Grade less, Assess more.

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Haunting grades?!

BOO! Are grades haunting your students?! Well, this week our professional learning group for mathematics had a lengthy discussion about the idea of a “gradeless” classroom. At first, many of the pre-service educators shot their hands up in protest or with intense questions. In fact, many of the concerns were actually about fear of parental retaliation! So this post I want to look at: (1) What is this gradeless classroom all about? (2) What does it look like? and (3) Is it right for my classroom?


GRADELESS CLASSROOM

screen-shot-2016-10-28-at-11-38-34-amA gradeless classroom DOES NOT mean that students don’t receive grades. It does NOT mean that the teacher does nothing. It DOES NOT mean that students and parents are in the dark. What it DOES mean is: greater transparency

According to our class discussions, we agreed that a gradeless classroom switches the focus from letter or number grades to learning and feedback. The idea is that students receive meaningful feedback from their teacher, their peers, and themselves (assessment AS learning anyone!?). As a result of this, we expect students concentrate less about getting a grade and more about how to use their feedback.

WHAT IT LOOKS LIKE

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Source: Interactive Achievement – Sally l’Anson – http://interactiveachievement.com/tag/descriptive-feedback-for-students/

The gradeless classroom highlights the extreme usefulness and importance of feedback systems before any concrete grade is given. We can use assessment for learning and assessment as learning to achieve our improvement towards meeting the success criteria or curriculum expectations.

This looks like constant formative feedback, but with time to act on the feedback to actually create learning! In “Making It Count: Providing Feedback as Formative Assessment“, Troy Hicks emphasizes that we must move from a fixated student product to having multiple opportunities to reflect and move forward in learning. The key word here is multiple – if we only have students review their work once, are they really learning or are they simply correcting their work?

Students also need to become evaluative of their own work. If we give students the opportunity to give themselves a grade, they are most likely going to choose a letter/number without reason. However, if we are constantly practicing self-assessment then we offer students the opportunity to reflect on where they are, where they want to go, and how they can get there! “Evaluate” is next to the top of Bloom’s taxonomy for learning and it is imperative to learning for students to do so. Edugains is a great Ontario resource to help re-structure your opportunities for self-assessment in the classroom.

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Source: The collective wisdom of authors published in the September 2012 issue of Educational Leadership: “Feedback for Learning.” (Volume 70, Issue 1).

IS IT RIGHT FOR MY CLASSROOM?

In my opinion, there is always a place in education to increase formative and useful feedback processes and switch the focus off of the actual grades. That being said, explicitly stating that your classroom is “gradeless” can seem difficult, especially if you have not prepared your students to use or give feedback. Many educators also worry about the parental reaction to saying their child will be in a gradeless classroom. This can be magnified here in Ontario where we have students from cultures that value grades/performance over the learning process. However, our professor Shelly Vohra has explained that after educating parents on the process, they are almost all usually on board. This means that as an educator, if we are prepared and can support our reasoning for our methods, we can feel confident with implementing them.

I hope this feature has helped you understand the potential benefits of going gradeless or at the least, implementing better feedback systems in your classroom! Please let me know if you have any concerns or if you have tried this in your classroom! What has worked? What was difficult? What should others know about?!

– A

USEFUL LINKS

Teachers Throw Out Grades – FB Page

https://www.facebook.com/groups/teachersthrowingoutgrades/

#TTOG – Twitter Feed

https://twitter.com/search?q=ttog&src=typd

Going Gradeless (Edutopia)

https://www.edutopia.org/blog/going-gradeless-student-self-assessment-matt-weyers

Ditching Grades

https://thejournal.com/articles/2016/03/15/panel-ditch-grades-now-focus-on-student-learning.aspx

Visualizing Technology in Math

This past week in our professional learning group discussed the importance of visualizations in mathematics and also looked at the role of technology in the mathematics classroom. For this post I would like to touch upon the importance of visualizations and diagrams and also the ways in which we can responsibly use technology in the math classroom.


