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Making Sense of Mental Math – Number Talks 0

Posted on December 03, 2014 by Allison Dyjach

“All students can learn mathematics and deserve the opportunity to do so.”  -The Ontario Curriculum, Mathematics Grade 1-8

When I ask you to answer the math problem 5 + 7, I’m sure that most of you could come up with the answer of 12 pretty quickly. But, if I asked you to explain the process or steps that you used to get to the final answer of 12, it might take you a bit more time to think about it. This same thing happens when we ask students math questions. They are often able to give us an answer, but when we ask them to explain their answer, describe a strategy that they used, or even just write out their answer step by step, we can be left with something in between a blank stare and a beyond puzzled expression. Although our students may be able to give us a correct answer on a test or worksheet, we may have no idea what process they are going through to get that answer. The same goes for a wrong answer. If a child gives a wrong answer, but we can’t seem to figure out where they veered off course, we won’t be able to guide them back onto the path to success.

During my most recent school placement, my school ran a professional development day on a new classroom tool called “Number Talks.” Some of you may have heard of the concept, developed by Sherry Parrish, but to me this was brand new. The main purpose of a number talk is to dissect a mental math problem with your students, and discuss and evaluate the different strategies that can be taken to solve that problem.

For example, I used a number talk with my Grade 4 students when discussing how to show a specific time on an analog clock. Students were tasked with telling me how they would show 7:35. I emphasized to them that they not only had to give me the right answer, but if they wanted to respond they would also have to tell me how they knew where to put the hands on the clock.

The “Number Talk” response signal. Photo: http://hzn165.blogspot.ca/2012/11/day-38-number-talk-with-1st-graders.html

The Number Talk incorporates another great strategy that can be used not only during these discussions but also as a general classroom management strategy. When students are thinking of their answers, they are not to put their hand up or shout out any answers. Instead, they hold a fist on their chest, and if they can find one way to answer the problem, they simply stick their thumb up. If they find a second way that they can solve the problem, they stick up another finger, and so on. This way, the teacher is able to assess students’ understanding, but other students are not distracted (or discouraged) by their peers’ progress.

After students were given ample time to figure out their answers, we took time to hear different strategies of knowing where the hands should go on the clock to show 7:35, some including counting by 5’s, going straight to 7:30 and adding 5 etc. We listened to all of the different methods that students had used, discussed their effectiveness (eg. counting by 1’s to get to 35 was not found to be very effective by my students!) and talked about which strategies different students preferred to use.

I have to say that as someone who grew up simply memorizing math times tables and addition facts, this was a wonderful concept to be introduced to. I found them to be extremely effective as a “Mind’s On” activity and to get students thinking about how math operations and concepts really work. Although math is generally a subject that allows for very little deviation, this activity shows students that there are often ample strategies that they can use to solve math problems. Number Talks give them that bank of strategies to use for math problems, and it also allows teachers to learn what is really going on in the minds of our students, even if we are asking them “simple’ questions like 5 + 7.

“Number Talks” guidebook by Sherry Parrish. Photo: https://grade2commoncoremath.wikispaces.hcpss.org/Number+Talks

There are some great resources out there for teachers interested in incorporating Number Talks into their classroom. This article written by the Parrish gives a short and simple introduction into the concept and even walks through an example with student dialogue and diagrams.

For further learning, you might want to consider buying Sherry Parrish’s book “Number Talks Common Core Edition, Grades K-5: Helping Children Build Mental Math and Computation Strategies.” Youtube is also a great resource to see some real Number Talks in action. Here is a favourite of mine, but just by searching “Number Talk” you will be able to find many more.

Do you use Number Talks in your classroom? Do you think this is a useful strategy to help kids delve deeper into math comprehension? What are some other strategies you could use to help understand students’ mental math processes better? Let us know what you think below!

 

Allison Dyjach is a Faculty of Education student at Queen’s University in Kingston, Ontario. Connect with her on Twitter @AllisonDyjach, or follow more of her Bachelor of Education experiences on Instagram @allisondyjach

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Thirteen Steps to Easy Long Range Planning 0

Posted on October 20, 2014 by Lauren

[OR: How I Spent My Summer Vacation…]

This summer I knew that I was going to be starting a new job in September. I have spent the past couple of years teaching in a self-contained grade 1/2 class where all of the students had IEPs with at least some curriculum modifications. I was focused on IEP goals. My new job was going to be in a ‘regular’* grade 1/2 class. I needed to figure out what teaching would look the same and what gaps I would need to fill in order to cover the whole curriculum. The following is a glimpse into the madness to my method.

*As a side note, I really dislike the term ‘regular class’, but it is widely used; some schools use the term ‘community class’.

