In this session you will consider how student learning is impacted by the ways in which students engage and interact with the questions you pose and the tasks they work on. You will:
Learning is affected by the opportunities students have to relate incoming information to what they already know and then restructure their existing knowledge or construct new ideas when appropriate.”
Make a list of questions that you might ask students using the set of figures in the PDF below. Record your questions in your journal.
Question Categories
Teachers use different types of questions for different situations.
In this activity, you will sort questions into three different categories.
Click on “show” to read about the different categories.
Factual Questions
In this first category, students answer questions targeting specific mathematical facts. They will be challenged only to recall previously learned or memorized concepts or terms. Teachers will find out whether their students know specific math facts. The teacher will gain little information about whether their students understand the concept or term.
Reasoning Questions
Reasoning questions require students to construct to reconstruct from memory, logically organized information. There are several sub-types to consider:
Open Questions – not calling for reasoning
Unlike factual questions, a wide range of acceptable answers exists for Open Questions – not calling for reasoning. Students have an opportunity to describe conceptual ideas and definitions, even though they have not yet learned a formal name or term. For instance young students may describe a triangle as being pointy, three lines, ‘slanty’, looks like a roof, etc. before knowing that it’s a triangle and that all triangles are closed figures with three sides and three vertices. Teachers learn about their students’ cognitions that can be used in introducing new concepts and in planning individual needs. Students have opportunities to:
Go back to the questions you recorded in your journal.
Categorize your questions into the three types: Factual, Reasoning and Open – not recall for reasoning. Did you have all three types of questions? Try rewriting some of your questions to be fit a different category.
If we as teachers are to find out what our students already know so that we can help them use that understanding to construct new knowledge, we need to focus on questions that will assist us in achieving that goal.”
Did you know?
Questioning by Steve Hastings, updated 2013, TEP
5 Powerful Questions Teachers Can Ask Students by Rebecca Alber
The Right Way to Ask Questions in the Classroom by Ben Johnson
In this activity you will listen to a professor who researches bilingual students’ math learning as she shares what she has found ELL students need, watch a bilingual classroom engaging in math, and view different video clips of ELL classrooms as you focus on ways to support English Language Learners’ math learning.
What do English learners need in mathematics classroom?
Listen to Judit Moschkovich, University of California, Santa Cruz, as she shares what English learners need in the mathematics classroom.
Record your reflections and questions from listening to Judit Moschkovich and reading Jim Cummin’s paper on ELL and Mathematics in the Mathematics Classroom.
The students in this third grade bilingual classroom have been working on a unit on two-dimensional geometric figures for several weeks. Their experiences included vocabulary such as names of different quadrilaterals and vocabulary that describes their attributes in both Spanish and English.
Students had been talking about shapes and the teacher had asked them to point, touch, and identify different shapes. The teacher identified this lesson as an English as a Second Language mathematics lesson, one where students would be using English in the context of folding and cutting to make Tangram pieces.
You will view a very short clip of the introduction. Watch this third grade class as they discuss what they know about rectangles two times. Use the transcript, pp. 1-2,in the document, Never Get Together.
Reflect on the following in your journal.
Judit Maschovich, U.C., Santa Cruz, makes five recommendations for ELL students and shares her reflections on the students and teachers in the video, Never Get Together. While these recommendations are for ELL students, they are equally appropriate for all learners.
Record you reflections about these recommendations for English Language learners in the mathematics classroom in your journal.
Watch at least one of the video clips below. The teachers and students in these videos are doing a Number Talk. These clips were chosen because of how each teacher structured and engaged the students in the number talk experience. The different structures can be enacted at any grade level. Notice the teacher’s role and the ways student interact.
Respond to the following question in your journal.
Which instructional principles and strategies described in English Language Learners in the Mathematics Classrooms are enacted in the video you watched?
Watch Guess My Number
Students interacting and extending understanding can only be done if we understand the nature of learning, which is the ability to participate in an activity beyond our autonomy level, and the importance of nourishing student voice and agency.”
RESEARCH BASED RECOMMENDATIONS FOR INSTRUCTION THAT SUPPORTS ACADEMIC SUCCESS FOR ELS
Racial and Linguistic Diversity in the Classroom, 2nd Edition Implementation Guide (Any grade) TERC
Mirrors & Windows Into Student Noticing by Higinio Dominguez, NCTM, February, 2016
Understanding Language, Stanford University
In this activity you will solve number puzzles, reflect on what knowledge you needed to solve the puzzles and think about ways to provide support for students to successfully engage in solving the puzzles. Finally, you will look at a lesson planning protocol called Thinking Through a Lesson Plan (TTLP).
