Math – Page 5

September 30, 2018 Michelle Fenn Combined Grade Classes, Constant Learning, Curriculum Planning, General, Inspiring Students, Math, Resources

Tools and Resources for Math Talks

One of the reasons that I spent so many years teaching the primary grades is that teaching math to older students terrified me. Growing up I struggled with math. I changed schools in the middle of my grade three year and missed a great deal of multiplication and division instruction which haunted me for the rest of my math learning. I remember crying at the kitchen table over my homework and my father being distraught over not being able to help me. I totally understand how a student feels when they shutdown and “can’t” get it. That understanding along with having excellent tools and resources helped me immensely when I taught grade 4 and 5 mathematics.

Math Growth Mindset

Jo Boaler is a professor of mathematics education at Stanford University and the co-founder and faculty director of youcubed. This fabulous website provides unique, research based instructional approaches to teaching math. There are videos for students of different age ranges and the “Week of Inspirational Math” was what helped me to create a positive math learning environment with a growth mindset in my Junior grade classroom. It doesn’t have to be the first week either-you can do it at any point. Jo Boaler has also co-written a series of mathematics instructional resources called “Mindset Mathematics” for each of the junior grades.

Math Talks

Number Talks: Whole Number Computation, Gr K-5: A Multimedia Professional Learning Resource became my go-to resource when I began daily number talks with primary students and it made the transition to teaching math in the junior grades much easier. The format of math discussion remains essentially the same no matter what grade level. It is an expensive resource but well worth it. If you want to give math talks a try there are some more affordable online resources that you can use as well.

Math for Love is a website that provides a number of online math talks for K-5. EduGains gives a brief synopsis of how to develop your math learning community in your classroom. Another great online resource for daily math talks is Which One Doesn’t Belong? This website provides all sorts of pictures for math discussion. Eventually my students began creating pictures for other classes to use for their math talks after using the examples on the website. Math Talk Resources is a comprehensive spot for math talk information and connects you to many different math talk resource websites.

When students have the opportunity to discuss math and hear fellow student’s different perspectives, they begin to see their own entry point into every math problem. They also begin to see the value of challenging each other’s ideas respectfully and adding to one another’s ideas. “What do you see and what do you wonder?” is a much friendlier way to open up math discussion than, “Who can give me the answer?” I am convinced that because my students engaged in respectful math talks they were able to transfer these skills into other discussion topics in our classroom. For me, the anxious math teacher, math talks became the highlight of our daily math lessons and sometimes, the highlight of my day.

July 1, 2018July 1, 2018 Michelle Fenn Assessment, Challenging Topics, Combined Grade Classes, Constant Learning, Curriculum Planning, Differentiated Instruction, Genius Hour, Inquiry, Inspiring Students, Inspiring Teachers, Integration, Learning in a Real Life Context, Math, Modern Learning, Professional Learning and Growth, Questioning, Report Cards, Resilience, Student Ownership, Students as Teachers, Technology in school, The Global Competencies, Use of Technology

Why Coding is Important Part One

I consider myself a fairly techie teacher. However, until recently I hadn’t really tried my hand at coding or robotics. Well, I had, but I had lost interest as I quickly felt as though I was out of my depth. So, I did what I always do when I really want to learn something about teaching, I go to a colleague that has the knowledge and I try it WITH the students. Collaborative inquiry.

Until recently, I didn’t see what the big deal was or why it was important to teach coding to students. Yeah, playing with robots is fun but what does that have to do with curriculum? When I started working with and learning coding along side students I had a change in mindset. There is a lot of math, strategic planning and visualization in coding. Coding may not always directly relate to curriculum content-that is true. However, in terms of teaching students about the deep learning competencies, coding is key. If you aren’t sure what I mean by the deep learning competencies; they are referred to as the 6 C’s. Here is a link to the New Pedagogies for Deeper Learning paper but I have extracted a summary of the 6 C’s for a quick reference:

Character: Character refers to qualities of the individual essential for being personally effective in a complex world including: grit, tenacity, perseverance, resilience, reliability, and honesty.

Citizenship: Thinking like global citizens, considering global issues based on a deep understanding of diverse values with genuine interest in engaging with others to solve complex problems that impact human and environmental sustainability.

Collaboration: Collaboration refers to the capacity to work interdependently and synergistically in teams with strong interpersonal and team-related skills including effective management of team dynamics, making substantive decision together, and learning from and contributing to the learning of others.

Communication: Communication entails mastery of three fluencies:digital, writing and speaking tailored for a range of audiences.