Thirteen Steps to Easy Long Range Planning

  1. Pick a subject area- I started with math because it is one of my favourites and the specific expectations are pretty specific (who would have thought?!).
  2. Get your long range plans ready and know which strands you are going to report on in each term- I already knew loosely what big ideas/ strands I wanted to cover in each month. For K-8 math in Ontario it is expected you will report on 4 of the 5 strands in each term. Some school boards dictate what you will report on, mine does not. I decided on Term 1: Number Sense, Data Management and Probability, Measurement and Geometry. In Term 2 I will also report on Patterning and Algebra, but not Data Management.
  3. Set up a calendar system- I labeled pieces of paper with the months Sept-June and laid them out on the floor. Because I am teaching a split class I also made two columns and labelled them Grade 1 and Grade 2.
  4. Print the curriculum for the grade- I printed all of the math curriculum for grades 1 and 2.  http://www.edu.gov.on.ca/eng/curriculum/elementary/subjects.html
  5. Colour code- I used crayons because it was quick and cheap (no colour ink). I shaded each strand a different colour. Number Sense white, Measurement pink etc.
  6. Cut apart the specific expectations- If you are comfortable with the curriculum then you may want to keep some pieces together.  For example, I knew that I was going to teach the patterning expectations together so I didn’t need to cut them apart. If you teach more than one grade then you will want to be careful the pieces separate.
  7. Start lining up specific expectations with your long range plans- I started with September. I knew that I wanted to focus on reviewing some basic number sense (counting, number recognition etc.) and that the calendar routine would be a big part of the first weeks of school. I found the expectations that fell under these two categories in the grade one curriculum and then matched up the corresponding grade two curriculum directly beside it. This was also a good chance to review the similarities and differences. I moved through the first term and paused.
  8. Double check the term- Does everything make sense? Are there are any other expectations that could go together? Do I have enough material to report on? At this point I found that I still had a lot of expectations left to cover in term 2. Too many? I decided to write the number of weeks available in each month. I needed to be realistic. The first week of school was about routines and relationships so I didn’t count it. The last two weeks of June are full of interruptions and happen after reports are due to the office so I didn’t count them either.
  9. Fill in the second term- I went back to my long range plans and filled in the rest.
  10. Double check again- Again I checked to make sure it was realistic. I knew that addition and subtraction strategies would take a serious chunk of time, but we will probably breeze through 2D shapes. I also checked to make sure the grade 1 and 2 expectations lined up. There are a couple of times that the grade 2s will be working on expectations that the grade 1s don’t even touch on (e.g., multiplication and division), I needed to think about how that time will best be spent with the grade 1s.
  11. Glue the pieces down- I actually used tape so I can keep moving them.
  12. Remember that plans change- I did all of this before I even met my class. We may need more time for some expectations and less for others. I do know that the year will fly by so I need to be aware of the time line.
  13. Keep the overall expectations/ big picture in mind- I got into the really nitty gritty because it made sense for me. I’m not going to lose sleep if we don’t get to every single specific expectation, but I do know exactly which ones I am willing to gloss over and which ones I will slow down for if necessary.

Long Range Math folioPhoto: **Natasha loved the idea — here’s what it looks like for Grade 7**

 

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Mathematical Interpretations 0

Posted on August 03, 2014 by Natasha

Multiple interpretations…?? Let’s find out where our kids are going wrong.

What math resources are you using for the upcoming year? Share your resources below…let’s build our Resource Bank.

I would recommend Dr.Marian Small’s “Making Math Meaningful.” It provides examples of misinterpretations and how to guide students to finding solutions

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FREEBIE D/L: Patterning Task: Role-A-Rule 0

Posted on November 28, 2012 by Natasha

Spice up your patterning unit with this fun game…err…task.

[[[Patterning-Role-A-Rule <download PDF>]]]

Use it as a sand-alone task or add it to your math centers!  Enjoy :)

– Natasha

Preview

Preview

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Long Range Planning: The Lounge Podcast: Episode 9 4

Posted on July 25, 2012 by Natasha

We’re back with another great episode of The Lounge Podcast.  We were extremely lucky to have Lisa Dabbs from Edutopia.org and Edutopia’s New Teacher Connections Group Facilitator Skype in for the show.  She was able to enrich our conversation, give us lots of great tips and web 2.0 tools, and advise us where to start when it comes to Long Range Planning.

Cursive Calendar - photo by: Your Secret Admiral

photo by: Your Secret Admiral

I think it’s safe to say that this topic is very important to think about at this time of year (and as the school year goes on…after all, we consider plans to be working documents).  We all agreed how valuable and powerful the act of collaborating with a grade/division team plays in the process of long range planning and how successful backwards design/mapping can be when creating strong plans.

Listen in to hear our conversations about long range plans, curriculum, split/combination classes, backwards design/mapping, web 2.0 tools, staying organized, Post-It Notes, Pinterest, Evernote, Twitter, Live Binder, and more!

Find Lisa on twitter, Wednesday nights at 8:00pm EST for the New Teacher Chat (#ntchat).

This is by far one of my personal favourite podcasts yet! Huge thank you again to Lisa Dabbs for joining us…it was a pleasure to have you on, and we hope you’ll come back to continue the discussion another time.  Andrew and I really appreciate all that you are doing for new teachers.

SHOW NOTES

Each episode features three segments:

  1. Topic Discussion
  2. Quick Tip for Tomorrow
  3. The Rookie Resource Bank

Topic: Long Range Planning

photo by: Pedro Vezini

photo by: Pedro Vezini

Quick Tip for Tomorrow: Something you could do the next day in class with little or no prep and is applicable to most grade levels.

