Since my last blogpost about Changing Results, we have had three sessions: two full days and one after school session.
In our full day session in late October, we began by reading an amazing anthology written by Richmond Primary educators called "What If?" This collaborative resource details the learning journey of several Kindergarten teachers who asked important questions that were reflective and responsive. We felt this was similar to our work, with the exception that our inquiry questions were focused on one child.
Inspired by the teachers in Richmond, we decided to take time to ask ourselves, "What do we believe about children and learning? We began by writing our thoughts on sticky notes and then categorizing these. Next we came together in small groups to with our notes and worked collaboratively to formalize our thoughts. It took time and few iterations but as you can see/read below, this was important work. We hope to continually revisit these beliefs and let them guide our work this year.
Connected to this, we spent some time thinking about the language we use to describe our students. Sometimes when describing our case study students or during classroom visits I have heard students referred to as "low, struggling, or at-risk". We've all done it, myself included. These deficit based terms stand in stark contrast to the aim of Changing Results. The Changing Results initiative is about honouring our students and believing in their abilities. Our goal is to accept children as they are - to discover and celebrate their strengths - to find out what they know and take action to help move them forward. Janice Novakowski wrote a thoughtful blogpost on "What does it mean to be a 'low' math student?" She asks teachers some important, challenging questions. We used some of Janice's thoughtful questions, in combination with some other quotes and dictionary definitions, as provocations for a deep discussion about the importance of our professional language.
My colleague Ginny Tambre, who is the Changing Results for Young Readers Advocate, serendipitously was reading Charlotte's Web just before our session and came across the following passage. She wondered if Charlotte knew something we, as teachers, could learn from. What power lies in the words? Do we live up to what others believe about us?
Perhaps, we could try to be more like Charlotte and with our strength-based words we could develop children who believed in themselves. Together we committed to making a change in the language we use and seeing where that takes us. Below is a copy of what we created:
When we reconnected again this past week, we continued to talk about the power of our language as teachers, and how what we say matters. Two of our teachers led us through an activity for our book club. We are reading Tracy Zager's Becoming the Math Teacher You Wish You'd Had. They asked us to read and sort several statements teachers often use into piles that would or would not encourage student risk taking.
Some phrases were easier to sort than others. We discussed that our tone and intonation matter, as well as our knowledge of our students. For example, the phrase "I have a great challenge for us today" may cause some confident students to feel excitement; whereas, a student with a diminished belief in their mathematical abilities, may be intimidated by this statement.
It was another reminder that what we say matters. As teachers, we hold a great deal of responsibility in setting the tone of our classrooms. If we want to create safe spaces where our students believe in themselves, take risks, see mistakes as learning opportunities, then we must intentionally develop this. We do through our daily interactions with our students, the learning opportunities we design for them, and through taking the time to reflect on our actions to ensure they match our core belief and intentions.
And with the blink of an eye, another year has passed! The recent winter holiday was wonderful. We had two weeks off after Christmas which allowed time for much reflection on the year, a renewal of energy and spirit, and time to think about my 2018 One Word. Choosing a single word to guide my year has been a tradition I have been doing since 2012. I've written previous blogposts here and here. I've never been a big fan of New Year's Resolutions, as they felt a bit like a pass/fail test; whereas, choosing a profound word to inspire and create intention in your life sounded far more inviting!
Placing emphasis on "hygee" helped me to move beyond a year of sadness (the loss of mom) and into a place where I could take comfort in the sanctuary of life. Simply being home with my family, or time spent alone, or through togetherness with others, I felt love, joy and a general sense of well-being. Small things like nightly walks with the dog and Scott, a cozy pair of socks, lit candles, new jammies, and hearing "I love you" from either M & M - all of these things brought me gratitude, serenity and inner peace. This was much needed.
In September, I started a new position in my school district. I went from multiple roles to a district position where I support teachers and students in Numeracy in a broader sense. With any change, there is a ton of learning and challenges. There are also many positives, like developing relationships with 'new to me' colleagues. My learning curve has been steep and my pace has been insane (a result of not knowing what I don't know, wanting to do well, and the high expectations I place on myself). A pace like this doesn't leave important time for reflection and causes the work-life balance to tilt. My colleagues shared their wisdom with me, but as we know, learning needs to be experienced. And I needed to learn from my own experience.
