math

October 30, 2021 Melissa Turnbull Kindergarten, Math, social emotional learning

Which One Doesn’t Belong? (WODB)

Have you ever tried ‘ Which One Doesn’t Belong?’ (WODB) in your classroom?

WODB is a short, number talk used to get students thinking before beginning a daily lesson or math activity. Students are shown a picture like the example attached below (from mathbeforebed.com). Students take a close look at the picture and decide which object they think does not belong. After sharing their ideas, students are asked to explain their thinking to justify their answer. Here is why we love WODB in our Kindergarten class:

There are no wrong answers

This gives students the confidence to share their thoughts and encourages them to take risks in their learning.

WODB shows students that there are multiple ways of solving problems

I am finding that aside from building confidence in students’ attitudes towards math, this activity builds community. Students typically begin with a strong opinion on why their answer is correct, but begin to understand and uncover the varying perspectives of their peers. It is also a great activity to practice turn taking, active listening and showing kindness towards others with different ideas.

There are multiple entry points

This activity is inclusive and allows students to use their own mathematical language to describe which one they believe does not belong. Students can participate in this activity regardless of their understanding of specific math concepts. In Kindergarten, with students ranging in various stages of development – this activity gives myself and my DECE partner a window into their thinking.

WODB promotes mathematical thinking and the use of mathematical language

When justifying their answer, students begin to use math words like bigger, smaller, shorter, taller, less, more and begin to use the names of shapes, numbers or symbols they are learning about. Students can activate their prior knowledge and apply their current knowledge while they work with educators to extend their knowledge. I often reframe what students are saying and repeat it back to them. For example, in the picture shown below a student may share that they think the “blue” one does not belong, “because it’s blue and the others are not” and I may say, “(student name) thinks that the blue rectangle piece does not belong”.

WODB can be used in any grade level

While I am currently enjoying this activity in Kindergarten, I think about all the ways this activity could be used with students of any age. As students learn new concepts, WODB could include pictures of fractions, decimals, equations and more. When students get comfortable engaging in WODB activities, they can even begin to create some of their own pictures to challenge their peers to think critically.

Which one do you think does not belong?

February 29, 2020February 29, 2020 Will Gourley Challenging Topics, Education Funding, General, Making a Difference Through Education, Math, Media Literacy, Modern Learning, solidarity, Why unions matter

6/194 and cross-curricular life learning

6/194 and cross-curricular life learning.

This blog title could also read, “Why a small fraction means so much to the future?”

I am trying to make sense out of some pretty important numbers that are affecting us. By us, I mean students, their families, and educators. “Us” also means the entire fabric of society that we share and by which we are covered. Since the currently elected government is seeking to tear this fabric apart without regard to the long term social and financial consequences, I thought it would be good to consider this post as a cross-curricular exercise and include social studies along with the math.

Whoa!(Math)

6, the number of days ETFO members have walked on the picket line fighting for public education.
194, the number of days in a given school year that we spend in the classroom making public education incredible.

Now a few more relatable figures.

3/97 or 0.030927835, just a shade over 3%. I had to simplify the fraction. Ironically, it’s the same amount that the government has legislated an offer to 83 000 ETFO, 117 000 educators (OSSTF, OECTA, AEFO), and 55 000 CUPE education workers in Ontario. Yup! 1% per year over 3 years.

Back to 6/194

That hole in our paychecks from this fight to protect and preserve public education hurts and the offer of 1% per year is unconscionable. Not surprisingly, the government padded their own pockets with 14% and took 7 of the last 12 months off(insert lesson about irony here). Since we’re talking about irony, why not share a real life teachable moment? I’m thinking a critical thinking exercise about the veracity of facts, content, and the credibility of media outlets especially where they originate or how news gets fabricated.

Want another amazing lesson? Check out this thread by @ms_keats This thread offers a wonderfully considerate lesson via Twitter after the MOE suddenly made Reg 274 an issue during negotiations with ETFO. Sadly, talks broke off, but since education is always their priority, the public can trust that the government was back to work at the bargaining table the next day because they are committed to a deal(Is sarcasm in the curriculum?). Isn’t that what unions and their employers do in good faith in a democratic society?

Wait! What?(Social Studies)

What do you mean the government wasn’t at the bargaining table?! This is a realistic expectation because we are teaching our students(grade 5) that Canada, therefore Ontario is a civilized society governed by lawmakers who are always respectful of the rule of law and the Canadian Charter of Rights and Freedoms? I contend that the current government is engaging in a systemic violation of our Charter Rights as citizens as their thoughtless actions threaten the rights to opportunity in the future of 2 000 000 students and the collective bargaining rights of 200 000 educators “not to be subjected to any cruel and unusual treatment or punishment”. This line from the Charter is not limited to the criminal justice system, and any intentional underfunding of education through ruthless cuts is tantamount to punitive legislation and is contrary to our Charter rights.

