Math – Page 6

November 21, 2017 Deb Weston Assessment, Homework, Interviews, Math

Does Homework Work?

The Purpose and Politics of Homework

After teaching for over 18 years, one topic which is frequently addressed in parent/teacher interviews is homework. Often parents see homework as being critical to academic success. It’s a topic often debated and never really resolved, even for me as a teacher and as a parent.

In my teaching practice, parents consistently ask me for homework. They believe that doing homework, such as math sheets, makes their children smarter and better students. Parents often feel that “busy” work, such as math and language sheets should be provided by teachers.

Alfie Kohn, an American author and lecturer in the areas of education, parenting, and human behaviour has examined this topic on many fronts. According to Kohn, “no research has ever found a benefit to assigning homework (of any kind or in any amount) in elementary school {i.e. grades 1 to 6). In fact, there isn’t even a positive correlation between, on the one hand, having younger children do some homework (vs. none), or more (vs. less), and, on the other hand, any measure of achievement” (Kohn, n.d.). In other words, homework is not linked to academic achievement in the early grades. Kohn does mention that in middle and high school, homework does impact math and science achievement, especially in higher socio-economic communities.

As a teacher, for homework, I usually assign 30 minutes of reading every night. But parents often scoff at my suggestion that reading is homework, probably as it produces no visible work. In addition, when assigning journal writing, for homework, it usually does not get done. Parents find it hard to get their children to write a journal … parents state “it is a lot of work because my child resists writing”. Now they have a glimpse into my job as a teacher. I believe that parents want homework to keep their children busy and it reminds them of the days when they did their homework.

I find it frustrating that when I do assign homework like bringing in materials for class projects, it does not happen. Often collecting homework is more work for me, especially when I have to chase after students for it. Ironically, I do not use homework for assessing students because it is completed away from school and may not have been done by the student.

So what is the purpose of homework?

1. Practice: Is the purpose of homework to promote practice of concepts?

Yes, homework can be useful in practicing math concepts or writing in the form of journals. In this case, it is important for homework completion to be advocated by the student. Teachers or parents cannot force a student to do this work. When parents ask me how to make their child complete homework, I often cite the phrase “you can take the horse to water, but you can’t make him drink”.

In my own parenting experience, with all my encouraging and some threats, I could not make my son complete his homework. I state this after spending hours working beside my son to get his homework done. In using this strategy, in the end, the responsibility of completing his homework was passed on from him to me … and it was not my homework! When my son entered high school, I gave up on the homework battle and he proceeded not to do his homework on his own. He completed high school and went on to post secondary school where he did not do his homework. My daughter was a different story. She had solid learning skills and a strong work ethic. I only got involved with her homework when she needed help. As a hard worker, she exceeded her brother in her academic success as university is about being smart and working hard.

When I assign homework, as a teacher, I wonder what level of stress I am putting on parents who try to help their children with homework I send home?

2. Completion of work not completed in class: “Work not done in class is homework!”

As a middle school teacher, I have observed two types of students – those who complete work in class and those who socialize in class. The middle school years are an exciting time for students as peers become very important in their lives. Hanging out with friends becomes the main reason for coming to school. Returning from holidays results in many hours of catching up with peers. Due to this very social time in students’ lives, individual and group work assigned in class is not always completed in the timeframe assigned by teachers. This means teachers need to allow more time for work.

As a teacher, it has been suggested by parents of not keeping middle school students on task or not giving enough time to complete assignments. The bottom line for me is that I give plenty of time for work to be completed and do my best to keep students on task. I challenge anyone to keep 30 grade 8 students, with varying academic abilities, on task while helping several other students in need. It’s like trying to herd 30 cats. When parents complain to me about their child’s incomplete work, I state that the student simply did not use class time wisely and needs to finish the work at home.

In my middle school experience, often students need to complete work at home because they did not complete it in class. Several times, students have returned essays and assignments to me that is completed at the “university level” and it is clear that the student did not complete the work on their own.

In the end, homework still remains a contentious topic. As a middle and high school student, I did homework to complete assignments and practice for math tests. I was not an A student at the time, but my homework routine allowed me to develop solid work habits for my future education.

After writing this blog, I still have no clear answers as to the effectiveness of assigning homework probably because each student is different. This school year, I will be assigning math homework as my grade 4/5 students are as keen to do it as their parents are to see it assigned. I’ll reflect on how this year progresses and see if it impacts my teaching and their learning. And I won’t make it too hard so the parents understand it too.