Having four months in the new role, and understanding the power of a word to make a positive impact, this year my 2018 word is CULTIVATE. I truly believe that we create the life we want. Joel Osteen, speaks of the power of "I AM" in his book, The Power of I Am. He says "whatever words follow the words 'I am' will determine what your experience will be. You can either speak defeat or power into your life".
Generally speaking, I consider myself a fairly optimistic, positive person, but these past few months professionally, self-doubt has crept in. Similar to a first year teacher, I have felt overwhelmed, compared myself to others, and felt an overall a lack of confidence. Herein lies how my One Word 2018 originated. Brene Brown, talks about WholeHearted Living in her book Daring Greatly which I read this past summer. She refers to ten guideposts.
Professionally, her ten guideposts struck a chord with me this holiday when I picked up her book again. I saw myself and a need to cultivate. If I want to create a life where the words that follow "I am" include "enough and happy" I needed to stop speaking defeat into my life. Things need to change; I need to cultivate.
Moving forward professionally, I will:
What word will guide you this year? #oneword2018
With Halloween only two days away, I am wondering how teachers are connecting with their students' interests in this holiday to design engaging Mathematical learning experiences. There are some outstanding children's literature books that provide wonderful connections to mathematical concepts. Some of these include:
How Many Seeds in a Pumpkin is a classic. Using a class pumpkin, or individual student pumpkins, students can:
- estimate how many seeds will be in their pumpkin
- use a graph to help them determine how to carve the class pumpkin
- estimate and then measure the circumference of their pumpkin using strings
- estimate and measure the height of their pumpkins using cubes
- count the number of lines around the pumpkin
Another fun Halloween book is 2x2 = Boo! This book can be used to explore multiplication. Similar to the classic game Circles and Stars by Marilyn Burns, students can roll two dice and play "Spiders and Webs". Students will need cotton balls or large elastics for the webs and some mini spiders, which can be found at the dollar store this time of the year. The first dice rolled represents the number of webs the students will need to make and the second roll will represent the number of spiders they need to place in each web. They will build these. Then using a whiteboard students can explore writing a "groups of" statement (e.g., 4 groups of 8 spiders is 8 + 8 + 8 + 8 or 4 x 8). Recently I visited some Grade Three classes to engage in Number Talks. I used images of Halloween cookies placed in arrays to spark multiplicative thinking. The students were able to see the equal groupings and made connections between repeated addition and multiplication, as well as the commutative property (e.g., a x b = b x a). I've shared these images under the Instructional Ideas tab so that others may used these and the app Skitch to have similar discussions with their students.
This is just a small sample of ideas. There are many other Halloween books, including Franklin's Halloween where you could delve into looking at combination problems. Others I'm excited to check out include Bats on Parade and Bat Jamboree! I would love to hear more about your favourite Halloween children's books and any Halloween'y Math lessons you've tried. Please leave some ideas/comments below!
In September of 2015, the Surrey School District began its Changing Results for Young Mathematicians initiative, as part of the British Columbia Provincial Numeracy Project. Several District's were involved, each enacting the project in different ways.
In Surrey, the initiative took a similar format to Changing Results for Young Readers and followed the key phases of the Spirals of Inquiry written by Linda Kaser and Judy Halbert. Teachers began by spending time closely scanning their students and selecting a case study student based on questions that were emerging from their observations. Through reviewing the information they collected, they began to focus in on one area and asked themselves "What might I be able to do that could make a difference for this child in relation to..." Some of the teachers' questions included trying to build students' confidence in math, fostering students ability to communicate their understanding, improving a students' number sense, assisting students' in developing a growth mindset and positive disposition towards math, and building students' conceptual understanding of mathematical concepts. Each of the teachers took different actions to achieve results. Every six weeks we would come together as a group to check in and collaboratively reflect upon our actions. We asked "What did you try? What did you observe? What worked? What didn't? Where to now?" Generally speaking, teachers participated for two years. This cyclical process continued every six weeks and ended in June with teachers capturing the process of inquiry through writing two learning stories: the first included the story of their case study student; and the second story was their own.