If that wasn’t enough to light a legal inferno, then consider that a 6 – 1 Supreme Court of Canada ruling affirmed that collective bargaining rights are human rights, and the role of collective bargaining has “in promoting the core values of “human dignity, equality, liberty, respect for the autonomy of the person and the enhancement of democracy.””

I’m sharing the quote below with bolded and underlined main points, if my MPP, the MOE, or the Premier read this;

“the Supreme Court proclaimed labour rights to be human rights, and boldly declared for the first time that collective bargaining is a “constitutional right” supported by the Charter.“

So our elected officials who have violated the Charter should now have to face the consequences for their malevolent disregard for the rights of its citizens. Right? I won’t hold my breath as legal cases against governments spend years in the courts. However, we cannot allow our elected officials to rule by decree without accountability to the whole public whom they have sworn to serve.

Civics does not equal civility

When will they pay for selling out the future and for the harm they will inflict to the well-being of the students in our province? We will not lose count of the lies, the streams of misinformed statements, the factless rhetoric, the accusations, the doubling down, the vilification of our noble profession, and of the requests we have made for them to come to the table and negotiate.

I also contend that the current government is angling its way towards a secondary agenda authored by pernicious profit seekers including publishers and private education providers looking for a piece of the public education pie. These steps do not appear to benefit our students. Our steps on the picket line have shown more to the public of our commitment to excellence than any sound bite, attack, or child care bribe put forth by the government. There is strength in our numbers.

Come to think of it, I have kept count of the steps I have stepped – 90 000 plus, the waves I have waved to drivers honking in support – 1 000s, the dozens of encouraging conversations conversed on the picket line, and the 3 people who waved with their middle fingers while yelling single syllable words.

It’s my first strike as an educator. Yet, it feels like our current fight against this government’s assault on public education is nothing new. Everyone remembers what Mike Harris and his ilk did in the 90s. The Ford Regime is Harris 2.0 complete with vitriol and misinformation spewing from a cadre of party whipped sychophant proxies acting as media drones du jour. In response, teachers are standing in solidarity together fighting for respect, transparency, and fairness on behalf of all Ontarians who will be directly affected by cuts to education now and in the future.

Teachers believe this so much, that have given up 3% of our wages already. We know that we are part of a world class education system because we work in it everyday. The results speak for themselves which is why it is so frustrating to see people trying to dismantle what is working well.

6/194 is a small fraction especially knowing how teachers, especially in 1997, fought for us. This will mean even more to the students of Ontario who will bear the burden or benefits because of our actions in the future.

Thank you for reading and for sharing on social-media.

Coding in Kindergarten

I have taught every grade from K-8 in some way, shape or form. I can say that without a doubt or apology I have more respect for Kindergarten teachers than any other grade level. Hands down. I have loved every grade I taught while I was teaching it. I was young and without children when I taught Kindergarten and can say that there is no tired like Kindergarten teacher tired. That being said, I absolutely love going into Kindergarten classes with robotics. Unabashedly Kinder friends approach you to ask your name and promptly tell you about the “owie” on the bottom of their foot as soon as they walk in the door.

I work with Bee Bots in Kindergarten classes to teach sequencing, estimation, problem solving, geo-spatial reasoning through coding. Bee Bots are a rechargeable, floor robots designed for early learning. It is easy to operate and does not require any other equipment.

We start as a whole group using the hundred’s carpet and decide how to move Bee Bot from our start to another point on the carpet. Students decide upon the directions and we program them in to find out what will happen. Wonderful mistakes happen here and we need to clear the code and start again. When we achieve our goal as a group there is much rejoicing!

It isn’t really about teaching Kindergarten kids how to “code”. Coding is used as a vehicle to teach many other transferable skills. Planning, organizing and communication are just some of the learning skills that come from using the Bee Bots. If you have access to the mats as featured in the photos, you can automatically see the ties to language and math concepts as well. There is a romance period that needs to take place when the students first get their hands on Bee Bot. However, even if they don’t know the words for “right” and “left” at first, they get to know them quickly through the use of Bee Bot. Bee Bots in many of our Kindergarten classes now have homes and some have villages made from found materials so that Bee Bot can be coded to go to different places. The possibilities for creativity really are endless.