Creativity: Having an ‘entrepreneurial eye’ for economic and social opportunities, asking the right questions to generate novel ideas, and demonstrating leadership to pursue those ideas into practice.

Critical Thinking: Critically evaluating information and arguments, seeing patterns and connections, constructing meaningful knowledge and applying it in the real world.

I reflected on these 6 C’s as I wrote the learning skills for my grade 4/5 students this year. I spend the most time on my reports creating the Learning Skills for each student. They are personal and they reflect each individual student. As a parent, it is what I am most interested in reading about my own child. The 6 C’s are competencies not only for school, but for life. While students were exploring coding I had them working in pairs or small groups to give them the opportunity to communicate, collaborate and show leadership. When the code didn’t work, they were able to go back and find the error and correct it and try it again with results right away. Sometimes they found it painstaking and I had to let them work through that and they were glad in the end when I didn’t give them the easy way out and they solved things on their own. When they learned something in coding, they quickly wanted to share their learning with other students. I gave basic instruction about the program to start using a youtube tutorial and then let the students go. Students who often don’t do well in groups with “typical” academic tasks often excelled as leaders in coding because it is a divergent way of thinking and they had a self-check strategy built into the task. It was incredible to witness the amount of learning that was taking place.

You don’t have to have robots to code. There are online coding websites that teach kids to code such as code.org and Scratch. The students even as young as grade 3 are easily able to use these sites to code. Scratch Jr. is available for younger students. The sites have great tutorial videos and somehow the students seem to just start discovering and creating things intuitively. They begin helping each other when they see that someone has created something cool and ask the creator to show them how to do it too.

I am proud to say that I can now code a square, star and a small obstacle course using blocks and a Sphero robot. My students discover new things every day and share them with me. It is definitely a new age in teaching.

May 31, 2018May 31, 2018 Will Gourley Celebrating Success, Making a Difference Through Education, Math

Demystifying

Inside

Here’s some Math for you.

May 31 + 1 = June = tomorrow

Despite its awkward elegance, this is only a temporarily true statement. In less than 24 hours it will be 364 days until it is true again. I am not sure 1/365 is a good ratio for truth. Despite these odds, I want to share some figures with you. So happy last day of May 2018 to all of my colleagues in education. Isn’t Math fun? Don’t worry, there will not be a test at the end.

From a fractional point of view we will have completed 9/10ths of our instructional months at the sounding of today’s dismissal bell. That equates to roughly 180 days +/- in the classroom.

At 350 minutes per day in school(lunch excluded) that means approximately 70 000 minutes of planning, instructional, assessment, supervision, leadership, counseling, and communication time this academic year, so far. Multiply that by our membership of roughly 80 000, it means we have worked about 5.60 billion minutes or 93.3 milion hours inside of school walls in 9 months.

Add in the other 110 000 educators teaching from K to 12 in our province, I might need a new calculator.

Outside

Now consider the time spent in education outside of school. Let’s say that 4/5s of our union membership brings home anywhere from 2 to 3 hours of work with them each evening(180 days x 150 minutes x 64 000 members = 1 728 000 000 minutes or 28.8 million hours).

And then there’s the weekends. On average I spend 3 to 4 hours per weekend, reading, planning, and assessing. Let’s say 200 minutes to be safe(not conservative) over 40 weekends per year that is another 8000 minutes or 133+ hours for me. Now if 60% of our colleagues are also doing this, it means an additional 383 million minutes or 6.38 million hours.

Are you still with me? I also lead clubs and coach which adds at least another 90 minutes per week. 90 minutes x 40 weeks = 60 hours or 1.5 weeks of a work year spent coaching and mentoring. If 50% of our teachers are doing this it adds another 2.40 million hours since September. All invested in the lives and well being of learners beyond the classroom.

When I add it all up in the past 9 months our membership have worked roughly 133+ million hours since the start of the year. Dividing 133 000 000 hours by 80 000 educators we get an average of 1662.5 hours over 40 +/- weeks or easily 41.563 hours per week – again a fairly spartan(not conservative) estimate.

I know that these figures appear subjective, but I have intentionally minimized many of them to allow for possible inaccuracies to avoid sensationalizing data. However, I am seeing the extremes and maximums far more often than not. When I calculate the time I spend in this calling, it is far greater than 50 to 55 hours per week. My spouse might argue it’s well past 60 hours per week.

I just see it as time well spent and 100% sure I’m not alone.

Thank you for all the minutes and hours you pour into education. I look forward to finishing the final 10 % of this year strong. Wishing you all the same.