This year we have 13 teachers who are participating in their second year. They come from the following five schools: Hjorth Road, William Watson, White Rock, Cambridge, and Beaver Creek and teach Kindergarten through Grades Five. During our first session last Wednesday afternoon, we began by forming a circle and "arriving". Each of us took a turn sharing a bit about our experience last year in the initiative and finishing our sharing with the following phrase "... and that's what brought me here today!" It was evident through what was shared, each teacher realized the powerful, positive transformations that can occur both for themselves professionally, as well as for their case study students when they participate in a collaborative professional inquiry.
Following our "arrival" we broke into three small groups and each group was tasked with re-creating the spiral of inquiry. They were given red yard, the key headings (e.g., Scanning, Developing a Hunch, Focusing, New Learning, Taking Action, and Checking), descriptions of the headings from the article linked above, and excerpts from the learning stories these teachers had written at the end of last year.
It was so interesting to see how each group created a different shaped spiral. The discussions were rich... "should 'new learning' come before taking action, as we need to learn before we move forward OR should it come after checking, as we learn from checking what is working and what isn't and based on this we enter the cycle again." And "it sounds like this teacher shifted her question based on what she observed, so do we need to take and create another circle on top of the first, as she is in her second cycle?" Each group asked for more yarn as they felt there wasn't enough to show the recursive nature of inquiry. Although all names had been removed, the teachers smiled when they read excerpts they had written. This activity helped us to reconnect with the important work ahead of us.
Next, it was time to delve in. We chatted about how we were getting to know our students. What were we noticing? Beyond gathering initial Numeracy assessment (e.g., WDTK, Early or Late Numeracy Assessment), we wondered what questions we should be paying attention to when selecting our case study student? We were appreciative of Carrie Gelson's blogpost on "The Power of Observation" where she suggested powerful questions teachers can ask themselves during daily classroom activities to help them learn about their new students. For example, during a math activity, Carrie asks "Who is a self-starter? Who takes risks? Who likes to work with others? Who is persistent?" These are important considerations. We discussed what other questions came to mind when thinking about our own classroom contexts. Letting the answers to these questions, as well as any other information the teachers had gathered, guide us, we requested that by our second session in October the teachers would return having selected a case study student and with a completed scanning template. These teachers collaboratively created this template last year.
We really look forward to another year of collaborative professional inquiry - working together, remaining curious, asking important questions, checking out hunches, delving into new learning, and taking action for our deserving students! Together we can and will make a difference!
Note: I use the pronoun "We" throughout, as I have the good fortune of working with my friend and colleague Ginny Tambre, Surrey School District's Changing Results for Reading Advocate, to collaboratively plan our sessions.
Last week I continued to work with two teachers at Betty Huff who teach Grade 3 and 3/4. On Monday, I popped by their classes to assist in introducing patterning. Inspired by Kristen's Gray's blogpost on Talking Points, which she used as a pre-assessment, we decided to try this strategy with the Grades 3/4 class to see what the students knew about patterns, as well as reveal any misconceptions they may have. We reviewed the revised curriculum for Grades 2-4, in particular the learning standards for patterning to determine the talking points to use. I've added the word doc file for the patterning talking points below the post, should you wish to adapt these and try it with your class.
Since "Talking Points" was new to the students, we decided to adapt it from its original version. For those of you who have never heard of Talking Points, you'll want to read either Kristen Gray's blog post or the one on Cheesemonkey Wonders site. Instead of using Talking Points in small groups, which we will do one day, it was decided to begin by using it with the whole class so the students could see how the activity works.