Below are some resources you can share with parents to help them support their child’s learning.

http://www.edu.gov.on.ca/eng/literacynumeracy/parentGuideLitEn.pdf

Reading and Writing with Your Child

http://www.edu.gov.on.ca/eng/literacynumeracy/parentGuideNumEn.pdf

Alfie Kohn Comments about Homework

https://www.washingtonpost.com/news/answer-sheet/wp/2012/11/26/homework-an-unnecessary-evil-surprising-findings-from-new-research/?utm_term=.c2875ad9cb3a

November 19, 2017November 19, 2017 Michelle Fenn Celebrating Success, Combined Grade Classes, Constant Learning, General, Inspiring Students, Inspiring Teachers, Integration, Learning About Your Students, Math, Mentorship, Professional Learning and Growth, The Arts

Connecting Area and Perimeter to Art-Piet Mondrian

Whenever possible, I search for ways to integrate the curriculum to create deeper learning opportunities for students and connect to the world around them. It has always been easy to make connections between geometry and art. Measurement and art wasn’t something that I had integrated much before. However, in working with my Teacher Candidate from the Trent University Faculty of Education program, we were excited to see what the students would create. It only goes to show you that when teachers are able to work collaboratively, wonderful programming ensues for students.

We have been working on perimeter and area for a little while, but students were still having trouble figuring out the difference between the two concepts. We started by giving the students 9 square tiles. Students were asked to create a 3 x 3 array of square tiles and determine the perimeter and the area. The perimeter was determined to be 12 and the area determined to be 9. From there, students were given a number of different challenges to reduce the area but maintain the perimeter of 12. The challenges grew increasingly difficult.

1. Reduce the area by one square unit but maintain the perimeter of 12 units.

2. Reduce the area to 7 square units while maintaining the perimeter of 12 units.

3. Reduce the area to 6 square units while maintaining the perimeter of 12 units.

4. Reduce the area to 5 square units while maintaining the perimeter of 12 units.

5. Reduce the area to 4 square units while maintaining the perimeter of 12 units.

6. Reduce the area to 3 square units while maintaining the perimeter of 12 units.

After having the students share their different solutions we thought we would show the students artwork that Ms. Marchiori created inspired by Ellsworth Kelly’s “Colors for a Large Wall”. In a guided math lesson the students figured out the area and perimeter of different parts of the artwork. The way in which students figured out the answers to the area demonstrated that they had a much better understanding of the difference between area and perimeter than they had previously.

At this point, we wanted to get into the artwork and considered the work of Piet Mondrian. Piet Mondrian is famous for the work that he created using primary colours, horizontal and vertical lines and squares and rectangles. Perfect for working with area and perimeter and for incorporating the different elements of art.

Ms. Marchiori showed the YouTube video of Piet Mondrian’s artistic life in a nutshell. Afterwards, the students then created their own Mondrian inspired artwork using chart sized grid paper (6’X6′) and crayon. To continue our math focus, the students then had to calculate the area of each of the colours that they used and write that on the back of their art “plan”. From there, the students used acrylic paint on canvas with grids drawn in pencil to recreate their “plan” for their art.

A few of the finished artwork samples;

This artwork would also connect to fractions. Students could express their colour content in a fraction, reducing it to it’s simplest form and then compare which colours covered the largest fraction of the area of the painting. When the artwork is complete, the students will be adding an artist’s message about what they learned during the process about area and perimeter, about the elements of line, colour and shape and about Piet Mondrian. This week we will be creating Mondrian inspired artwork while exploring balance and colour in art using much of the same grid technique but with the medium of crayon resist and watercolours.

November 5, 2017January 28, 2018 Deb Weston Curriculum Planning, Math

5 Things Teachers Need to Know to Teach Math

$Math Wordle$

Here’s 5 things that are important to know if you teach math …

Mathematical objects or learning objects (i.e. using manipulatives or models)

These help students figure out and explain their thinking. Manipulatives (concrete or virtual) tend to draw out students’ need to explain and focus on different representations and meanings of mathematics concepts and models. In addition, learning objects/manipulatives can actually act as models of understanding (Tichá & Hošpesová, 2009). Objects are especially valuable for students still functioning at a concrete level of thinking. Helping students chose appropriate manipulatives is important as protractors are not usually used to measure straight lines.