VISUALIZATIONS

Visualizations are an important way to approach math instruction and are important for students to access as strategies to solve problems. Jo Boaler has a lot of great information about using visualizations in the math classroom and notes that it is well known that visual math improves performance. Through our class discussions, we also touched on the importance of using visual solutions as a way to fully understand the math processes instead of simply memorizing a formula. When we encourage visualizations we can reduce the memorization needed by increasing the key information our students understand.

TECHNOLOGY

In teacher’s college, there is a high emphasis on facilitating 21st century learning skills of communication, collaboration, critical thinking and creativity. Many times, we discuss the use of technology to achieve these goals and demonstrate our skills. However, I believe many pre-service teachers (and perhaps in-service teachers) are still confused about the EFFECTIVE use of technology in the classroom.

Continue reading

Rich Ta$ks

FINANCIAL LITERACY AND RICH TASKS IN MATH

Last week, we focused on making mistakes in the math classroom and how we can design learning to allow for these mistakes. This week, our professional learning group looked to build on this knowledge by exploring at rich tasks. As a group we defined what a rich task was:

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Rich Tasks  – Andrew Morris (2016)

The OAME also offers an alternative, but similar, explanation of rich tasks which is adapted from NCTM‘s Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions. This week, I am also responsible for hosting a webinar that explores facilitating financial literacy through math. What could more appropriate for teaching financial literacy concepts than the use of rich tasks?! As a former banker and a self-directed investor, I feel very passionate about educating our students about the importance of making sound financial decisions and how the money world works around them.

ONTARIO AND FINANCIAL LITERACY

An elementary Ontario curriculum that outlines the expectations for financial literacy does not exist, BUT there is the Financial Literacy Scope and Sequence which highlights the areas for financial literacy in each of the existing curriculums. This document is an excellent starting place to find entry points to incorporate financial literacy into unit plans. I do agree that a solid financial base comes from the combination of explicit and implicit financial teachings. My hope is that educators will continue to keep financial literacy as a core part of their teaching in all subjects, especially during math. At the end of my post, I will add a list of resources that I have used during my webinar as well as some other blog posts that look at financial literacy strategies.

RICH TA$K$ EXAMPLE

This rich task was adapted from from Kyle Pearce on tapintoteenminds.com. This is an amazing resource – please check it out! The final slide I made outlines the ideas behind this financial literacy rich task:

This task has clear connections to number sense and numeration in the Ontario Mathematics curriculum for multiple grade levels depending on the solutions given.

(Ex. Grade 8 – Quantity Relationships –  express repeated multiplication using exponential notation pg. 111 // Grade 6 – Quantity Relationships – solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1 000 000 pg. 88)

This task is differentiated by being open routed – different grade levels can be expected to solve using age/developmentally appropriate strategies. It connects to financial literacy big ideas of compounding interest and savings. It uses many of the process expectations, including reasoning, communication, problem solving, and selecting computational tools and strategies. It is also engaging and relevant to the students’ lives. It is therefore a RICH TASK.

It is clear to see that we can develop rich tasks to approach financial literacy in the classroom. I am so excited to enter my placement and watch my students explore mathematical concepts through the useful financial literacy lens. What other resources do you use? What kind of rich tasks have you explored your students?

– A

RESOURCES (will update)

Elementary Financial Literacy – Brian Page (Edutopia, 2014)

  • A blog post breaking down more resources

Big Ideas in Financial Literacy (Money As You Learn)

  • My favourite resource that breaks down some big ideas and their age-appropriate levels

Practical Money Skills Canada

Financial Literacy Resources by Grade (Edugains)

Designing Opportunities for Mistakes

An abundance of research and blog posts exist that point to the learning that happens when our students make mistakes. This week, I wanted to explore some ways to use this knowledge in the classroom/as a class. There are certain ways that educators can set the whole classroom environment to embrace mistakes, but going further I want to find ways that teachers can create math questions/scenarios that leave room for mistakes to promote learning.


MISTAKES IN THE MATH CLASSROOM

As I read about mistakes, I kept thinking, “OK great we need mistakes to happen, but I can’t force my students to get it wrong…so what do I do?”. I could not find many articles specifically on how to create openings for mistakes in the classroom. However, many of the ways we can do this, we already are familiar with. The following is a list of key ideas I compiled that I believe are essential to creating opportunities for mistakes in the math classroom (or all subjects!)