Prior to coming to the carpet area, we had the students read each of the five Talking Points and where it said "Round One" they marked whether they agreed, disagreed, or were unsure of the point. Next we gathered at the carpet and each student was asked to share aloud what they wrote and give a reason why. The other students listened to each of their peers but did not add any comments. As we went around the circle in the first round, the teacher and I quickly realized that although many students agreed "Patterns are predictable," they really had very little understanding of increasing or decreasing patterns, positional patterns, using numbers to describe patterns, and whether or not patterns could help us solve problems. Most students explained that they "couldn't remember doing that last year" or "I've never tried that". This was really important formative assessment. The teacher and I realized that we needed to spend some time revisiting repeating patterns and exploring positional patterns before we could investigate increasing and decreasing patterns. We wondered whether what the children knew was representative of their knowledge or perhaps indicative of lack of experiences with these types of patterns? In speaking with another Grade 3 teacher, she mentioned that they had only worked with pattern in September and not since.
Being responsive to what we were hearing, we knew that moving ahead into Round Two wouldn't necessarily cause any new thinking, as so many were unsure. We decided to tweak our plans and had the students return to their tables and engage with creating patterns. We had set up materials prior to the class and in retrospect, I wish we had of provided a table area where all the materials were the same (e.g., same size and colour) such as beige toothpicks for the students to explore creating patterns using one item in creative ways such as positional patterns. There were opportunities for students to build increasing/decreasing patterns. We hoped these experiences might activate more prior knowledge and/or cause students to shift some of their thinking.
After about 30 minutes we had the students stop what they were doing and do a gallery walk. Then we cleaned up and met back at the carpet. The students recorded their thoughts in Round Two and we went around the circle and shared again. This time, the students had more to say. Their rationales were stronger, as they could connect with an experience. We stopped after the second round because we wanted the students to have time to write in their Math Journals. We asked the students to write:
Here are a few of their responses:
I was pleased to see how some students used examples to explain their thinking.
The next time the teachers have the students reflect in their Math Journals, they will highlight examples like this, so students are able to see how using examples can strengthen their arguments.
Additionally, when reading their reflections, it became evident that students did not have some of the mathematical vocabulary around patterns. For example, in the last journal below, the student wrote "...patterns are predictable because you can always know what comes next when you do 3 or 2 shapes". I wonder whether she understands the term elements or what a pattern core is? These are important for clear communication.
I am excited to continue to use Talking Points to explore students' understanding. We will revisit these points again upon completion of this unit (and likely there will be a blogpost!). Although the teachers will wrap up the patterning unit at some point, the teachers realize that this does NOT mean they are done patterning for the year. As we know from the First Peoples Principles of Learning, "Learning takes time and patience". We need to remember that learning is recursive. Patterning WILL be revisited throughout the year. These teachers intentionally will include patterning in their daily number routines (e.g., an image of pattern is presented and students guess the rule, predict the fifth term, etc.), including patterning activities daily math investigations and weekly rich problems, and whenever it makes sense to do so.
Today I had the pleasure of working with a lovely Kindergarten class at Jessie Lee Elementary to introduce Counting Collections.
I began by reading aloud the book If A Chicken Stayed for Supper by Carrie Weston. In this delightful tale, five little foxes sneak out of their den, despite being told by their mother to stay home while she goes out looking for dinner. While out playing, the foxes begin to worry that perhaps one of them may get lost in the dark. The eldest fox, Tufty, decides she will take charge and count her brothers and sisters. She taps each fox on their nose but forgets to count herself and mistakenly thinks they have lost someone. All of the foxes begin to cry. Next, the second eldest fox, Mufty, tries his best to count, pulling each fox's tail but again he forgets to count himself and ends up with a count of four. Again, the foxes think they are one short. In the end Mother Hen comes to the rescue and lines up all the foxes and taps each one on their head. The foxes yap with joy! "You've found one of us! Thank you! Thank You!"
I use this engaging story to springboard children's ideas about strategies they can use to keep track of quantities when counting. We discuss, what different ways did the foxes and Mother Hen use to help keep track? How do you keep track? To assist the students with one-to-one correspondence, we provided five and ten frames, as well as small soup cups for the students to use should they wish to. We explored how these 'tools' help us to organize our items and potentially see groups of items. For many students, having cups available to place one counting collection item in at a time, helped them to keep track. Sometimes at this age children will skip an item when counting or count the same item twice. Additionally, not all children have a solid understanding of the stable order of the numbers (e.g., they might say "one, two, three, five"... skipping four). Counting collections provides a wonderful opportunity for one-to-one correspondence, learning the correct of numbers, and cardinality (knowing the last number you say represents the total amount of the set) .