Solve the following number puzzles. The solution has to fit all the clues on each puzzle. Use your journal to record your thinking as you solved each puzzles.
You may want to use a 300 chart as you solve the puzzles.
Record your responses to the following questions in the journal.
How has solving a few puzzles helped you think about facilitating the students’ experiences with the puzzles?
What questions or challenges do you anticipate student having?
How can you make sure all students have an entry point?
What support or extension would you prepare?
Read Tasha Becomes a Learner
The following excerpt is from My Kids Can, Chapter 20. Read how one student becomes a confident, independent math learner.
Record your responses in the journal.
Tasha’s teacher supported her as she became more confident and independent. How will the “Learning Behavior Observation Record” help all your students take responsibility for their learning? Be specific.
In their book, 5 Practices for Orchestrating Productive Mathematics Discussions, Peg Smith and Mary Kay Stein present and discuss a framework for orchestrating mathematically productive discussions that are rooted in student thinking. The framework identifies a set of instructional practices that will help teachers achieve high-demand learning objectives by using student work as the launching point for discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated. The authors outline a ”“road map” of things that teachers can do in advance and during whole-class discussions. 5 Practices for Orchestrating Productive Mathematics Discussions, Preface, p. vii
Smith, Stein and their colleagues developed a three-part lesson planning protocol based on their five practices. The TTLP protocol is a guide for a teacher or grade level team as they plan a lesson. The teachers review and experience the math in the lesson in advance, anticipate strategies, misconceptions and errors that could occur during the lesson, decide how to engage the students in the lesson so all students have a starting, determine what to observe and how to keep track of student learning. The teacher uses this information to determine the focus of a class or small group discussion.
The authors shared examples of strategy planner charts teachers used to first record strategies they anticipate will happen during the lesson and later keep track of what students are doing during the lesson. To learn more, read the following documents about the TTLP and observations.
Share your thoughts on the practices for productive conversations and the Thinking Through a Lesson Plan Protocol in your journal.
When we introduce complexity in the problems we ask students to solve and challenge them beyond what they think they can do, we give them the opportunity to struggle a bit—an opportunity that many students never experience in mathematics from elementary school through high school. A look at those American classrooms where teachers and students invite complexity shows that the kind of mathematics problems students can really sink their teeth into (and consequently might struggle with) are often more interesting and engaging than the problems we have traditionally provided in math classrooms. It turns out that offering students a chance to struggle may go hand in hand with motivating them, if we do it right.”
In this last activity you will return to your Sam and your Charlie – current, former, or ones you recall having had – and reflect on ways you will support them in their math journey.
Teachers are faced with the challenge of meeting the needs of the range of learners in their classroom. A class of students could include students who excel in math, underachievers, English Language Learners, students who have gaps in certain areas of mathematics and students who have particular learning needs. Many factors affect math learning for students in a classroom. Some questions teachers wonder about include:
There are many more questions to ask.
Teaching Practices and Strategies
Teaching Practice Action Plan
Set two to three teaching practice goals. Describe how you plan to enact your goals. Record your thinking in your journal. Share your plan with others in the Discussion Forum.
Think about your Sam and your Charlie – they might be current students or former students. For each one, reflect on ways you (are) plan to support them in their math learning through your math teaching. What are the 2-4 goals you want to set for Sam and Charlie. How do you plan to implement these goals? Record your plan in your Sam and Charlie Journal.
What invites students to learn? Because students vary, what is inviting will vary as well. In general, however, students have at least five needs that teachers can address to make learning irresistible: affirmation, contribution, purpose, power, and challenge. Sometimes, teachers find that the learning environment is key to meeting student needs. Sometimes the mode of instruction is key. Generally, environment and instruction work in tandem to invite, inspire, and sustain student learning. Together, they make the content important.”
Standards for Math Practice, NCTM, Hunt Institute
Share the teaching practice goals you plan to focus on for the remainder of they year. Describe how you plan to enact your goals. Read the goals of other participants. Comment or give input.
Complete the Session 6 Notebook page using the indicated prompts.
In the final field of your journal, reflect on the key take-aways from this session for your own learning and record ideas that you will implement to support math learning.
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