Connectedness (i.e. to real life and to all strands of math)

Teachers need to make connections between and among different math strands as well as concepts and procedures. Math concepts are interrelated for example, multiplication is repeated addition and subtraction is the opposite of addition. Division and multiplication are interrelated and opposite and are interrelated to fractions, decimals, and ratios. Teachers need to make these connections to prevent students from using math concepts and procedures in isolation. Further, teachers need to connect math to real world applications such as How do carpenters make sure a door is installed right? … they measure the diagonals to make sure they are equal (equal diagonals means the door is installed at right angles). The teaching of math is not presented as a “unified body of knowledge” when taught in singular isolation (Ma,1999, p.122).

Multiple Perspectives (i.e. solving problems different/flexible ways)

Teachers need to stress the idea that multiple solutions are possible but also explain that some approaches to solutions and methods are more appropriate in certain situations. This multiple perspective allows students to be flexible in their thinking and understanding of the content.

Basic Ideas (i.e. key ideas/understandings)

When teaching math, teachers stress basic ideas and key understandings. For example, when solving a problem, students can use an equation to provide proof of their answer. Showing their answers different ways can reaffirm their proof.

Longitudinal Coherence (also known as curriculum and learning trajectories i.e. how curriculum is related between grade levels)

Teachers need to be aware of what is being taught at all levels of the elementary math curriculum and not just the grades that they are teaching or have taught. When teachers know the math curriculum well, they know where their students’ learning has come from and where it is going. When only knowing the assigned math grade level being taught, teachers miss out in identifying students’ gaps in their math learning. When there is a gap in learning a math concept, teachers can employ “numeracy recovery” just as “reading recovery” is used to help struggling readers. When teachers take opportunities to review key understandings, they can put in place the appropriate foundation for students’ future math achievement.

An effective way of presenting this knowledge is following the development of a specific math concept through the grades – see Grade 1 to 6 Multiplication Learning Trajectory below.

Multiplication Learning Trajectories with curriculum

Collaboratively Yours,

Deb Weston

References:

https://buildingmathematicians.wordpress.com/tag/teaching-mathematics/

https://www.mathrecovery.org/pdfs/how-it-works/Math-Recovery-Research-White-Paper.pdf

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Tichá, M., & Hošpesová, A. (2009, January). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In meeting of CERME (Vol. 6). From proceedings of CERME 6, January 28th-February 1st 2009, Lyon France INRP2010 1

October 1, 2017April 15, 2018 Deb Weston Assessment, Celebrating Success, Making a Difference Through Education, Math

Why our public education system is awesome!

$PISA 2015 results by country Math$

Recently, during a discussion in an AQ course @ed_rego, we started talking about math scores and the effectiveness of Ontario’s public education system. Ed Rego mentioned Ontario and Canada’s success on the international front. Not only do Canadian students rank high on the international front, its public education system also makes a difference in students’ lives. Let’s look at some reveling data first.

1. Canada ranks high in international testing.

In my studies on education, I discovered how well Canada does on international test scores, especially in relation to the United States. The Organization for Economic Co-operation or OECD conducts yearly tests to rank countries based on performance in science, reading, mathematics (Program for International Student Assessment or PISA) and trends in international mathematics and science study (TIMSS) in both French and English. Students are randomly selected by age (15 year olds for PISA) or by grade level (Grades 4 and 8 for TIMSS).

In 2015, Canadian 15 year olds ranked 4th in science , reading, and mathematics among the PISA results tied with Finland. Singapore, Japan, and Estonia were the only countries to surpass us (Chinese countries include Taipei, Macao, Hong Kong, and B-S-J-G China) . The United Kingdom came in 10th place and the United States came in 20th place. The trends show Canada varies only slightly between testing years. Also note, in Canada, all 15 year old students, of all abilities, participate in our education system and thus would be possible participants in the PISA testing. Also note that Canada does not have weekend “Cram School” as part of our educational landscape. Cram School focuses on rote learning and not critical thinking. In addition, some countries stream students with learning challenges away from formal education. A breakdown of PISA 2015 results for specific provinces can be accessed below.

In 2015, Canadian students ranked 8th in grade 8 mathematics surpassed by Singapore, Korea, China Taipei, Hong Kong, Japan, Russia, and Kazakhstan. England ranked 10th and the United States ranked 11th. Norway students ranked 14th in mathematics. Finland scores were not listed. In science, Canadian students ranked 13th in grade 8 surpassed by Singapore, Japan, China Taipei, Korea, Slovenia, Hong Kong, Russia, England, Kazakhstan, Ireland, United States, and Hungary. Norway students ranked 18th in science. A breakdown of TIMSS 2015 results for specific provinces can be accessed below.