For more information about Counting Collections, please check this blogpost and under the Ideas section - Counting Collections.
Sept 29th update:
An important point another Numeracy Teacher (thank you Janice) reminded me of, is the focus on working with partners in September. Counting Collections is something we do with others. In the K class on Wednesday we discussed how we work with partners. How do we respond to a partner when we hear there name called with ours? We modelled some positive options, including giving a "high five" and saying "I'm happy to be your partner". In a respectful classroom community, students need to understand that they will be required to work with others in friendly ways. We included the students in helping us to determine how to work out who chooses the counting collection bag and who chooses the tools. On this day, it was determined that the taller partner would choose the collections. We also modelled how to help each other to organize the collections and take turns counting.
I've also had some questions about the yellow stickies. I've always had stickies and markers available in my tool kits for students who wish to record their estimate and/or to record their actual count. At this point in the year in Kindergarten, many students are just learning how to form numerals, so writing the numerals should NOT be a requirement. The stickies are there if students wish to use them, but many won't and this is fine. In reflection, I think I would take the stickies and markers out of my tools bin when working with Kindergarten students for the first several months, as writing numerals is not one of the learning intentions of this activity. If teachers were wondering whether their students could match a quantity to a numeral, there are many other, more engaging ways to do this (e.g., build a set, roll and make the matching playdough number)
This week I visited a Grades 3 and Grades 3/4 class at Betty Huff Elementary. The two teachers and I met during the first week of school and worked collaboratively to discuss how to begin the year. I am working with these teachers this term to support their professional inquires which focus on developing their students curricular competencies in relation to content, as well exploring what inquiry-based practices could look like in mathematics.
We began by creating a mini-unit exploring the following questions: What is math? What does it mean to do math? Where does math live in the world? Additionally, we wanted students to begin to explore their own identity as a math learner. This is an important aspect of BC's redesigned curriculum. The Positive Personal and Cultural Identity is one of our core competencies and includes the awareness, understanding, and appreciation of all the facets that contribute to a healthy sense of oneself . We wondered how our students saw themselves as Mathematicians.
We began with an activity I had seen on Graeme Anshaw's blog where he asked students to share their personal histories with mathematics. The teachers gave each student a sticky and ask them to write or draw how they felt about math and why. Then students were invited to share their thoughts with the class and place their sticky on the line spectrum. The teachers commented how through this activity they were able to learn about the mindsets students held with regard to mathematics. As you can see the Grade 3/4 class held more positive views, while the Grade 3 class was more mixed. The teachers remarked how curious they were to dig more deeply into these stories and work with these students to shift some of their negative feelings.
I visited the class on the second day of the mini-unit. We began with the question "What is Mathematics?", and surprisingly, we learned that not all children had an understanding of the word "Mathematics". They didn't realize it was just a longer version of the word "Math"... an important reminder that all children are "mathematics language learners" and we must pay attention to the language we use.
When reflecting upon the charts, we were able to see similarities to the work that Tracy Zager and Deborah Nichols reported hearing from a Grades 1/2 class (pg. 11 - 13 in Becoming The Math Teacher You Wish You'd Had). It seemed that our students felt mathematics was mostly about computation. Their experiences had been many worksheets, which they felt was really hard.
Inspired by Tracy Zager's suggestions to use books to help expand children's view of mathematics, we read aloud On A Beam of Light: A Story of Albert Einstein by Jennifer Berne. Before beginning the book, we passed out "Notice/Wonder" sticks to the students. We asked them to raise their "Notice" glasses if they noticed anything in the book that they thought represented mathematics, which we would add to the chart. Additionally, student were asked to raise their "Wonder" question marks if they thought they might have seen or heard something that could be added to our chart, but were unsure. Credits go out to Beth Kobett who shared the idea of Notice and Wonder sticks on Twitter.
