples

Teacher revoices a student’s reasoning.

Amplify or draw attention to an idea Provide more mathematically precise

or correct language Mark the value of an individual

students' thoughts for exploration

The way I am interpreting what you are saying is __. Is that what you meant?

So, I heard you say two things: ___ and ___.

“ So Justin was saying that 210 is the same amount as 21 tens.”

Student Amplify another students ideas Can someone else say that in his or her own


revoices another student’s reasoning.

Encourage students to use more or less mathematical language or precision

To make sense themselves and to advance the other students’ reasoning and understanding.

words? Take a minute to look at <student>"s work.

Now, I want someone elseto explain her strategy.

“Whatdid you hear Marcus just say using your own words?”

Probing a student's thinking.

Allow the learner to transform, modify, or correct their contribution or thinking.

Assist students in further articulating ideas by elaborating or justifying.

Make a student's thinking available to other students for follow-up

Why does that work? Can you say a little bit more about your

thinking? I am not sure that we are all clear on what you were thinking when you said that?

Can you come up to the ____ and show us what you mean?

"You said that you just thought about a rectangle to find the area of the triangle, please come up to the board and show us what you meant."

A student justifies or proves someone else’s reasoning.

Allow students to take someone else's approach and use it for themselves.

Allow students to disagree/agree with someone else's idea, approach or explanation

Extending another student’s idea. Uses justification or proof to allow

for respectful discussion of ideas.

Do you agree or disagree? Why? Can someone continue with <student>'s

train of thought? In what situations do you think that

<student>'s method would be more efficient that the one we discussed yesterday?

“Can you explain why you think Sarah’s strategy will work for this problem?”

Wait time employed by teacher and students.

Provide students with time to process a question or response.

Hold students accountable for thinking and doing mathematics

Encourge broader participation

Pause without sayning anything (5-7 seconds).

I want you to think individually, without saying anything yet.

Think about this for a few seconds and write down any questions you have.

Ideas adapted from: Chapin, S., O’Connor, C. & Anderson, N. (2009). Classroom Discussions Using Math Talks to Help Students Learn, Grades 1-6, Second Edition. Sausalito, CA: Math Solutions Publications. and Herbel-Eisenmann, B., Cirillo, M., & Steele, M. (2013). (Developing) Teacher Discourse Moves: A Framework for Professional Development. Math Teacher Educator, 1(2).

Next Steps in the High Quality Discourse Progression As the students become comfortable with math talk the teacher can turn her attention to purposeful questioning and patterns of questioning

.


Teacher and Student Actions

Observations in many classrooms employing more intentional and thoughtful purposeful questioning reveal some commonly occurring teacher actions and student actions (NCTM, 2014, p. 41) and shown in Figure 2. Teachers can gain helpful ways to orchestrate classroom discussions by considering Smith and Stein’s five practices for effectively using student responses in whole-class discussions (NCTM, 2014, p. 30)

Figure 2. Purposeful Questioning-Teacher and Student ActionsPose Purposeful Questions

Teacher and Student ActionsWhat are teachers doing? What are students doing?

Advancing student understanding by asking questions that build on, but do not take over or funnel, student thinking.

Making certain to ask questions that go beyond gathering information to probing the thinking and requiring explanation and justification.

Asking intentional questions that make the mathematics more visible and accessible for student examination and discussion.

Allowing sufficient wait time so that more students can formulate and offer responses.

Expecting to be asked to explain, clarify, and elaborate on their thinking.

Thinking carefully about how to present their responses to questions clearly, without rushing to respond quickly.

Reflecting on and justifying their reasoning, not simply providing answers.

Listening to, commenting on, and questioning the contributions of their classmates.


THE ART OF QUESTIONING IN MATH CLASS

Adapted from Compiled by Mary Gardner, Regional Office of Education, http://www.roe8.com/profDev.

Phrases for enhancing questions: “Tell me more about what you were thinking.” “How did you decide that?” “Elaborate for others in the class so they can check their thinking.” “Can you justify that?” “Give us your insights about arriving at the answer.” “What steps did you take?” “Tell us more about what you are thinking.” “What made you think of that?” “To a person on the street who does not speak “Math,” tell how you decided that . . . “

A “Try-to” List: Try to use effective pauses and wait time. Try to avoid frequent questions that require only a yes/no answer or simple recall. Try to avoid answering your questions. Try not give verbal and non-verbal cluesTry to follow up student responses with questions and phrases such as, “why?” or “tell me how you know” or “think about how you can put Jim’s response into your words.” Try to avoid directing a question to a student mainly for disciplinary reasons. Try to follow up a student’s response by fielding it to the class or another student for a reaction. Try to avoid giveaway facial expressions to student responses. Try to make it easy for students to ask a question at any time. Try to ask the question before calling on a student to respond. Try not to call on a particular student immediately after asking a question. Try to ask questions that are open-ended. Try to leave an occasional question unanswered at the end of the period. Try to keep the students actively involved in the learning process.Try to keep questions neutral. Qualifiers such as easy or hard can shut down learning in students.


Encouraging Your Students to Ask Questions in Class. Note the subtle difference. The first set sounds as if you do not want questions; the second set implies that you both want and expect questions.

Instead of you asking questions this way: You might try asking questions this way: "How many of you understood that?” “Everybody see that?” “This is a ________, isn’t it?” “Are there any questions?” “You do not have any questions, do you?” “Would anyone like to see that again?”