1. Encourage students to seek challenges

Carol Dweck – the pioneer of the growth-mindset – says, “I want challenges to become the new comfort zone” (PERTS, 2016). If we can encourage students to seek challenges, then the mindset of the educator and the student are aligned. As we discussed last week, there are many ways to encourage this growth mindset beginning with something as simple as praising based on ability (“You’re smart!”) but on effort (“You worked hard to achieve this”).

2. Make mistakes part of their work

This idea from Kelly O’Shea asks students to make an intentional mistake in their solution to a problem. They are able to choose a mistake that one of their group’s members made along the way to finding the solution, or create a mistake they feel other students might make. Unintentional mistakes are also welcome (as always!). Explicit mistake activities are a great way to get students to ask questions about mistakes rather than just pointing them out. This also asks students to reflect on the experience and review how struggle can be part of the learning process. My professor, Dr. Shelly Vohra, also highlighted an exit strategy that asks students to choose a favourite mistake they made during their math activity – a similar strategy to the one above.

3. Give work that encourages mistakes

This video highlights work with younger learners, but is very applicable for all ages. Let’s look at steps we can take to give work to encourage mistakes appropriately…

  • Find your student’s Zone of Proximal Development (ZPD). Vygotsky, in this paper, says that the ZPD is the difference between what the learner can do with help and what the learner can do without help. Instruction and questions should be catered to the ZPD so that our students can struggle, but struggle appropriately. The question is, how can we differentiate this for all students? Answer – question types!
  • In her blog post, “Open Ended Questions in Math”, Dr. Vohra explores the benefits of using multiple question types in the classroom – specifically open-ended and open-routed questions. Here is a chart she developed based on the work by Marian Small.
  • Within open-ended and open-routed questions we can also assign parallel tasks. Parallel tasks are sets of related tasks that explore the same key idea but are suited to different levels of student readiness. The Ontario’s Capacity Building Series Differentiating Mathematics Instruction suggests that using open-ended, open-routed and parallel tasks are imperative to differentiated math instruction.

If we use questions that have either multiple solutions or multiple ways to get the answers, we leave MORE freedom for students to mistakes. In my opinion, this is a beautiful way (theoretically) to encourage mistakes through the work educators give students!

WHAT NOW?

In our professional course setting, we worked in groups to take closed-type questions from popular math textbooks and change them into either an open-ended or open-routed questions with a parallel task. This seems like a solid step towards creating improved math instruction techniques. Creating open-type questions takes a lot of time and perhaps workshops like these would be useful to in-service teachers as well. There are some resources with open-type questions, but what do you think about in-service workshops focusing on building an open-ended question database? Also, please share any more resources you may have OR any ways you leave room for mistakes for learning in your classrooms!

– A

Resources

O’Shea, K. (2012, July 5). Whiteboarding Mistake Game: A Guide. Physics! Blog!. Retrieved from https://kellyoshea.wordpress.com/2012/07/05/whiteboarding-mistake-game-a-guide/

Ontario Ministry of Education. (2008). Monograph:  Differentiating Mathematics Instruction. Toronto, ON: Queen’s Printer for Ontario.

Ontario Ministry of Education. (2011). Monograph:  Asking Effective Questions. Toronto, ON: Queen’s Printer for Ontario.

PERTS. (2016). Make Challenge the New Comfort Zone. YouTube Video. Retrieved from https://www.youtube.com/watch?v=2d1CQS8YNRY

Vohra, S. (2015, April 30). Open Ended Questions in Math. [Image]. Retrieved from https://techdiva29.wordpress.com/2015/04/30/72/

Vygotsky, L. S. (1978). Interaction between learning and development (M. Lopez-Morillas, Trans.). In M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds.), Mind in society: The development of higher psychological processes (pp. 79-91). Cambridge, MA: Harvard University Press.

Don’t Call Me “Smart”!