Below is the mini-unit we created including using ideas from Tracy Zager's book, Jo Boaler's inspirational week of maths, and Graeme Anshaw's blog. Feel free to leave any feedback you have on our mini-unit. We welcome your ideas and suggestions! I am curious how did you start your year with your Mathematicians?
Friday was the Provincial Professional Development day in our province, BC. I had the pleasure of co-presenting with Lisa Schwartz, Richmond School District's Literacy Consultant. You might be asking yourself why a math educator like myself would be presenting with someone with a literacy background. Well, not only are we friends, but over the years in our discussions about teaching, we have come to realize that their are many commonalities between developing readers and mathematicians. In our presentation we shared many of our favourite children's books and how we have used them for both literacy and mathematical learning intentions.
In Laney Sammons book Building Mathematical Comprehension: Using LIteracy Strategies to Make Meaning, she uses a chart to discuss the similarities readers and mathematians share.
These similarities are yet another reminder that our habits of mind, or core and curricular competencies, as now called in our revised BC Curriculum, are important! In order to develop as mathematicians or readers, our students need to:
It is this knowledge about the importance of our processes to develop understanding, that is one of the central tenets at the heart of the new curriculum. Our curriculum is no longer solely focused on content. Although, I would argue it never was. The processes in the 2007 BC Math IRP mirror many of the curricular competencies, but through the physical design of the "Know, Understand, Do" (KUD) model, the curricular compentencies have been lifted and made a priority.
Using this framework, as well as a belief that learning needs to include all of our children, Lisa and I worked with several children's literature books to create learning intentions for both literacy and numeracy. The following is an example of one of the books I used.
Brown Bear, Brown Bear, What Do You See? by Bill Martin Jr. is a classic picture book that students and teachers have enjoyed reading aloud for years. Using the book, we designed learning intentions for all, some and a few, as you can see below.
Working with a Kindergarten class, I did an interactive read aloud and engaged with the book prior, during, and after reading to make predictions, ask questions, explore mathematical ideas, and engage in problem solving. Hintz and Smith (2013) describe this process as "mathematizing". Mathematizing is a way of looking at the world through a mathematical lens. Through reading motivating children's literature books, students are inspired to read and write. They are also able to make connections and build their schema in meaningful ways.
The Kindergarten teacher and I were not sure if the students would be able to represent how many animals they saw in the story. When we used the concrete felt animals the students could touch and count, using one-to-one correspondence to count and tell how many (cardinality). Once back at their tables, it was going to be more complex to represent what they were seeing and hearing in the book. We were excited to see the different strategies the students might think of to use. Some used tally marks but without a diagonal line crossing over four vertical lines. A couple students drew pictures, and a few used checkmarks. Their representations provided excellent assessment for learning because we could see the child's sense-making through the images they created. We made note of a few children who were beginning to use numerals to tell information. As well, by reflecting on the emerging tally marks, we knew one of our next steps would be to explicitly teach how we organize tally marks. The representations also provided us a record that we can use for assessment, to compare to later in the year to note any differences and growth.
Following this lesson, the students enjoyed reading the story once again and following it up with sequencing the animals in the story. Everyone had fun reading the story aloud as a class, while touching their sequencing strips. This familiar story gave all of the students an opportunity to see themselves as readers. Later in the week, the Kindergarten teacher worked collaboratively with the students to co-create a class book, with a similar pattern. This new, class authored book is now a class favourite.
What I was reminded of while planning for this presentation, is that teachers do not have to simply use books with explicit mathematical concepts to explore math concepts. Instead, I believe almost any book could be used because when you dig deep enough, in my experience, math can be found in just about any situation. What favourite books have you used with your young Mathematicians? I am always looking for new ideas.
Hintz, A. and Smith, A. Mathematizing Read Alouds in Three Easy Steps. In Reading Teacher. 67(2), May 2013.
Sammons, L. (2011). Building mathematical comprehension:. Huntington Beach, CA: Shell Education.
I love returning to school in September. I get giddy with excitement purchasing school supplies and can't wait to meet my new students.
This year my two kids have started Grades 6 and 8. They also share my love of picking out colourful pencils, pens, binders, and such, but since we didn't know what was required for high school I told my son we would purchase his supplies at the end of the first week.