May 29, 2018 Arianna Lambert Inspiring Students, Math, The Arts, Use of Technology

Are Artists Mathematicians Too?

I’ve always thought that the Arts and Mathematics were 2 separate things that never should meet. If someone was good at Art there was no way that they would be great Mathematicians and vice versa. Was I ever wrong! This year I’ve had the privilege of working with a co-op student in my classroom who is an amazing artist. She has truly engaged my students in activities that always seem to lend themselves to Math and this got me thinking more and more about the connection between the Arts and Mathematics.

Last year I was introduced to a Kandinsky Math Activity by a colleague in the TDSB, Amanda Brown. Blown away by how her students were connecting geometric concepts to Kandinsky’s Art pieces, I started to see more and more the value of helping students to understand sometimes abstract concepts in Mathematics through Art. I tried her activity with students last year and they loved it! This year, I’m giving it a try with a bit of a different twist with my current group and the conversations are rich and meaningful and students are understanding the concepts with more clarity.

You wonder what the activity is all about? Well, this is what we did this year.

I started by asking my students to think about Geometric Concepts that they were familiar with. They mentioned things like 2D and 3D shapes, attributes, lines, angles and we started to create a list of terms that they already knew and I added a few more based on the curriculum. I then asked students to think about some of these terms and we moved to create a word wall to help us. It was easy with familiar terms because they used pictures to describe what they knew of a circle or a square but when we got to a scalene triangle, it was a little more challenging. Some students took it upon themselves to find online math dictionaries to help them with the definitions and wrote them out for our word wall but still found them abstract. Where might we find a scalene triangle or need to know what one is in the real world? Now the fun was going to begin.

After taking look at some of the amazing abstract pieces created by Kandinsky and with a knowledge of Screenshot 2018-05-29 at 8.51.58 PM the terms we were going to be investigating, students were asked to look at some of his works and identify the geometric concepts contained within. They were amazed by the number of concepts that could be found in his works. They measured angles and classified them as acute, right or obtuse. They compared shapes and lines, some even realizing that some of the shapes were created by other shapes and lines intersecting.

Screenshot 2018-05-29 at 8.52.12 PM Once we had the chance to investigate Kandinsky’s works, we set off on a mission to try to create our own Kandinsky inspired works using Google Drawings. In pairs, students used at least 7 of the concepts that we were learning about to create abstract, labeled digital drawings.

After a little practice with a friend, they were asked to independently create their own work of Art using at least 10 concepts using paper, pencils, markers, pencil crayons and paint. We discussed how mood is created through the use of colour and they have been hard at work ever since.

It’s so refreshing to see all of my students – even the ones who don’t necessarily feel strong in Mathematics – thrive in experiences like these when the concepts taught are connected to the Arts or to real life applications of Math. When they’re fully engaged in the work and feel successful in their understanding, application and communication of the learning, that’s when I see my Artists come alive in the Math class in ways that are truly amazing. So, to answer my question…yes, Artists might very well be Mathematicians too! Screenshot 2018-05-29 at 8.51.44 PM

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.

March 29, 2018 Arianna Lambert Inspiring Students, Inspiring Teachers, Math, Modern Learning, Play-Based Learning, Students as Teachers, Use of Technology

Digital Breakouts

Escape Rooms have been all the rage as of late. Over the past couple of years, I’ve learned about and used breakouts in my classroom to engage students and as a tool in assessment for and assessment as learning. Essentially, it’s a Google Slides presentation or a Google Site where there are links to different elements of learning and a form where students or colleagues can enter their responses.

Last week, I was fortunate to work with an amazing group of teachers during #TinkeringThursdays and we spent the time breaking out and considering applications for the classroom. I have to say that students tend to be a little more resilient in trying to solve problems but in this process, it was interesting to see teachers as learners and to consider what students might experience when presented with tasks that challenge them and push them to problem solve.

Breakouts with students

As mentioned before, I enjoy using Breakouts as assessment for and assessment as learning. For me, it allows me to see whether or not my students can apply some of their learning to solve puzzles collaboratively. A couple of weeks ago, I worked on a decimal breakout with my students as a means for assessment for learning. I wanted to understand what they already knew about decimals. Now I used this breakout before with students who were a little further along in their learning and it was great to see that my current group of students took the time to view the videos in order to learn or understand a concept in a deeper way, whereas my previous students were more able to apply their learning to solve the problems. Either way, there was the support needed to help guide them as they problem solved. When we work on breakouts, I usually have students work in groups of 2 or 3 so that they have the opportunity to collaborate and possibly look at a problem from a different perspective.