For more information about using Bee Bot in the classroom, check out these resources:

https://krgarden.ca/media/hold/the-beebot-robot

https://blog.teaching.com.au/5-mathematics-bee-bot-lesson-ideas-for-the-classroom/

April 2, 2018 Michelle Fenn Classroom Management, Combined Grade Classes, Constant Learning, Curriculum Planning, Differentiated Instruction, General, Inquiry, Inspiring Students, Integration, Math, Modern Learning, Questioning, Resilience, Resources, Technology in school, The Global Competencies

Deep Learning in Inquiry (Part 2)

In reading part one of my inquiry blog, one might think, “That’s all lots of fun, but building a bee house isn’t exactly something that I can write on the report card.” You would be absolutely right. The learning is imbedded in the exciting things. It is intentional and it is authentic. Connecting with a local expert, using technology for research and having hands on activities with students engaged scratches the surface of inquiry. Our deep learning with this unit began with the types of questions that we were asking. I noticed that when the students began asking questions on Padlet that Siri could have easily answered many of their questions with one or two word answers. This lead to a series of lessons on “THICK” vs. “Thin” questions. We added better questioning to our goals.

The students also noticed that I had included a lot of infographics on the Padlet. Infographics are seen everywhere in social media to communicate information efficiently and visually. However, students need to know how to use this information, how to synthesize it, how to put it into their own words and how to source it. We spent a significant amount of our language periods on reading and interpreting infographics.

Source:Visual.ly

Our learning goals and success criteria went way beyond making houses for bees and honey tasting. Students wanted to DO something to help bees. We created our learning goals and criteria together:

Early on in the inquiry we watched an informative YouTube video called, We Can Save the Bees Together. Sarah Red-Laird, bee enthusiast and scientist, gave us a number of ideas of actions that we could take. The students decided that one of the things that they wanted to do was to call for stronger legislation about mono cropping and pesticide use in farming. They wanted to write letters to politicians and change makers. In addition, when Susan Chan, local bee researcher visited, she “planted the seed” about creating a non-stinging bee friendly garden in our school yard. This prompted students to write letters to local school officials to solicit assistance and guidance. One of our students from Curve Lake First Nation decided to write the Chief and Band Council to ask them to consider building a bee friendly garden in their community. The desire for letter writing lead to a series of lessons on how to write a professional letter, how to proofread and how to edit in a meaningful and authentic learning context for students. The students also felt that educating others about conservation of bees was important so they are now working on developing presentations that they can take to other classes as well as media advertising to share their learning and call others to action.

In math, we had been focusing on data management. It fit in perfectly to what we were doing with our inquiry! There is an incredible amount of data about bees on the Statistics Canada website. We read real graphs with information that the students cared about, we labelled the important parts of the graphs and we will be creating our own surveys and graphing the information from different areas of our inquiry.

Statistics Canada

Honestly, the best part of inquiry is when the students start to direct their own learning. I guide them. I provide thought provoking questions and “what if” scenarios. They make choices and feel good about doing something that is affecting real change. Inquiry is empowerment for students. This students aren’t done with this inquiry yet-they have many more plans ahead! Stay tuned.

January 30, 2016January 30, 2016 Will Gourley Constant Learning, Differentiated Instruction, General, Questioning

Waiting is worth its weight.

I wanted to share a post about the joys of waiting.

No it is not Health curriculum based so uncover your eyes and read on.
It might be worth the…time spent before something happens.
Ha! You thought I was going to write the word ‘wait’ there.
Dang it! I just did.

In the Tom Petty and the Heartbreaker’s song The Waiting the chorus goes, “the waiting is the hardest part” and in the classroom it is no different for teachers.

There are a lot concepts to cover. There are a lot of assessments (for, as, and of learning) to record. And yes, there are a lot of students to teach. One thing there does not seem to be enough of is time. So in an average, active modern learning environment, there is little time left to permit students to engage in anything but what Daniel Kahneman refers to as System 1 Thinking. Yet, what we need to be doing, more than ever, is allowing our students and ourselves to engage in System 2 Thinking.

Here’s a graphic comparing the two. Click to enlarge.

Understanding and implementing think or wait time in my classroom has changed the dynamics of learning for my students. It is no longer a contest to see whose hands can defy gravity the fastest or longest. It has increased the number of participants and ideas shared. It has deepened our discussions in many subject areas such as Science, Social Studies, and Literacy.

For my part, questions are crafted, whenever possible, that require the awkward silences achieved while learning and thinking beyond automatic or immediate responses. Letting students know before they respond that no hands will be acknowledged until think time has happened for the entire class has helped transition my instruction.