These PISA and TIMSS scores show strong results for both Canada and Ontario, particularly in light of the latest decrease in mathematics EQAO scores in 2017. From these results, I can conclude that Canada’s public education system does a very good job educating our students, even on an international level.

Note: I did not analyse the breakdown of grade 4 test scores as the introduction of specific Canadian curriculum differs in mathematics from other countries.

Canada’s 15-year-old students among best global performers in science, math

Breakdown of Canada’s PISA scores for 2015.

2015 mathematics TIMSS results

2015 science TIMSS results

TIMSS 2015 Ontario result breakdown

2. Canada teaches students how to critically think and engage in rational discourse.

As Heather Mallick of the Toronto Star stated, our public education system teaches “to value thought over feeling, reason over passion” (Mallick, Toronto Star, November 12, 2016). Canadian teaches do not accept writing with statements without supporting details that come from credible sources. Teachers teach the difference between real news and false news.

3. Canadian public education socializes students.

All students, from all backgrounds (i.e. age, gender, cultural background, socio-economic status, or ability) participate in Canada’s public education system. Students are not segregated based on background, culture, or socio-economic status. Students all learn together. Teachers teach values of inclusion for all and education for all. Students learn to get along with others from many different backgrounds and many different places in the world. And this level of national inclusion, is one thing that makes me proud to be a Canadian citizen and a Canadian teacher.

Ontario’s Equity and Inclusive Education Strategy

4. Canada’s public education is equitable and democratic.

Canada’s public education system (almost) compensates for disadvantages that impact student learning. Canada’s public education system gives students from all background (due to age, gender, cultural background, socio-economic status, or ability), an opportunity to succeed in school. Newly-arrived immigrant students rapidly integrate enough to perform the same as their Canadian classmates. Dr. John Jerrim (UCL Institute of Education in London) stated that Canada’s high league table ranking reflects the narrow socio-economic gap in school results. The outcome is that Canada’s score show a very high average, with relatively little difference between advantaged and disadvantaged students. The OECD states that Canada supports social equity as “Schools should provide a good education for all students, regardless of their parents’ education or career. PISA assesses to what extent differences in education outcomes are associated with the social status of parents as well as the performance gap between advantaged and disadvantaged students. It also identifies the share of students who perform well, despite coming from disadvantaged backgrounds, known as resilient students.” (OECD, 2015)

PISA 2015 Key Findings for Canada

How Canada became an education superpower

I end this blog with the words of John Dewey …

It is no accident that all democracies have put a high estimate upon education; that schooling has been their first care and enduring charge. Only through education can equality of opportunity be anything more than a phrase. Accidental inequalities of birth, wealth, and learning are always tending to restrict the opportunities of some as compared with those of others. Only free and continued education can counteract those forces which are always at work to restore, in however changed a form, feudal oligarchy. Democracy has to be born anew every generation, and education is its midwife. (Dewey, 1916, The Need of an Industrial Education in an Industrial Democracy)

Let’s celebrate Canada’s public education system success as a democratic and well educated nation – for I believe this is why we are one of the best places to live in the world.

Collaboratively Yours,

Deb Weston

This blog was inspired by an article written by Heather Mallick, Toronto Star, November 12, 2016.

September 29, 2017September 29, 2017 Laura Bottrell General, Math, Professional Learning and Growth

A Week of Inspirational Math

To begin the year of math instruction, most of the junior division teachers in my school decided to try Jo Boaler’s “Week of Inspirational Math” on YouCubed. Jo Boaler is one of the leading researchers in mathematics education and focuses largely on developing mathematical mindsets. On the website www.youcubed.org, there are many high quality resources for teachers and parents based off her research. I am quite familiar with some of the resources, having explored it during staff professional development days. I was quite excited to get into the classroom and try it out for myself.

The Week of Inspirational Math, actually expanded to three weeks, provides student videos and lesson plans that include rich, open ended math tasks. They are described as low floor, high ceiling tasks, meaning that they have many access points for all levels of learners and allow for multiple solutions and higher level thinking. The tasks, sorted by grade level, touch upon different strands of math as the days progress. Each lesson is accommodated by a video for students, usually of Jo Boaler herself, creating and framing mindsets for math.