"Thumbs up--I got this, Thumb sideways--I am still working on this, Thumbs down--I have questions" Have students hold thumbs close to their heart so only you can see. Note who has questions and get back to them later.

“Okay--I want three questions about ___ from the group that will help us all understand better?”

“Now, write a question on your white board and hold it up."

“Now, what questions may I answer?”

Phrases That Encourage Participation: It is useful to have a handful of effective ways to start your questions that will motivate all students to participate. Here are some to try.

What others can you think of? “Don’t raise your hand--yet; just think about a possible answer. I will give you a

minute . . . “ “Everyone—picture this figure in your mind. Is it possible to sketch a possible counterexample to this statement? I will walk around to look at your work and select three students to share their results with the class.”

“Find an example of this statement and write it down. In just a minute, I will tell you possible ways to check your example to see if it indeed makes the statement true.”

“Put the next step on your paper and write a reason to justify this step. Raise your hand when you are ready and I will be around to check in on you.”

Phrases That May Fail to Motivate: There are some questions that you might want to avoid. Why? Because often you end up answering your own questions and “permitting” students NOT to participate—that is, students are not required to take responsibility to develop a response depending how the question is phrased.

“Does someone know if . . . “ “Can anyone here give me an example of . . . “ “Who knows the difference between . . . “ “Someone tell me the definition of . . . “ “OK, who wants to tell me about . . . “


POSE OPEN QUESTIONS

Successful questions provide a manageable challenge to students – one that is at their stage of mathematical development. Open questions are effective in supporting learning. An open question is one that encourages a variety of approaches and responses. Consider

“What is 4 + 6?” (closed question) versus “Is there another way to make 10?” (open question)

“How many sides does a quadrilateral figure have?” (closed question) versus “What do you notice about these figures?” (open question).

Open questions Help teachers build student self-confidence as they allow learners to respond at their own

stage of development. Intrinsically allow for differentiation. Responses will reveal individual differences, which

may be due to different levels of understanding or readiness, the strategies to which the students have been exposed and how each student approaches problems in general.

Signal to students that a range of responses is expected and, more importantly, valued.

Huinker and Freckman (2004, p. 256) suggest the following examples: As you think about… As you consider… Given what you know about… In what ways… Regarding the decisions you made… In your planning… From previous work with students… Take a minute… When you think about…How else could you have …? How are these ____ the same? How are these different? What would you do if …? What would happen if …? What else could you have done?

What Teachers Can do to Build a Risk Free Classroom and Support Students Plan relevant questions. The essence of good questioning is in planning questions that

are directly related to the concept or skill being taught. Phrase questions clearly. Clear and concise phrased questions communicate what the

teacher expects of the students’ responses.


Do not direct the question to anyone until it is asked. This forces all students to pay attention and requires more students to answer the question mentally

Encourage wide student participation. Distribute questions to involve the majority of students. Balance responses from volunteering and non-volunteering students and encourage student-to-student interaction.

Allow adequate wait time. Give students time to think when responding. Allow three to five seconds of wait time after asking a question before requesting a student’s response, particularly when high-level questions are asked. The more time a teacher waits for a reply from the students the better the response and will encourage other students to participate.


TRANSITION TO PRACTICE and SUPPORTING TEACHERS:

Trouble-shooting some of the challenges teachers face when increasing the math talk in the classroom and using more open and focusing questions. An effective way to support teachers is to work with small groups or even one teacher and identify what they perceive as challenging situations, some frequent ones teachers name are listed below. Then brainstorm together the cause of the challenge think of some ways to address the challenges.

Analyzing the Challenging Situation

Some Ideas for Trouble Shooting Challenges

My students will not talk

The same few kids do all the talking

Should I call on students who My students will talk, but they will not listenWhat to do if students provide a response I do not understandI have students at different levelsWhat to do when students are wrongThe discussion is not going anywhere--or at least not where I plannedAnswers or responses are superficialWhat if the first speaker gives the right answerWhat to do for English Language Learners


Resources

Chapin S., O’Connor, C., & Canavan Anderson, N. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions.

Herbel-Eisenmann, B. A. & Breyfogle, M.L. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484-487.

Huinker, D., & Freckmann, J. L. (2004). Focusing conversations to promote teacher thinking. Teaching Children Mathematics, 10(7) 352-357.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (n.d.) Principles to actions professional learning toolkit. Retrieved September 2015. From http://www.nctm.org/ptatoolkit/.

Reinhart, S. D. (2000). Never say anything a kid can say. Mathematics Teaching in the Middle School, 5(8) 478–483.

Sullivan, P., & Lilburn, P. (2002). Good questions for math teaching: Why ask them and what to ask. Grades K-6. Sausalito, CA: Math Solutions.

Schuster, L., & Anderson, N. C. (2005). Good Questions for math teaching: Why ask them and what to ask. Grades 5-8. Sausalito, CA: Math Solutions. Small, M. (2012). Good Questions – Great Ways to Differentiate Mathematics Instruction. New York, NY: Teachers College Press.

Smith, M. S., & Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics and Thousand Oaks, CA: Corwin Press.

Smith, M.S., Hughes, E.K., & Engle, R.A., & Stein, M.K. (2009). Orchestrating discussions. Mathematics Teaching in the Middle School, 14 (9), 549-556.


Documents

vcoms.wildapricot.org · Web viewUnderstanding slope as a proportional relationship, a rate of change, and as a measure, degrees from the horizontal. Procedural fluency (computing)