  • Andrew: About Me heads
  • Natasha: SMARTboard attendance
  • Lisa: One Little Word (http://goo.gl/NbNHO)
The Rookie Resource Bank: any electronic, print, or event resource that we found helpful in our first few years of teaching.  Of course, these are all applicable to all teachers.
Quick Shout Outs
  1. We will be working this summer to develop some content – what would you like to read about? Email or send us a tweet.
  2. Please join our discussions on Facebook.com/TheRookieTeacher
  3. We are also spending time gathering some great ideas for the classroom on Pinterest (http://bit.ly/rookiepins)

Like what you’ve heard? Have more questions? Contact us:

Rookie Teacher Online

We are always looking for ideas, feedback, tips and tricks of the trade.  Find us on Twitter @RookieTeacherCAFacebook.com /TheRookieTeacher.  If you are looking to get involved with our team, please contact us!

Thanks for listening. Join us for our Summer Podcast Series. Topics included will be: More about AQs, Classroom set up, the first day of school, Applying for Jobs, Setting up your Day Book, Developing classroom routines for your first month of school.

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Communicating in Math 1

Posted on February 10, 2012 by Michelle

Why is communication important in mathematics?

Communication is an essential piece in the learning process – it provides students an opportunity to justify their reasoning or formulate a question, leading to gained insights about their thinking. In order to communicate their thinking to others, students must be given authentic tasks to reflect on. Through cooperative learning, students can learn from the perspectives and mathematical processes of others. Further, they can learn to evaluate the thinking of others, building on those ideas for their own assessment.

Check out this Scholastic webinar on “Connecting the Literacy and Math Challenge”.

Teaching Strategies for Mathematical Communication

1. Math Word Walls

The purpose of the Math Word Wall [MWW] is to identify mathematical language that students need to understand and use. If they are unfamiliar with this vocabulary, they will struggle to effectively apply strategies in the problem-solving process and will have difficulty communicating their thinking with others.

♦ Introduce math vocabulary using relevant objects, pictures and/or diagrams. Visuals are KEY!

♦ Clearly explain word meanings and make connections frequently

♦ Do not teach math vocabulary in isolation — use open-ended questions to helping students understand mathematical ideas and model how to use mathematical terms correctly.

Check out these MWW resources – ideas for math walls and mathematics word wall

2. Children’s Math Literature

Using literature in math can spark students’ imaginations, helping to dispel the myth that math is dull, inapplicable, and inaccessible. Reading about math can help reach at-risk students who struggle in the mathematical process, opening their minds to the ever-present phenomenon in their world that is math!

  • Integrate the curriculum — teach mathematical concepts and skills through literacy
  • Helps to motivate and engage students in problem-solving experiences connected with real world
  • Addresses different learning styles and helps to promote an appreciation for both math and literature

Check out these resources for teaching mathematics through literature –

Math in Children’s Literature

Living Math Book List

Children’s Math Literature

Math Book List

Children’s Literature in Mathematics

 3. Writing in Math

When students are encouraged to write in math, they examine, express, and keep track of their thinking, which is especially useful for assessment and differentiation. To enhance and support their learning, students must first understand the reasoning behind writing in math. Further, they need to understand how to write in math – explain and model mathematical writing using details such as pictures, numbers, and words. Students’ writing can be used as springboards for classroom ‘math chats’, highlighting different approaches to problem-solving.

Be sure to provide writing prompts

  • What do you think? What idea do you have?
  • What are you confused about?
  • What did you learn?
  • Describe what was easy and hard for you.
  • What type of math concepts do you find interesting?  Why?
  • When I hear this math word, I think….
  • If I could ask for one thing in math, it would be…
  • Tell me about your prediction.  Were you right or wrong?
  • What strategies do you like to use the most? The least? Why?

Check out Writing to Learn Math to get started with journaling in your math class!

4. Math Talk

When students are given an opportunity to talk about math, they are better able to clarify their own thinking, ‘talk out’ misconceptions, and learn from others’ problem-solving strategies. It is the role of the teacher to facilitate these discussions by engaging students in sharing and listening, questioning and responding, and agreeing and disagreeing. During ‘math chats’, the teacher can further assess students’ understanding of concepts and redirect or differentiate instruction based on the students’ immediate learning needs.

However, the classroom must be a safe and inclusive learning environment so that students feel comfortable to share and make mistakes publically. Students need clear, highly set expectations on what ‘doing math’ looks like, sounds like, and feels like in the classroom. Once the ground rules for respect have been established, then authentic mathematical dialogue and collaboration can evolve…that’s when the real learning begins!

Math think-alouds can engage students and help them to make their way step-by-step through the problem-solving process. Best of all, they can be used quite effectively both in school and at home! For more on getting students to talk, check out these Math Teacher Tools!

Watch as these students from the Calgary Science School ‘talk math’ – thanks to Amy Park for sharing!

- – -

How do you […or will you] encourage communication in math in your classroom?

Original post at The Learning Journey Blog

 

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