Last week we looked at rebranding math – shattering the stereotypes and beliefs that have clouded the minds of many students. This week, we naturally transition our focus onto the mindsets of our students and the messages educators and parents/guardians convey. Quite simply, we’re looking at “fixed” vs “growth mind-sets”. A “growth mind-set” is one that understands the correlation between effort and achievement and has a strong will to work hard to improve and grow. A “fixed mind-set” is a belief that talents or intelligence are pre-determined fixed traits that can only improve so much.


THE RESEARCH

Perhaps the most famous researcher and author on this subject is Carol Dweck, a Stanford University professor who has spent many (40) years conducting research on the ideas behind the mindsets. She advocates that the Secret to Raising Smart Kids is that we shouldn’t “tell kids that they are [smart]”, rather help them focus on the process (Dweck, 2015). This highlights the dangers of praising students on fixed qualities, such as being talented or smart, because it stifles their efforts to grow and paints mistakes as failures instead of opportunities to learn and improve.

The test results, especially in visual form, really highlight the importance of the messages we give our students… but is it enough to just praise efforts? As we discussed this in our professional learning environment, I couldn’t help but think – if we only praise children for their efforts than we miss the overall objective of actually growing.

MESSAGES

Turns out, Carol also realized that many people seem to have misinterpreted the results of her studies. Educators cannot simply claim they have a growth mindset without conveying positive messages that promote learning. Messages and message-framing are important in and outside the classroom. You can find thousands of growth mindset messages online with a simple search, but I believe an equally important aspect of these messages is the consistency with which they are delivered. The educator AND the parents/guardians all need to convey similar messages and beliefs.

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(Espinosa, 2015)

ENVIRONMENT

In my grade 7 placement last year, my mentor teacher did not allow the students to say, “that was easy”. I loved this rule. “Easy” is a perspective, not a fact and stating something seems easy does not foster a safe environment for learning. If we want students to value effort and view mistakes as learning, the classroom needs to be set up for this. If a student is finding things “easy”, then the educator needs to find a way to help that student grow – a next step for learning or a problem situated in their personal zone of proximal development. Perhaps there is even a value in teaching our students to complement each other on the growth they see in their peers and friends.

BUZZ —-

“Growth mind-set” is clearly a buzz word in education these days, but for good reason. I hope as an educator I can apply strategies in the classroom and deliver the messages to create this growth environment, especially in the math classroom. There is no “math person”, rather every student can learn math because our brains have the capacity to grow! Please let me know some strategies and messages you have found to be successful in your math classroom (or classroom in general)!

– A

Resources

Anderson, J. (2016, January 12). The Stanford professor who pioneered praising kids for effort says we’ve totally missed the point. Retrieved from http://qz.com/587811/stanford-professor-who-pioneered-praising-effort-sees-false-praise-everywhere/

Dweck, C. S. (2015, January 1). The Secret to Raising Smart Kids. Retrieved from http://www.scientificamerican.com/article/the-secret-to-raising-smart-kids1/

Espinosa, O. (2015, June 18). Try one more time. [Image]. Retrieved from https://orlandoespinosa.wordpress.com/2015/06/18/one-more-time/

Ragan, T. (2014, January 30). Carol Dweck a Study on Praise and Mindsets. [Video]. Retrieved from https://www.youtube.com/watch?v=NWv1VdDeoRY

Rebranding Math

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Andrew Morris, 2016.

New Year, New Problems

As the new school year begins, the coverage in the media has quickly switched from back-to-school excitement to current issues in education. The most popular news comes on the back of the latest results from the EQAO testing which revealed a decrease in mathematics scores. The Canadian Press (2016) reports that this year, in Ontario, only 50% of students achieved a score at the math standard – a drop from the 58% in 2012. As a result, the government has put forward a 60-million-dollar plan to improve students’ test scores in mathematics. There is much to say about this (including my opinion on standardized testing), but check it out the link to explore some more about this plan. As I head back to the first ever* second year of teacher’s college, this news is extremely relevant and important.