Breakouts with colleagues

Over the past year, I have had the opportunity to present sessions on Digital Breakouts to colleagues and it’s been so much fun. In each session, we start with a breakout and I’ve seen this as a great way to engage in learning in a fun way. This got me thinking about how we might be able to use breakouts to engage colleagues in new learning in staff meetings or PD sessions. Rather than having information delivered, could this be a tool where we – like our students – discover and learn on our own? I’m starting to think about more applications for breakouts with colleagues so stay tuned!

Next Steps

While writing this blog, I started to think about gamification in the classroom. How might it engage some learners and what might the implications be for students who truly enjoy learning in this way? It also had me thinking that it was great that students had an experience in learning though a breakout, but what’s next? How might we use student-created games to not only facilitate their own learning but collaborative learning in our classrooms? My next step is to get my students to start creating their own and getting them to consider how they develop their questions and how they determine what information might be helpful to others solving the problems in their games. Again, I’ll keep you posted. In the meanwhile, if you’re interested in trying the breakout that we used for #TinkeringThursdays, click on the image below. The last couple of slides have important information on creating your own.

Also, please feel free to share how you are using games – like breakouts – in your classroom for student learning or learning with colleagues. I would love to hear from you!

December 12, 2017December 12, 2017 Deb Weston Differentiated Instruction, Diverse Learning Needs, Math, Resilience

Math Instruction for Struggling Readers

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As a learner, have you ever felt really frustrated because you know you can do the work but you just have a barrier that prevent you from moving forward?

This is how struggling readers feel when they try to complete their math assignments and assessments but cannot read the words. Did you know that most content area text, including social studies, science, and math, are written several reading levels higher than where the students are at in reading? Did you know that most students are introduced to 1000 to 2000 new vocabulary words per each year? (Harmon et. al., 2005).

The reality is that in order to do math, students need to be relatively good readers.

In order to put you, the reader of this blog, into the perspective of a struggling learner, I’ve included some simulations below.

Try them and experience what your struggling student readers experience when doing their math work!

Reading Issues Simulation

Experiencing Math Issues

Experiencing Attention Issues

Experiencing Organization Issues

Experiencing Writing Issues

So, as a teacher, how do you support students with struggling readers in math? In order to support struggling readers, teachers need to understand their students’ deficits and strengths!

Math challenges faced by students with reading disabilities

Understanding the math questions due to weak phonemic awareness and decoding strategies
Dealing with math vocabulary
Movement and/or reversals of text & numbers
Remembering dates, names, numbers, list that lack context (i.e. random)
Processing during tests & assessments
Limited executive function due to brain function being used to read text
Challenges with rote learning such as math facts

Strengths of students with reading disabilities

Curiosity, gets new concepts linked to meaning
Enjoys puzzles & building models
Excellent thinking skills in comprehension, reasoning, & abstraction
Excellent listening memory
High success with practicing reading in subject-area vocabulary
Often excels in subjects not linked to reading such as math, computers, visual arts, science, and other conceptual subjects

By understanding students’ deficits and strengths, teachers can build on this understanding to help struggling readers excel in math.

Supporting students with reading disabilities

Use decodable, easy to read, text and sight words in math problems
Engage students curiosity so they can explore the meaning of new concepts
Use puzzles & show models to solve math problems
Teach math through discussions and group work to take advantage of excellent listening memory
Explicitly teach and support math vocabulary with a visual math wall and math dictionary
Extra processing time during class work and assessments
Take advantage of students’ excellent thinking skills in comprehension, reasoning, and abstraction
Support learning with assistive technology (e.g. Google Read/Write & Open Dyslexic font)

As I am a teacher with a reading disability (i.e. dyslexia), colleagues have often asked what it it like to be dyslexic … well, I found a website that simulates dyslexia. After showing colleagues my world of reading, I explain that I have developed strategies to read like reading words as pictures and reading conceptually. Students will develop their own strategies through hard work and resilience.

Check Out the Dyslexic Reality Here!

Using an adaptive font can significantly help students to deal with word and letter reversals. I use an Open Dyslexic font on my web browsers and in my word documents.

OpenSource Dyslexic Font

As a teacher, I ask you to be patient with your students who are struggling readers because with work and effort, one day they will become strong readers …. because not all students are good readers … yet!

Collaboratively Yours,

Deb Weston

References

Harmon, J. M., Hedrick, W. B., & Wood, K. D. (2005). Research on vocabulary instruction in the content areas: Implications for struggling readers. Reading & Writing Quarterly, 21(3), 261-280.

What it’s really like to read with dyslexia

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