Last weekend, I took the necessary time to review my son's course outlines. Generally they were as I expected but it was a comment from my son that caused me pause. He told me that he needed more pencils and a bigger eraser for Math. He said that all his Math work had to be done in pencil and the erasers at the end of pencil weren't going to be big enough to erase mistakes. Herein, is where my mind started buzzing with questions.
This long-standing tradition of using only pencil in Mathematics so students can erase their errors doesn't make any sense to me! We don't insist on using only pencil in any other subjects, so why Math? In writing, when students review and revise their work, they simply write on top or under what they have written, cross one word out and add another and add indentation marks to show where they have added. This makes it possible for teachers to see the trajectory of learning. Likewise, when children read to us and they make a mistake, we don't halt them and say "stop, that's incorrect"; instead we give them time to see if they catch their mistake and self-correct and then we discuss the error and strategies to help the student. The practice of writing in pencil so that we can erase mistakes in Math runs contradictory to all the current research we know about developing growth mindsets, honouring process over product, and capitalizing on opportunities to move our students' learning forward. Jo Boaler writes
Studies of successful and unsuccessful business people show something surprising: what separates the more successful people from the less successful people is not the number or successes but the number of mistakes they make, with the more successful people making more mistakes (Mathematical Mindsets, 2016, p.g. 15)
If mistakes are a necessary part of our learning process, then why are Math teachers asking children to erase them? I believe mistakes should be seen positively, as they show what the child currently understands and any misconceptions are opportunities for learning to occur. Furthermore, we know from both research and experience that when we build classroom communities that are safe to take risks and use errors for instruction, we have the potential to increase our students' understanding (Bray, 2013). Why would we give up this opportunity by encouraging erasing?
I have wrestled with this idea before. Two years ago I sat frustrated trying to figure out my son's understanding about adding fractions with different denominators.I knew he had some misconceptions but I couldn't make sense of his thought process because the work he brought home from school had been fully erased. He had shown his teacher his work and was told to erase it and re-do it. I then asked his teacher to please refrain from having my son erase and explained my rationale.
Here we are two years later with more knowledge about the importance of mistakes as part of learning and I am unsure if we are further ahead. I would like to be able to tell you that both my children are using only pen in their Math classes but that wouldn't be the truth. They don't want to stand out against their peers or make their teachers unhappy so they continue to use pencil... but they no longer erase (at least that I can see).
As I move forward supporting both teachers and students in Math classes this year, I will be bringing with me a beautiful tin of colourful pens, with all sorts of interesting designs, including some that are smelly! We will use these to record our Mathematical thinking and understanding and there will be NO ERASING! All thoughts will be valued and mistakes will be seen positively, as part of our learning and growing process!
I am interested to hear others thoughts on this topic and the role pencils and erasers play in your Mathematics classes. Please feel free to add a comment.
Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages, and innovative teaching.
Bray, Wendy S. 2013. "How to Leverage the Potential of Mathematical Errors." Teaching Children Mathematics 19 (7): 424-431.
A couple of days ago I tweeted that I thought I was going to like this resource and some folks asked me to let them know my thoughts. Well, as I thought, this book did not disappoint!
Authors Linda Dacey, Karen Gartland, and Jayne Bamford Lynch share some engaging new number games and puzzles and twists on old favourites like "Go Fish Numbers" (e.g., students search for "packs" of three matching representations of a given number). They also share a few free online games for each conceptual area. Although I really liked the games/puzzles in the book, what impressed me the most were the points they raised around the teaching of games/puzzles; these were highly insightful! Some of my take aways from the book include:
My only suggestion (and this is for the editor) - is that I wish there was an online url link where I could go and print out the blackline masters in the standard 8.5 x 11 size. It is just a minor detail but one that would save me time and as teacher, that is something we could all use more of.
I highly recommend this resource and intend to use it this coming year!
I am a Numeracy Helping Teacher with the Surrey Schools District. Each day I am thankful for being able to work with amazing students and teachers in an area I am passionate about ~ Mathematics!
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