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Archive for the ‘Assessment and Evaluation’


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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Observation and Anecdotal Notes – Record Keeping Made Easy – Assessment & Evaluation 0

Posted on July 18, 2013 by Natasha

BUZZWORD: Triangulation (Conversations – Observations – Student Products)

This is a great way to summarize our job as educators.  We will have meaningful conversations with our students, listen to the vocabulary they use during peer to peer conversations, and prompt them to think deeper and more critically about their learning.  We will observe how they approach new, routine, independent, partner, group, and class tasks.  We will watch as they think out processes, make mistakes, and get messy.  We will assess, evaluate, and provide descriptive feedback on all the products that they pour their heart and soul into.

Most importantly, we will track and record it all.

But how?

CONVERSATION:

What methods do you use to track students? Old fashion pen to paper?  Technology application?  Comment below, on Facebook, or Twitter.

https://www.google.com/search?as_q=teacher+assessment+and+evaluation&tbs=sur:fc&biw=1280&bih=569&sei=M_3mUfr4FKaDywGT24HgBQ&tbm=isch#tbs=sur%3Afc&tbm=isch&q=teachers%20teaching&revid=1889124126&ei=Av_mUdJirobJAbO4gKAM&ved=0CAsQsSU&bav=on.2,or.r_cp.r_qf.&fp=40a59d8e4f21729c&biw=1280&bih=569&bvm=pv.xjs.s.en_US.QXiTEk6XjhM.O%2Cpv.xjs.s.en_US.QXiTEk6XjhM.O%2Cpv.xjs.s.en_US.QXiTEk6XjhM.O&facrc=0%3Bteachers%20teaching%20kids&imgdii=_&imgrc=_

photo via CreativeCommons

EXPERT OBSERVATION:

Conferencing and reporting are changing

Knowing What Counts Conferencing and Reporting Second Edition

Knowing What Counts Conferencing and Reporting Second Edition

“The process of conferencing and reporting is changing from a teacher-directed, end-of-term event to a collaborative ongoing process designed to support learning.  Many educators and parents/guardians not recognize conferencing and reporting are taking place when

        • students show and talk about work samples with someone at home
        • parents look at their daughters website and respond to her by pointing out their favourite parts and asking questions
        • an uncle comes to view a nephew’s portfolio during a portfolio afternoon and writes a note telling three things he noticed about the work
        • students invite their former kindergarten teacher to a poetry performance where they demonstrate their skill
        • student, parents, and teacher meet to look at student work and to set new goals

Parents, students, and teachers are identifying conferencing and reporting practices that effectively communicate and support student learning.”  (Knowing What Counts: Conferencing and Reporting: Second Edition – K.Gregory, C.Cameron, A.Davies, 2011)

Teacher Comments

Growing Success: Government of Ontario

Growing Success: Government of Ontario

“In writing anecdotal comments, teachers should focus on what students have learned, describe significant strengths, and identify next steps for improvement. Teachers should strive to use language that parents will understand and should avoid language that simply repeats the wordings of the curriculum expectations or the achievement chart. When appropriate, teachers may make reference to particular strands. The comments should describe in overall terms what students know and can do and should provide parents with personalized, clear, precise, and meaningful feedback. Teachers should also strive to help parents understand how they can support their children at home.”  (Ministry of Ontario Document, 2010)

PRODUCT:

Observations/Anecdotal Notes

Download a copy of Natasha’s Observation and Anecdotal Notes Blackline Master over at her TeachersPayTeachers Store.

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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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Giving Feedback Part 2 0

Posted on December 18, 2011 by Andrew

photo by: Generationbass.com, flickrcc.net

As a teacher who is focused on giving effective feedback to my students, I find the biggest obstacle is time, and I use organization to help maintain levels of feedback in my class.  Here are some strategies I have gathered to help with time/organization:

Treasure Books: Each student maintains a small workbook/notebook  of the feedback when we conference. We use the same 3 part feedback, and both the student and I write in the book. I also staple/glue conferencing assessment sheets we might do together (to essentially create an anecdotal notebook for each kid).

Daily Conferences: I have assigned students to each day of the week, in the same order, so I can ensure I either meet with all four of them as a group for guided instruction, or have a student-lead conference on a individual basis.

Blastoff

photo by: jurvetson, flickrcc.net

Success Criteria: Students help create checklists and visuals for their own work and then we use them. Each checklist is interactive based on the criteria of the assignment. For example in an assignment on re-telling a fiction story, you could have the student circle their setting in yellow, underline the resolution of the conflict in purple, etc.

What do you do to organize your time so that is most productive for you and your students?  Leave a comment below or join the discussion on Facebook.

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Giving Feedback Part 1 0

Posted on November 20, 2011 by Andrew

Giving feedback, and in particular specific and actionable feedback, is the big push as a goal for teachers in my school as well as our Board. As an opener to the topic at our most recent PD Day, one of the principals shared this analogy made by the comedian Jerry Seinfeld…

“I always did well on essay tests. Just put everything you know on there, maybe you’ll hit it. And then you get the paper back from the teacher and she’s written just one word across the entire page, ‘vague.’ I thought vague was kind of vague. I’d write underneath it ‘unclear’ and send it back. She’s return it to me, ‘ambiguous’. I’d send it back to her, ‘cloudy’. We’re still corresponding to this day…. hazy…. muddy…” Jerry Seinfeld

As a Primary Teacher, our Grade team created a framework that we shared with our students to make sure they understood our feedback and could use it to help inform and improve their learning. We made it with a visual diagram and used common language in the hope that students would be able to use it on their own.

Our analogy breaks our feedback into three parts, on the theme of Pirates and Treasure.

secret by MistoAcrilico

Secret by MistoAcrilico (flickr)

First, we look for “Treasure” in what they have done: the things really stand out as amazing aspects of a student’s written work.

Second, we look for the “X Marks the Spot”: where could students find their next treasure (one thing they could improve on).

Finally (and what I would say is the most important aspect) is the “Map”: we as teachers have to give them advice and direction on how to get to the next set of “Treasures”.

We are currently in the process of gradually releasing that idea to the students to see if they can self or peer assess using that framework. I’ll let you know how it works over the next few weeks in my classroom.

In my next post I’ll list other acronyms, mnemonic devices and strategies for feedback that were presented at the PD Day.

Looking forward to your feedback!
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