Mathematics

Resource Review & Synopsis 

Number Talks, Helping Children Build Mental Math and Computation Strategies (K-5) - Sherry Parrish 

This is a resource that we will be using in order to support our students when teaching and learning the Number Sense and Numeration strand of the Ontario Mathematics Curriculum. I view this strand and resource as a way in which to teach students a fundamental concept they may apply as they build upon and move throughout the other strands (i.e., Measurement, Patterning and Algebra, Data Management and Probability, and Geometry and Spatial Sense) and when these strands meld together to form rich tasks. Defined below is the definition of Number sense taken from the curriculum document itself. I have highlighted some terms that reflect and align with the aforementioned resource and Parrish's requirements for mathematically proficient students; accuracy, efficiency, flexibility. 

"Number sense refers to a general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgements and to develop useful strategies for solving problems. In this strand, students develop their understanding of number by learning about different ways of representing numbers and about the relationships among numbers. They learn how to count in various ways, developing a sense of magnitude. They also develop a solid understanding of the four basic operations and learn to compute fluently, using a variety of tools and strategies. A well-developed understanding of number includes a grasp of more-and-less relationships, part-whole relationships, the role of special numbers such as five and ten, connections between numbers and real quantities and measures in the environment, and much more. Experience suggests that students do not grasp all of these relationships automatically. A broad range of activities and investigations, along with guidance by the teacher, will help students construct an understanding of number that allows them to make sense of mathematics and to know how and when to apply relevant concepts, strategies, and operations as they solve problems." 

Ontario Ministry of Education. (2005). The Ontario curriculum grades 1-8: Mathematics [Program of Studies]. Retrieved from https://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Think A.E.F when Number "Talking"
Parrish contends we must use our curriculum and way in which in instruct students in order to prepare them to be mathematically proficient and compute "accurately, efficiently, and flexibly." She believes our society is filled with students and adults who, "think of mathematics as rules and procedure to memorize without understanding the numerical relationships that provide the foundation for these rules" (Parrish, 4).

Accuracy = ability to produce an accurate answer
Efficiency = refers to the ability to choose an appropriate, expedient strategy for a specific problem
Flexibility = ability to use number relationships with ease in computation

Math guru Van de Walle highly agrees with this constructivist approach in which students connect "informal knowledge, intuition and invented procedures," in order to make meaning of mathematical concepts. http://ponce.inter.edu/cai/tesis/lmrivera/cap2.htm

Teacher's Role: The teacher moves into role of "all-knowing one" who imparts formulas and strategies onto empty student vessels into the role of facilitator who maintains student's focus on the subject, helps structure their comments, posing questions to push student thinking, interpreter of student's strategies, recorder of their ideas.

Say: "How did you solve that problem" instead of "How did you get that"


TIPS AND TRICKS 

1. Choose a location with close proximity to students for informal observations (are they using fingers, number lines, other students previous strategies, hundreds charts and do they have access?)
2. Give them time! (way longer than you think...) They may use a finger (thumb) to show they have their answer. If finished early, solve it another way and show that new strategy by showing 2 fingers on their chest.
3. All answers are accepted, respected, considered. Wear a BLANK FACE! No expressions, just questions for students to defend their thinking and provide reasoning so teacher's AND students can either agree or disagree with student in a respectful way so as to help disprove misconceptions.
4. Exit cards of computations problems as they leave the class on an index card. One side is the strategy that was shared with the class and other side is any way they choose.
5. Give a weekly computation assessment they must solve in 2 ways
6. Write Horrizontally 13 + 7 =
   and be careful of misuse of the = sign. Here is a sample problem written as the student was explaining and when the teacher was prompting.

7. Student Talk Time! Provide whole group, small group and individual opportunities to meet all students. See the Curriculum Services Canada resource from educator Carmel Crevola in which she discusses Teacher Talk Time and how much it dominates the classroom environment.

http://www.curriculum.org/k-12/en/videos/teacher-talk

I have added two more suggestions when implementing number talks based on the Q&A Session with Sherry Parrish featured on website/blog http://www.guided-math-adventures.com/ 

8. Start small! Use dot plates and basic computations at all grade levels. 

9. Make it a story! Instead of 13-7 say, "I want to read13 pages. I have read 7 already. How many more pages do I need to read? Context supports reasoning.  

