8P29 Post 9

Watterson, Bill. "Measurement Homework." Retrieved from http://www.bakadesuyo.com/2014/03/how-to-make-your-kids-smarter/

           This week we are working on teaching measurement, which is usually a relatively brief, albeit important unit. Regardless of grade, measurement is a unit that allows students to be hands on with their learning, using actual measurement tools to record and analyze real world things. I am thankful in Canada we use the metric system rather than the imperial system that the Americans use because honestly, I think the metric system is much tidier and easier to memorize in terms of converting between different units e.g. centimetres to metres.

            In the textbook Making Math Meaningful, Small uses a standard formula for introducing different measurement concepts to students. There are three phases involved: definition/comparison, nonstandard units, and standard units. With definition/comparison, students simply identify what concept they would be measuring and then become able to recognize how different items can be bigger or smaller than others in terms of measurement. Using capacity as our exemplar, students will learn that capacity is the maximum amount something can contain. Showing them two differently sized buckets filled with sand, they should be able to see that these two objects probably have different capacities.

The next phase would be measuring with nonstandard units. Students use a little scoop to put the sand in the bucket, noting that it takes 10 scoops to fill the bucket. This stage seems like one that with most students you could move on from fairly quickly into standard units because if your students can understand the bucket’s capacity is 10 scoops, it shouldn’t be that much harder to make the jump that the bucket’s capacity is 500 mL. You can apply this strategy no matter what the unit of measurement is, although as I mentioned before, depending on the class, I don’t think it’s necessary to linger on phase one and two.

Measurement can be incorporated/combined with different subjects because many fields of study measure things in some way. For example, something we did in class today that was very fun was measuring distance of a standing long jump. Group members had to estimate how far they would jump and then prove their worth by making the leap. This is a very common measurement activity in physical education, as many times teachers have students record their process throughout the year, noting how many push ups or laps they can do at the start of the year and recording changes in progress periodically. As touched on earlier, students can have a lot of fun with these sorts of activities. It give students a welcome break from simply sitting and answering questions from the textbook, although there is a time and place for that as well.

I did my final learning activity presentation today. It was a hard one to make because I had to go with my Plan B option when I realized my Plan A idea really wouldn’t work that well with the unit. I had been reading some Lewis Carroll and came across a word problem I wanted to use. I thought students would find it interesting to do a math problem made by the author of Alice’s Adventures in Wonderland. However, I realized that although the problem in question dealt with elapsed time and calculating distance, it really was more a question about rates than about measurement. Instead I made a word problem based on the show Adventure Time! I don’t think many people got the references, but then again, my audience was not a classroom of 8 and 9-year-olds (otherwise their enthusiasm and knowledge for the show would’ve been much higher). But I suppose that’s one of those inevitable things as a teacher. Sometimes you’ll want to do something and it won’t quite fit, so you have to use your Plan B (or C, D, etc.). 

8P29 Post 8

This week in class was pretty busy because we were looking at geometry and spatial sense. The geometry unit is huge no matter what grade you teach, so there is always a lot of ground to tackle, and almost an overload of things you can do with the class to help them learn. Manipulatives such as geoboards, toothpicks and modelling clay, and even blocks that young children play with are all appropriate for geometry because it is such a visual math unit.

Thinking about geometry and spatial sense is something that students can incorporate into their daily lives because shapes are everywhere. It is useful to have an awareness of one’s surroundings and the objects in them. An activity we did in class this week that I really enjoyed was a “geometry scavenger hunt” where you needed to go around the school and find different 2D and 3D shapes. Most of what you’ll find is rectangular prisms, but I lucked out and somehow found a dodecahedron and heptagon too, which are not really shapes that you necessarily expect to find every day.

One of the things I was reflecting on most this week is taking an interdisciplinary approach to the classroom. There are only so many hours in the day and if you teach all subjects to your students rather than them being on a rotary, it can sometimes be tricky to find time to fit everything in. One way to address this issue is by incorporating different skills or subjects into class projects.

"Geometric Paper Ornaments." Retrieved from
goo.gl/dw7Fyb

Geometry lends itself to art tidily. Drawing is at its core putting together multiple smaller shapes to put together a cohesive picture. It’d be good to show your students, especially those who love art, that learning to represent 3D shapes can really step up their drawing game. Having that knowledge of perspective and spatial awareness really enhances the realism of a drawing. When learning about 3D shapes, you could give your students an activity where they have to create a perspective drawing of a room or a city street. Students then have to establish a vanishing point, and then create a series of shapes (primarily cubes and rectangular prisms most likely) oriented towards their perspective point. I loved making drawings like that when I was in art class, without ever realizing it was helping me practice representing 3D shapes.

