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Math Conversations
Math Conversations
Math conversations may take place at any time during a lesson, from giving math talk prompts at the start of a lesson to posing an open question or parallel task that consolidates learning at the end of a lesson. Math conversations can focus on number routines, such as number talks or analyzing number strings. When analyzing graphs, images, and patterns, asking students questions like “What do you notice? What do you wonder?” or “Which one doesn’t belong?” can help further strengthen under standing of math concepts and spark deeper classroom discussion. Students can be encouraged to speak with a partner during a problem-solving task or to speak to the class during consolidation of learning. All of these different types of math conversations support students in consolidating their understanding of math.
Discuss:
Discuss:
After watching the video above...
How might we encourage the "star" pattern of discussion in an NSR?
Why is math talk considered to be a vital approach to learning mathematics?
As students are beginning to learn about a concept, effective conversations should:
As students are beginning to learn about a concept, effective conversations should:
activate prior knowledge and connect the current task to previous learning (“How is this like something you have done before?”)
gather information about students’ current level of understanding and ways of knowing (“How can you show your thinking?” “What math words can describe this?”)
As students progress with their learning, effective conversations should:
As students progress with their learning, effective conversations should:
make math explicit (“How have you shown your thinking?”)
probe thinking and require explanations(“How could you explain your thinking to someone just learning this?” “How do you know?” “Why did you represent the problem this way?”)
reveal understanding and/or misconceptions (“How did you solve this problem?” “Where did you get stuck?”)
When students are deep in the learning process, effective conversations should:
When students are deep in the learning process, effective conversations should:
support connections and transfer to other strands/content areas (“Where can you see this math at home? In other places?” “What other math connects to this?”)
require justifications and/or explanations (“Would this always be true? How do you know?”)
promote metacognition (“What was the most challenging thing about this task?” “What would you do differently if you solved a similar task again?”)
You will need:
You will need:
Ontario Mathematics Curriculum Expectations, Grades 1 to 8, 2020 Strand B: Number -scroll down to PAGE 5
Highlighters
📌Consider the following Number Progression and highlight expectations that NRs could help support
What are Number Sense Routines (NSRs)?
What are Number Sense Routines (NSRs)?
Short, ongoing daily routines that provides students with meaningful ongoing practice with number and operation. The purpose of engaging in these routines is to strengthen mental math skills and to build:
number relationships
computational fluency
A number sense routine can consist of a number string or a number talk. Number Sense Routines are in service of the following outcomes:
A number sense routine can consist of a number string or a number talk. Number Sense Routines are in service of the following outcomes:
visualization & representations (models)
math conversations (math talk)
proficiency & efficiency of mental computations (strategies)
Key Elements of a Number Sense Routine
Key Elements of a Number Sense Routine
keep Number Talks/Strings short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics
spend only 10 to 15 minutes on Number Talks/String
Talks/Strings are most effective when visited frequently/daily and are aligned to the conceptual learning in the math learning cycle
Number String vs Number Talk ... what's the difference?
Number String vs Number Talk ... what's the difference?
Number String
Number String
Number strings consist of a sequence of computational problems (or a series of dot patterns or quick images), with problems chosen so that a particular strategy is likely to emerge from students (e.g., compensation, doubling & halving) or number property is likely to be discussed (e.g., commutative property, distributive property).
Number strings are carefully crafted and often follow a pattern in which a few helper problems are presented to support students to solve a challenge problem. For example, solving 10 x 6 (helper) and then 7 x 6 (helper) should help students solve 17 x 6 (challenge). After a few of sets of helper-then-challenge problems, it is not uncommon for a number string to end with a challenge problem with no helper problem preceding it. The removal of the scaffolder helper problem is designed to help students to transfer strategies in smart ways.
Central to number strings is the use of models (e.g., ten frame, empty number lines, arrays, ratio tables) as a way to not only understand and analyze the strategies presented but also to make connections among the strategies. As with number talks, it is likely that conversations will naturally arise about how students chose their strategy and whether it was an efficient one; however, a greater emphasis is placed on exploring relationships between number values and problems.
Number Talk
Number Talk
A number talk refers to a practice whereby the teacher picks a single computational problem (or dot frame image) for the class to explore with the purpose of eliciting multiple strategies for solving the problem (or determining the total number of dots). This is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.
Ideally the teacher uses representations to help illustrate and clarify the strategies, so that the class develops a better understanding of the strategies. Beyond this, a focus of number talks is delving into the presented strategies to decide in which cases one strategy is more efficient than another and/or when a particular strategy might not be helpful.
Aligning NSRs to the Curriculum
Aligning NSRs to the Curriculum
Highlight:
Highlight:
the expectations that NSRs address in your grade or division on the Strand B: Number Progression
Critical Use of this Instructional Strategy
Critical Use of this Instructional Strategy
A single fact-focused number-string discussion is unlikely to result in all students adopting more flexible and efficient fact strategies; however, we have found that repeated engagement in such discussions over time does promote student reasoning about relationships, which in turn leads to increased fact fluency.
By cultivating a reasoning approach, we find that students are more likely to not only achieve automaticity with working with numbers (Henry and Brown 2008; Kamii 1999) but also establish a strong foundation for using number relationships to devise multi-digit computation strategies.
How could we punctuate NSRs to serve an urgent learning need?
How could we punctuate NSRs to serve an urgent learning need?
Examine:
Examine:
A school's use of Number Sense Routines to punctuate place value concepts
Primary Number String
Primary Number String
Junior Number String
Junior Number String
Intermediate Number String
Intermediate Number String
Precision Teaching
Precision Teaching
Think About and Discuss:
Think About and Discuss:
How might using number sense routines & math discourse have a high impact on student learning within a targeted area of need?
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