What about Math? Yes, even Math. Here’s an example to support think/wait time in Math from Kahneman’s book Thinking Fast and Slow that I share with students and adults alike:

A ball and a bat cost $1.10.
The bat costs $1 more than the ball.
How much does ball cost?

According to the book most people get this question wrong because they are engaging the wrong system of thinking. I did. So how can we as educators afford more think/wait time in all of our classrooms?

My suggestion is to slowly integrate it into your daily instructional routines. Be intentional with a few questions in specific subject areas to start. Be patient. The silence can be deafening at the start, but is worth it.

Want to know the answer to the bat and ball question?
Take your time. You’ll get it. It’s worth the wait.

February 27, 2015February 27, 2015 Shawna Rothgeb-Bird Literacy, Math

My Favourite Cross-Curricular Visual Arts Activities

I love Visual Art. It was always one of my favourite subjects in school and I was fortunate to have several teachers who engaged me in unique and exciting art projects. Tragically, I can’t have my students do Visual Arts all day, every day – bummer! Over the last few years, I’ve tried to find ways to integrate a bit of Visual Arts into many other subjects in ways my students don’t expect. Here are a few of my favourite projects from the last four years:

1) Quilts

What the project was: Working in groups, my class and another class of Grade 4/5 Middle French Immersion students designed, cut, and assembled baby quilts. At our annual art show, we ran a raffle for parents ($1/ticket). The proceeds from the raffle (over $300!) were donated to a charity. All of the material we used was donated by parents – much of it fabric ends from household projects, but some also salvaged from old pyjamas and blankets that were no longer wanted or needed.

What it taught my students: This project was a joint Visual Art and Mathematics project. From the VA side, it taught the use of tools (including electric sewing machines), complementary colours, patterning, and adapting to/solving design challenges. From the Mathematics side, it taught area and perimeter, measurement, and patterning.

What was challenging: We had 50 students cutting fabric, assembling quilts, and using sewing machines at the same time. The project took months (working one day a week) and the help of a few parent volunteers. I ended up giving up a few of my lunch breaks towards the end so that my students could finish their quilts before our art show.

2) Graphic Novels

What the project was: Students in my Grade 4/5 class each chose a fairy tale to retell in the form of a graphic novel. Their story had to be different in some way from the original without changing the overall message. They started by brainstorming, then created storyboards, then moved from storyboards to the actual comic panels.

What it taught my students: This was a joint VA/Language Arts project. From the VA side, it taught students composition, shading, line, perspective, and creating a narrative work of art. From the LA side, the expectations are always a little different depending on the grade level and program I’m teaching.

What was challenging: This project takes a long time. There are a lot of steps involved in getting to the final product, and students need a bit of guidance not to get too caught up in their storyboards. Many of them also needed to be encouraged to scale back their story so that it wasn’t 20 pages long – because 20 pages of comic panels is a LOT of drawing and colouring!

3) Carcassonne Variations

What the project was: Students in my Grade 4/5 Middle French Immersion class worked in groups to create their own versions of the board game Carcassonne. They had to plan/draw/colour their tiles and design a scoreboard. If they added any extra tiles that weren’t in the original game, they had to explain them with written rules.

What it taught my students: This was a joint VA/Mathematics project. I’ve used it to teach a variety of concepts in both areas. It changes a bit each year! For VA, I’ve used it to teach line, shape, colour, and texture. For Mathematics, I’ve mainly used it to teach probability (as the game involves drawing tiles from a bag) and fractions.

What was challenging: The first year that I did this project, I let students choose their own groups. Whoops! I ended up with several imbalanced groups – some with lots of artistic talent but who struggled with the mathematics side, others with lots of mathematical aptitude but who struggled with the artistic side, and everything in between. The next time I did this, I put students into groups, trying to balance artistic ability and mathematical aptitude… but as with any group put together by a teacher, occasionally my students had difficulty working together to plan and design a project like this.

Without going into too much detail, here are a few other Visual Arts activities I’ve done over the past few years:

Oliver Jeffers-inspired Picture Books (Visual Arts/Language Arts): We love Oliver Jeffers. His stories are whimsical, funny, colourful, and poignant. One of my favourite things to do with my students is have them create their own stories in the style of Oliver Jeffers. They get very creative!

Collaborative Mural (Visual Arts/community building): Each student received a piece of the mural without knowing what the final design would be. Their page had only black linework on it, with some areas coded to be coloured with hot colours and others coded to be coloured with cold. When they finished, we assembled them according to the numbers I had put on the back of each page.