I loved using this as my programming for the first few weeks of school. First, because it set the tone of positive mathematical mindsets in my classroom. One of the very first activities has students discussing what makes a good problem solving group member. They are invited to discuss what things they might like their classmates to say and do while consolidating math experiences. What a great way to establish classroom norms!

What I really loved about the Week of Inspirational Math was that it acted as a great diagnostic tool for me. By touching upon many strands, offering a large window of access points and relying heavily on math conversations, the program provided me with a great opportunity to get to know my students as mathematicians fairly early in the year.

Jo Boaler’s approach to teaching mathematics is based off of these seven positive classroom norms:

1. Everyone can learn math to the highest levels

2. Mistakes are valuable

3. Questions are really important

4. Math is about creativity and making sense

5. Math is about connections and communication

6. Math class is about learning not performing

7. Depth is more important than speed

The Week of Inspirational Math isn’t the only excellent resource available at YouCubed. I have been spending some time exploring the tasks, videos for students, parent resources and research articles available. YouCubed offers professional development courses both online and in-person. The website also lists a variety of texts and resources for teachers to use in the classroom. If you’re interested in learning more, head over to www.youcubed.org or check out Jo Boaler’s latest book, Mathematical Mindsets.

I am looking forward to continuing to use these resources with my grade 5/6 class in addition to many other wonderful resources out there! As a teacher, I sometimes feel that there is an overwhelming amount of resources, new research and ideas available. It can be quite time consuming to sort through and find what is meaningful to you and your students’ needs. There will never be a “perfect” or “right” way of teaching math, but I thought I’d share with you this resource that has worked well for me!

September 24, 2017 Arianna Lambert Inspiring Students, Learning About Your Students, Math, Start of the year

Empowering Young Mathematicians

I’ve always been a lover of Math. Even when I wasn’t particularly strong in a specific area, I always loved the thought of calling myself a Mathematician. Now I know it’s a huge leap from loving the subject to ascribing to being a Mathematician but hear me out for a minute. As many of my friends may know, I love Google so I thought I would ask my good friend for the definition and here’s what I found.

Magically, this definition empowered me to realize that I too can be a Mathematician simply by being a student of Mathematics. It didn’t say that I always have to excel in all areas. It simply says that I have to be a student. Now for the definition of student. Ok Google….

I’m going to go with the last definition. A person who takes an interest in a particular subject. So after much searching, I think it’s safe to embrace the term. The question is, how do I get my students to do the same?

Inevitably, when I ask my students to tell me about their Math experiences, there are many who already describe themselves as being “not good at Math” or state, “it’s too hard”. My task then is to reframe their experiences with Math, encouraging them to change their outlook.

At the beginning of the year, I’m always looking for new ways to engage my students in Math tasks as my assessment for learning. For the last couple of weeks, we have been doing Which One Doesn’t Belong activities and I have been asking my students to use Mathematical language to justify their answers. After a few rounds, one of my students started laughing and said, “there’s really no wrong answer so long as you explain what you are thinking”. It was interesting because it didn’t occur to many of them that there may be multiple possibilities to answering these types of questions.

This got me thinking and asking myself:

Is this what holds our students back from realizing that sometimes engaging in Math isn’t just about getting the right answer but exploring different pathways to finding solutions?
Is Math about allowing students to explore the different concepts and seeing where these concepts intersect or are useful in everyday life?
Can we reframe Math for our students so that they realize that so long as they take an interest in it and persist as students, they too can be Mathematicians and that it is not only about “being good at it”?
On Friday we were coding in Scratch and words like values, angles, turns, length were coming out. Isn’t that Math? Can we explicitly teach the concepts and empower them to create using them?

Ms. Lambert, the self-proclaimed Mathematician, is on a mission this year to work with students to empower them to embrace Math just a little more. I’ll keep you posted on our journey!

May 2, 2017 Mike Beetham Assessment, Challenging Topics, Combined Grade Classes, Differentiated Instruction, Diverse Learning Needs, English As Second Language (ESL), General, Math, Professional Learning and Growth, Resources

Overcoming Math Phobia

A phobia is defined as an extreme fear or aversion to something. This can often be associated with mathematics both by students and teachers alike. Human nature is such that when we feel we are not good at something, we therefore can’t be successful at it and we tend to avoid that what we will fail at. This self-fulfilling prophecy is often alive and well in a teacher’s or student’s thoughts.