Tell Me How You Really Feel

It is not unusual to hear how much students hate math class. In the above video, we can hear the negative opinions and beliefs about math and even gain some insight to how they are formed. Quite simply, students find math useless and difficult. This can lead to a cyclical process where students receive poor grades in math leading to decreased self-efficacy and increased perceptions of difficulty which again lead back to poor results. Another aspect are the stereotypes and perceptions associated with mathematics. North American media often portrays math as a negative subject and math is often stereotyped as a subject for boys, not for girls. Many people also believe that they are not a “math person” (which is just not true). My point is, there are multiple factors that contribute to this perpetual distaste and hate for math. However, the outlook for educators shouldn’t be bleak. In the Discovery Education video above, we hear that students who enjoy math enjoyed it because of what their teachers did! Change in attitude and standardize testing results will always require support from multiple environments in a student’s life, but there is at least one intervention point that we have control over – our classrooms.

Next Steps / Reflection

Where do we often go wrong? One of my classmates, Aaron Strong, suggested that math is often taught in a “vacuum” and is isolated from other subjects. This vacuum implicitly creates irrelevancy for students – math is meaningless. I also believe that this is a huge issue in our math education today. Change in the way teachers approach math will not be easy. There are many in-service teachers that are very set in their ways of teaching. As pre-service teachers I think we have an increased responsibility to bring new and fresh ideas to our schools.

This week has been useful in reopening my mind to the strategies I need to use to increase my resource pool and start thinking about math from an integrative viewpoint. As we continue to explore math this year, I will blog about the ways in which I hope to rebrand math because: (1) anyone can do it, (2) it is applicable in our lives and (3) yes, it can be fun!

– A

*My cohort is the first to enter a new two-year Bachelor of Education program in Ontario. Previously, the B.Ed. was achievable in one year of study.

References:

Discovery Education (2015). How do you really feel about math? YouTube Video.

The Canadian Press (2016). Only 50% of Grade 6 students met the province’s math standard.

Queen’s Printer of Ontario (2016). A renewed strategy for math.

 

Week of November 24th – Math Technologies

Exploring Resources

In this week’s session, we explored different types of math technologies. I will share a small collection of the resources we explored.

Graphing Stories: Graphingstories.com. This neat website is a resource that can be very valuable for teachers to get their students familiar with graphs. Students start with “stories” in video forms and have to try to plot the data on graphs. Students can decide the labels for their axis and then plot the points. Here is an example of our graph for “Height of Waist off the Ground” while watching a man on a swing.

Teachers can further extend this knowledge with reverse application and give the students graphs and have them attempt create a story.

Prodigy: https://www.prodigygame.com/. This website is Ontario-based math game for grade 1-8! Students battle against monsters, using math questions, to win coins and items. The game features customizable assessments and questions chosen by teachers to evaluate students. Teachers can choose from over 600 topics and view the students results in a highly organized way. Students can use several in game supports, including manipulatives and text-to-voice. Their profiles feature customizable avatars that use only first names of students to protect privacy. Parents are also invited to support their students learning.

Desmos Graphing Calculator: https://www.desmos.com/calculator. This online tool is sophisticated, but can be simplified by teachers to can explore mathematical language, ex. vertical and horizontal translations. Check it out!

Reflection

Technology is a key part of 21st century learning and it would be foolish and naive to leave it out of mathematics. This session was a key part to my continued growth a math educator. Reviewing the tools available and learning how to apply them has helped me gain confidence towards teaching different concepts using technology.
When I was in high school, I loved using the graphing calculators to explore tables of value and equations. Now, the tools we have available to explore and inspire math creativity seem endless. We can practice our math we learned in class or take chances to create new things in a fast and fun way. I’m excited to enter the teaching field with the skills to find and critically evaluate tools to use for math. I also have been consistently highlighting different math resources and games throughout my blog series. This collection will be helpful as I move into the lesson planning and internship stage of my teaching block.
This first semester of math has been great for me. I started with a closed mind about math and my willingness to teach it. As we continued our sessions and I listened to ideas and collected resources, I became more confident. Now, I find some excitement in being trying out some of the activities and games in my teaching placement. In December we will be starting Data Management, so I hope to try incorporating Graphing Stories to get my students critically thinking about what graphs represent.
– A