Melted Crayon Art (Visual Arts/Science)

December 7, 2014 Alison.Board Assessment, Classroom Layouts, Differentiated Instruction, Diverse Learning Needs, Math, Planning, Professional Learning and Growth, Resources

Teaching Math

I have always considered myself more of an “English Language” teacher. So, when I moved into the junior and intermediate classroom, I felt less confident in my abilities to teach math. When planning for the year, I surveyed some other junior/intermediate teachers for recommended resources. And when planning for the classroom environment, I made sure to have a corner dedicated to math, which includes a gallery wall, manipulatives, math dictionary and texts as well as tools like calculators.

Although I was given a set of textbooks, I don’t plan or teach from the textbooks. I print the curriculum expectations specific to the grade for each strand, and use them as my guide in planning the units. Then I refer to some other resources for ideas in activities that involve group work or problem solving. Some of favourites to support my math program are:

Introduction to Reasoning and Proof, Grades 6-8: The Math Process Standards Series, by Denisse R. Thompson and Karren Shultz-Ferrell
Nelson’s Ontario Numeracy Assessment Package
Good Questions: Great Ways to Differentiate Mathematics, by Marian Small

By referring to these resources, I am able to understand the concepts that need to be taught and how to differentiate using broader questions for the range of math learners in my classroom. I enjoy providing mini-lessons on strategies to support the students as well as encouraging them to share their strategies with me and the rest of the class. Our math class has become engaging and interactive, not repetitive and boring as I had feared.

We use a gallery wall to display group answers to problems. This has become an invaluable way to quickly assess understanding. Students are given the opportunity to view the gallery, see how others have solved the problem, respond with their own ideas or suggestions and acquire new learning. A week of math classes includes a range of instructional strategies, independent work, paired and group work. One of our common “go to” questions is “Does this make sense?” We are aiming for understanding rather than rote learning of facts and steps (as I learned in elementary school). So, I am enjoying learning with my students as I discover new ways to approach and solve math problems.

January 14, 2013 Alison.Board Assessment, Communication Tools, Communication with Parents and Guardians, Interviews, Math, Report Cards

Math in Play-based Learning

Math is integrated into most of the learning centres in the classroom. Although glancing around the room, it often looks just like play. To ensure that I am continually assessing for math, I keep a clipboard of observations sheets accessible. I prefer observation sheets that have a square with each child’s name that I can fill-in with any pertinent information I want. Then, by glancing at the sheet, I can easily see if there is a blank box and ensure that I seek out that child to observe. Looking around the classroom, I may see children measuring at the water table, sorting in the drama centre, or comparing shapes in the building centre. I approach and listen. Often, I can record their understanding with a phrase or a brief description. Then, I am able to clarify or extend their learning. For example, if a child is counting animal figures and gets stuck at 15, I may direct them to the number line to show them what was missed. Observation and recording them at play allows for assessment of their current understanding as well as an opportunity to support their learning.

At the beginning of the year, some parents may ask about the math program, as they do not see generic math sheets coming home in the backpacks. It is therefore a good idea to take photos of the children engaged in mathematical activities as you are observing them in the classroom. These can be added to a website to communicate to your families what math learning looks like in the classroom. Or you can print them to display in the hallway, add to a student’s portfolio, or keep for a parent interview.

Recording comments during circle time is also another way to demonstrate a child’s understanding of math. Last week, when the children were considering a number line together, one student pointed out that there were kid numbers and teenage numbers. He said, “The 1-10 are like kid numbers and the 11-20 are like teenager numbers!” Another day we did a group activity when reading the book One Monday Morning by Uri Shulevitz. Using connecting cubes we represented the characters, as someone new arrived, each day of the week. When the concrete graph was finished, a student observed, “It looks like stairs going up!” By recording these comments, I am able to add them to their math profile when writing reports or planning for further learning.

The photos show what math looks like in a play-based learning environment:

This child is using 1:1 representation with counters on the light pad to represent each individual in our class photo (her idea!)

This child has sorted the animals into two groups and is then counting them as she places them on the top of the drums (her idea!)

These students are measuring volume by filling a larger container with a smaller one.

The children grouped like objects, sorted them, and displayed them on wood blocks using 1:1 representation.

There are also opportunities for children to write mathematically throughout the classroom with pencils and paper provided, as well as number lines and number displays of quantity. They use magnetic numbers to put in order on white boards and they learn to recognize their phone numbers at the carpet (after learning their first and last names), then write their phone numbers at entry during sign-in. Children enjoy songs with counting and books with sequences. Math is happening all around the classroom and children are intuitive with math. When teaching Kindergarten, it is important to see it, name it, and record it!