I will be the first to say that at an earlier stage of my career I was very uncomfortable and unsure of myself when teaching mathematics. Sure I knew how to do math, but did I know how to teach something I was not very comfortable with. I had to do something to ensure that my skills and pedagogy were improving. Thus began a voyage of self-learning or self-guided professional development. Now, twenty-five years later I am still on that journey of learning about how to best teach mathematics so that my students learn and are engaged in their world that is so filled with math.

As with anything else you must find the right tool or vehicle for learning. I attended as many workshops as I could on mathematics. The Waterloo Region District School Board offers a wealth of learning opportunities for their teachers as does ETFO and the Ontario Association for Mathematics Education (OAME) (http://www.oame.on.ca/main/index1.phplang=en&code=home).

These are several key areas where you can start your journey of learning. I would like to share three key resources that have helped me become a more efficient and knowledgeable mathematics teachers. The first is the work of Dr. Catherine Twomey Fosnot. Her work and approach to the instruction of mathematics is the number one influence I attribute to my growth in mathematical instruction. I attended several of her sessions as well as visiting her site in Harlem. I would highly recommend her series ‘Young Mathematicians at Work’ as a classroom resource.

The second most useful tool I have come upon is the series entitled Super Source. There are many reasons why I like this resource. The first is the rich problem solving tasks that are in each book. There are a variety of tasks and each task is connected to an area of mathematics where it can be used like number sense or patterning. There is a book written for each type of manipulative (Base 10, Pattern Blocks, Tangrams etc…). The most valuable asset of this resource is that there is a section where the mathematics behind each task is explained to the educator (the big ideas) as well as suggestions on how to bring out the math in your students. As with any resource this provides a jumping on point where a teacher can then adapt the task to meet their needs.

The final resource I would like to share with you is one of the many works of Van de Walle. I used this resource as a teaching tool for myself. It helped me understand the concepts I was teaching and how to bring out both a level of engagement as well as a deeper understanding of mathematics in my students. I hope these resources prove to be as valuable a tool to you as they are for me in my teaching of mathematics.

February 20, 2017 Will Gourley Constant Learning, Differentiated Instruction, Field Trips, General, Learning in a Real Life Context, Literacy, Math

Express lane to learning

Recently, I was out shopping, and came upon something that’s not usually found for sale on the shelves at local grocers. Insight.

Funnily enough, it was probably there all along. I must have blown past a bunch of times while buzzing about my mental list of must buys. But this time, finding insight was meant to be. I’ll explain in 10 items or fewer.

https://www.flickr.com/photos/kirrilyrobert/2355105082/ CC by 2.0

Usually, upon walking into a store, I’m pre-occupied with my mental shopping list, figuring whether something is a good deal or not, and by getting out as quickly as possible. This requires the use of several life, mental Math, and critical literacy skills.

The act of shopping really requires planning and strategic thinking to figure out when a store will have the least amount of people as possible in it so that we may park, pickup a cart, procure, pay, and part. It is impossible to ignore the thought required for such seemingly innocuous trips that are made for our milk, bread, and eggs etc.

From now on, and armed with this understanding, I am going to use my trips to the store to seek out and share its valuable lessons. There’s knowledge to acquire about Math(Measurement or Number Sense), to Media Literacy(package design, use of space), and to the development of crucial future life/socialization skills in every aisle.

Consider the yogurt section for a moment; there’s something for everyone in that part of the dairy case. Where else could so many products co-exist so peacefully? In fact where else could such diversity exist(except Canada)? Here gluten free, lactose free, peanut free, Halal, Kosher, vegan, and meatatarian are available to all at the grocery store and share an inclusive space.

Then there’s the produce section.

While perusing here, I saw couples discussing, quite demonstratively, which bunch of Rapini to buy. Then I spied the apple aisle. There was a person who felt compelled to touch all of the apples in the case. I witnessed a grape thieve looking from side to side and then pop a few into her mouth. Here were real lessons on relationships, human behaviour, and decision making all before me waiting to be picked and extended into the classroom.

It’s like that in the classroom or a head of Iceberg(lettuce). Teachers work hard to make learning engaging, extendable, and relevant everyday.What most outsiders see is only the first leaf, layer or ply.*

Speaking of plies. I thought it would be fun for my students to calculate which toilet paper at the store was the better deal based on size and number of sheets per roll.