 

Week of November 17th – Data Management & Probability

Exploring Resources

This week’s math learning presentations focused on Data Management and Probability. We started by exploring experimental probability, then looked at theoretical probability and finished with a lesson on data collection. For the data collection, we were introduced to appropriate question construction. Questions should be clear and have discrete categories. We were asked to make our own questions and choose a fun way to collect data. My group chose the question, “Whose coffee do you prefer?” and gave 4 discrete options: McDonalds, Tim Hortons, Starbucks and Second Cup. Counters were placed in cups as a method to collect the data. The picture below is an example of this method we used.

After the lesson we explored several other probability resources. This included a “Horse Races” probability game. Students will use a chart to keep track of horses numbered 2-12. When you roll the dice (2) and land on a number, you move the corresponding numbered horse forward one space. The first horse to the finish line is the winner. Student’s can place bets on the horses they think will win. After the first round, it is imperative the educator stops the game and asks questions about theoretical probability. Students should note the numbers that have a higher chance of being rolled. An example of a lesson plan that uses this game can be found HERE, and bonus, it actually includes an online version of the game you can play!

For grades 4-6, OntarioMathResources.ca features a small but useful curation of data management and probability resources to help teachers get started with their lessons. Take a look.

For grades 7-8 , the Mathematics Assessment Resource Service has other probability and data management lesson plans and activities. It is definitely worth it to check it out.

Lastly, many of our presenters touched on the language of probability. When studying and teaching probability it is really important to be consistent with your language use and to clarify the meaning of the language to the students. The probability line, from mathisfun.com, is a great visual to explain the probability language on a scale of 0 to 1. I highly suggest showing some form of this visual with your class or working together to co-create something similar.

Reflection

I really enjoyed exploring some of the probability resources. I think this is an area of math that is fun and exciting, especially theoretical probability. One of the presenters talked about the misconceptions surrounding the independent and dependent events. I think this is one area of probability that I should become very familiar with before I start teaching because it will elicit many questions from the students.

I was talking to some teachers in Ontario, and many expressed that probability is usually left to the end of the year and sometimes gets overlooked due to time constraints. I think that as a teacher in the Ontario context, I need to be aware of this phenomenon and try my best to make data management and probability as important as the other strands in the math curriculum. As a kinesiology graduate, statistics and statistical significance were important concepts that underlined almost every single peer-reviewed study. I hope that I can pass on my knowledge of probability and significance with interesting and relatable material and context for students.

– A

Week of November 10th – Measurement

Exploring Resources

This week we looked at measurement topics such as perimeter, area, volume, mass, time and angles.

The concept of time as a measurement can be a little difficult to understand. We at different strategies to estimate, measure and record time. Students need to know the difference between analog and digital clocks. A really fun and interactive game we used to test the knowledge of analog clocks was a “clock bingo” game. The students each receive a bingo card with analog clocks and the teacher calls out/displays digital corresponding times. This activity is most suitable for grades 3-4. I also stumbled upon a cool Pinterest board that has neat activities for teaching time. You can check this out if you’re looking for some ideas.

This Scholastic blog has 10 great hands on strategies for teachers to use when approaching area and perimeter. In fact, one of our presentations included an activity from here. Students are to write their names in block letters on centimetre grid paper. They must find the perimeter of each individual letter and then combine the perimeters to find the total perimeter of their name. This is a great activity for the beginning of the year too as these names can go on the students math binders or as a name tag on their desks. Below is from Ellena’s math blog.. this is her example for our class!

Woolley, E. © 2015 Retrieved from http://woollenamath.blogspot.ca/2015_11_01_archive.html
One presentation explored volume. In grade 6, students must learn to estimate and measure volumes using the metric system. A neat activity we tried was using the cm block cubes manipulatives to estimate the volumes of empty boxes before we calculated their actual volumes. We tried this strategy on a rectangular prism (box of Kraft Dinner) and a triangular prism (Toblerone bar). When teaching measurement, it is important to remind students to be watchful with their units. Perimeter is linear (cm), area is in two dimensions (cm squared) and volume is in three dimensions (cm cubed)! The Khan Academy has a great set of tutorials for this topic.