10. Educate the parents! Have them in, send them links and webcasts or host a parent night with a demonstration. When the children are faster than their parents they will be hooked! 

11. We do NOT necessarily need to teach the strategies explicitly to students. Wait until they organically emerge from the students. 

Possible Strategies in Grade 1 


Making Landmark or Friendly Numbers for 28 + 29 
 - one student knew 25 + 25 = 50 so they used 25 as the friendly number and added the remaining 3 + 4 = 7 to make 57
- another used 30 + 30 and subtracted from the 60

Compensation for 28 + 29
- "i wanted to make an easy ten so I took one from the twenty-eight and gave it to the twenty-nine. That gave me twenty-seven plus 30
- "how did you add 27+30?" - teacher
- "I started at 27 and made 3 jumps of 10"
- "why three jumps of ten?"
- "because thirty is the same as three tens. So I counted from twenty-seven and went thirty-seven, forty-seven, fifty-seven.

Breaking Each Number into its Place Value
- i break apart the numbers and put all of the tens together and then all of the ones.
- (20 + 8) + (20 + 9 )
- I added twenty plus twenty and got forty and eight plus nine and got seventeen. I knew I had to put the forty and seventeen together next.
- (20 + 20) + (8 + 9)
- 40 + 17

Counting On in Ones

Counting on in Chunks
Doubles/Near Doubles

Breaking Each Number into its Place Value and Making Tens Combined

Adding Up
Counting Back
Removal
Counting All
Making Tens


Decomposing to Make a Friendly Number/Landmark Number

Removal or Counting Back

Adding Up in Chunks

Accountable Talk 

* I agree with ______ because _________

* I do not understand ________. Can you explain this again? 

* I disagree with ______. Can you explain this again ?

* How did you decide to _______?

Math Time Structure

How to set up your 60 minute math class. Sherry suggests,  

a) CALENDAR 10 minutes

b) NUMBER TALKS 5-15 minutes 

c) MATH INVESTIGATION or MATH MENU 25 minutes 

investigation - authentic classroom problem they are solving like how to organize the math manipulatives into easier-to-count groups of fives, twos, tens, or how a classroom snack may be fairly shared. We refer to these in our board as rich tasks, or open-ended problems. 

menu - collection of math tasks (i.e., games, fluency tasks, counting opportunities designed to allow students to engage in math. 

d)  WHOLE-GROUP PROCESSING 5 minutes 

ART

Click here to make a rekenrek 

http://www.k-5mathteachingresources.com/how-to-make-a-rekenrek.html

Question and Answer Section of the Book - love it! 

I have no idea what the student means???!!! Help! 

Sherry recommends we first ask the student to reexplain. Next, ask another student to explain their thinking. This will not only take away the "talk time" from the teacher but will help YOU as educator make meaning of their specific vocabulary and meaning we as adults may not understand. Asking a peer to interpret will help honor the student without responding with, "I have no clue what you are saying." A statement or thought like that from a teacher really reads, "I only know one way of solving this problem and am not open to understanding the LEARNING from you." This makes teaching SO much more exciting - believe me! If we still are unsure of the strategy tell the students you will take more time to consider it and ask colleagues for assistance. 

Two Stars and a Wish 

* 

* 

- I wish Sherry would provide examples of what NT's look like in a grade 1 classroom as she only provides examples from Kindergarten and Grade 2. That being said, our students may be at varying places and so we should not hold ourselves nor our children to be boxed within one grade. 

- I wish there were links to the Ontario Curriculum as only the Common Core Standards from the U.S.A are provided.

Manipulatives and Tools 

~ colour tiles
~ interlocking cubes
~ counters
~ ten-frames
~ rekenreks

Featured below is a table found from the French version of the curriculum providing an overview of the 5 mathematical strands 

Ontario Ministry of Education. (2005). The Ontario curriculum grades 1-8: Mathematics [Program of Studies]. Retrieved from https://www.edu.gov.on.ca/fre/curriculum/elementary/math18curr.pdf