Talk about a real life problem. Initially, I went around snapping pictures of the different packages and their details to build the questions. The class discovered that there’s a lot going on that can confuse consumers. We came away wiser for the time knowing we wouldn’t get rolled over by the manufacturers next time.

Your turn

Have you ever considered or taken a class to the local grocer? What about a super-type store à la WalMart(wish I could still write Zeller’s here)?

Or how about a homework assignment to include children in the planning and shopping? Who knows it might become fun, or democratize the food choices in some households. It may even lead to conversational and debating skills.

There’s a line forming behind me. Happy shopping. Thank you for reading. Please share and take time to comment to keep the conversation going.

*You thought I’d say tip since iceberg was used, but no!

December 7, 2016December 7, 2016 Laura Bottrell General, Math

“Unboxing” Math Instruction

“I’m not a math person”. This is probably a statement you’ve heard from someone at some point, whether it be a friend, colleague, student or even yourself. It’s something that I grew up truly believing. I grew up believing that I did not have a “math brain” and that it just wasn’t “my thing”. Today, I know this is a myth.

I learned this to be a myth about one hour into my Primary/Junior Mathematics course in my B.Ed program at Brock, taught by one of the most inspiring educators I’ve ever met. It was here I learned that everyone can learn math, there is no such thing as a “math person”, and that this was an unfortunate myth that has stopped many students and adults from success in mathematics.

So, why do so many people believe they can’t do math?

Traditional math instruction has been black and white – right or wrong. But isn’t the grey area where the real learning happens? When we box our students into answering questions that require only repetitive tasks, rote memory or simple procedures, we box them in to a world of right and wrong. We box them in by assigning them a grade “4/10” on a simple procedures task. We box them in by marking their work wrong if they haven’t solved the problem in the exact way we’ve taught them to. We box them in when we don’t give them the chance to show us what they are truly capable of. When we box them in, we send a message that they can’t do math.

We know that having a growth mindset is directly related to success, especially in mathematics. Right now in education we are moving away from straight forward, right and wrong math, and moving towards building an environment where problem solving, growth and exploration is more important. With instructional techniques like the three-part lesson plans and number talks, we’ve moved our instruction in the right direction. We also need to open up our math questions so that there is space within them for learning.

Last week I had my grade 2/3 students write a math assessment as a conclusion to our unit of learning. One of my students did quite poorly on the assessment and I was hardly able to understand what he was thinking when he wrote down one of his answers. When conferencing with him after, he explained his thought process to me. He misunderstood the question on the test so he answered it in his own way. After understanding his perspective on the question, it became obvious that he had solved the question in a much higher level way of thinking and clearly had a deep understanding of the concept. He told me, “I made my own math”. Well, how great is that? Had I just taken it for granted, marked it wrong and moved along to the next student, I would have missed this teachable moment. Instead, he left our conversation feeling proud of his abilities rather than feeling like he can’t do math. He left our conversation with a growth mindset.

What our students believe about their abilities in math directly affects their success. We need to set up our students with opportunities to challenge their thinking, try new things, explore and make mistakes. If our students believe they have unlimited potential in math, they will do great things.

Next time, I will replace that question with something process oriented and open ended. After all, I’m still learning too!

December 5, 2016 Kelly.McLaughlin Learning in a Real Life Context, Math, Students as Teachers, Use of Technology

Surveys that matter

Today was a very interesting day for learning that took a different direction than I anticipated. We started off talking about ideas for the holiday assembly when I mentioned to my students that I would like them to survey the grade to find out their interest. It seemed unfair to force a grade of students to be involved in an assembly unless they really wanted to. Five of my students surveyed the entire grade about how they wanted to be involved. It was great to see them learning the process of how to create a survey (using google forms) and then administering it to their peers. Twenty minutes later, we created one to see if and how we should decorate the class. This survey was then administered to our class by five other students. It was great to see students talking about percentages and comparing pie graphs in a context that was not even supposed to be a math lesson. Learning can take place in all contexts and it is awesome when it is student led and the teacher just sits back and lets the magic happen. I am letting my students survey the intermediate students to select their music for the next school dance. I am also hoping to survey the school in the near future about extra curricular activities they would like to see in our school. Data management is proving to be an all encompassing area of study and is creating amazing student leadership! Try it out at your own school and see your students become teachers. They loved seeing the results from their survey matter and saw how action took place right away.