Lastly, in our class we viewed a great resource for a “Minds On” portion of a lesson. This video is about unusual units of measurement and can be really useful to help students break the rigidity of thinking around the ways we measure. It also offers a bit of history on where our current measurements come from and it is simply entertaining and funny! Take a look!

Reflection

My father is the proud owner of an audio/visual company here in Ontario. Many summers I spent time working with his employees at various hotels, schools or office board rooms all over Canada. I can’t stress enough how valuable it was to know basic measurement principles. Every day we are encountered with measurement and conversions, but in my case it was extremely important to be accurate. We had to know the perimeter of the rooms, the lengths of the tables and screens, the volume of the speakers that needed to be cut flush into the wall. Having the measurement knowledge was extremely beneficial to me when realizing I had to make these calculations.
As we explored these concepts in our class and through the readings, my feelings we’re reaffirmed. My classmates highlighted relevant applications of measurements in our lives, especially with unit conversions and time. I feel extremely confident going into my classroom to teach this unit, regardless of age. I can’t wait to allow my students to explore measurement with manipulatives, make estimates, and then go out and apply their knowledge to real life situations. I also enjoyed adding to my knowledge base. Watching the unusual measurement video gave me some insight to where these expressions originated from.
– A

Week of November 3rd – Geometry & Spatial Sense

Exploring Resources

This week’s learning activities were centered around geometry and spatial sense. For 2-D shapes we used geoboards and toothpicks to demonstrate the qualities of the shapes. For 3-D shapes, we used clay and toothpicks to recreate the dimensions according to specific instructions. We also looked at creating nets of 3-D shapes and had time to construct various 3-D shapes using some pre-made nets.During the symmetry session, we had an opportunity use mirrors. We completed some half drawn images from a worksheet and also created half of an original drawing that was to be completed by a partner. The presenter also shared a tool from MathIsFun.com that allows you to create symmetrical drawings. Lastly, we looked at dissecting and combining shapes. Using tangrams was a fun way to explore the properties of 2-D shapes.

Near the end of our session we also reviewed some really cool applications that I would like to share! Click the links for more detailed reviews and to download.

Osmo is a one-of-a-kind app. This amazing app kit comes with a camera mirror as well as tangram pieces, letters and numbers. Even though it is on the pricey side, this app has some amazing classroom applications. One tangram activity has users creating shapes physically and the camera reads the pieces and displays the shape on the screen. Check out this video to see for yourself.

 

Slice It! is a neat app that requires users to slice shapes into a predetermined amount of equal pieces. It takes a good grasp of spacial sense to complete and is quite entertaining.

Foldify is an app that has users creating unique nets of 3-D shapes. Users can make simple nets or complicated nets (like a Spongebob character net) that have the option to be printed. Although its connection to the curriculum is more playful than serious, it is still fun for overall geometry knowledge and interest in the strand.

noiƚɔɘlʇɘЯ | Reflection

The lessons on Geometry and Spatial Sense definitely expanded my thinking as a math teacher. There are many valid and reliable resources that are available to create a fun and active learning environment. In my opinion, this unit of math is extremely hands on and visual. Students need to feel and see the shapes in order to get a fundamental understanding of their properties, especially with younger students. The use of tangrams, connect-blocks, toothpicks & clay, nets, or any other manipulatives to build and create 2-D or 3-D shapes has extreme value. I am excited at the opportunity to approach this part of the curriculum creatively with many good resources for my students. I really like the Osmo app. Even though it is expensive, it is a modern technology that beautifully combines kinesthetic and visual learning applications.
I also think it could be interesting to try and create cross curriculum activities that make use of geometry and spatial sense expectations. For example, I remember in Grade 5, my teacher had us constructing a method of transportation (ie. car or boat) in a woodshop type class. I would hope that as an educator I can build on an experience like this and incorporate mathematics expectations into an assignment to fully demonstrate the useful applications of math in our every day lives.
– A