Aude Sapere. "Two Point Perspective." Retrieved from
http://aude--sapere.deviantart.com/art/Two-Point-Perspective-City-337052681

Other art or craft-like projects that actually help students develop their geometry skills is through using nets to make shapes, such as animals, or by making geometric paper lanterns or ornaments with toothpick skeletons and tissue paper. Regardless, there are many ways to make geometry fun for students and keep them learning without them realizing it.

Geometry was never something I was really passionate about as a student; I always found rotation on a plane to be difficult for example. I also found it frustrating because in some geometry assignments, you’re marked on neatness, and I’m left-handed so my hand would smudge the pencil lead across the page and I would get marks off. But I think a way to get me more excited about the topic (and hopefully get the students excited too) is through some of the activities like the ones I just shared. 

It’s a Draft, not an Illuminated Manuscript: Making Revision Less Scary for Students

Anonymous. "Monk Working on Illuminated Manuscript."
Retrieved from http://goo.gl/MeIpbv

Eight-year-old Dominic has been entrusted with a most sacred and important task. Through a combination of inspiration from the heavenly Muses and his own memory, he must craft an account that will be preserved throughout the ages. All the writing is divinely inspired; there can be no room for error. Heaven forbid one thing be erased, changed, or altered from its original form. The time to finish his task is nigh. There must be no hesitation.

            What is his task you ask?

            Constructing a descriptive paragraph about his family’s trip to the water park in his writing journal.

            No, in truth there is nothing exceptionally important about constructing that descriptive paragraph. It’s fun, it helps develop Dominic’s writing abilities and practice his use of adjectives, and it’s a topic he’s fairly interested in. But it seems to be the case with so many students that the revision part of the writing process is something to be feared and avoided. It is almost as if they have chiselled their assignments into stone rather than scratched it out on a piece of looseleaf or typed it on their electronic device. To change something is both impossible and an indication of failure and weakness.

What Can We As Teachers Do To Help?

            Rest easy, gentle educators! There are many ways to help inspire revision. I gained much insight from Noreen Moore’s eccentrically named blog post “Revision Makes My Students Thirsty.” She too notices the strange effect revision has on her class and makes some suggestions about how to cause an attitude shift.

            One of the things she suggests, which I absolutely love, is exposing students to what some experienced and famous writers think about the writing process and how much time they spend revising. This can take the form of quotes from famous authors about revision around the classroom, or you can even show some early drafts of different authors’ works, and show how much the poem or story gets marked up and tweaked before it reaches its final form.

            If students can see that writers they hold in high regard, people they think are really smart and creative, are comfortable changing their work, perhaps this will help them in revising their own work as well.

Jane Austen's draft of Persuasion. Notice how much has been crossed out!
"Jane Austen Persuasion Manuscript." Retrieved from
http://www.janeausten.ac.uk/manuscripts/blpers/Front_(left)_board.html

Try Some Revision Activities

            There are also some activities you can do in the classroom to help light the fires of inspiration. There are the tried and true things you can do, such as peer editing or having the student read their work aloud (not necessarily in front of the class), so the student can distance him or herself from the piece and see what changes to make. Students can bring in music, images, photos, etc. that connect to his or her piece and see if that they can incorporate any associations from those images into their writing.

            Teachers can also try re-branding revision as play or tinkering. Revision can be scary, because it implies that there was something wrong with the piece of writing. Well, the writing may not be wrong in that it is grammatically incorrect, but it could use some tinkering in that there could be more figurative language to make the writing more colourful, or maybe there needs to be an additional character to flesh out the narrative.

Closing Thoughts

            Revision, proofreading, and editing are all important parts of the Writing strand of the Ontario curriculum, and need to be treated with the same attention, if not more, as the actual drafting of the piece. Helping students to see that revision is not scary, but to be encouraged, will help them now and in their writing for years to come.

            Very few things are set in stone, and students need to know that their writing certainly isn’t. And that’s okay! 

8P29 Post 7

Anonymous. "Teacher Lesson Plan Ecard." Retrieved from
http://www.teachjunkie.com/filing-cabinet/teaching-realities/
NOTE: This is not what happened to me when working on my
lesson plan haha!

           It’s getting to be an exciting time in teacher’s college because we’re starting to ramp up to actually teaching lessons to students! Woo! All the foundation work in every class, not just 8P29, is finally going to be applied and put to a practical use.

This week I worked on my first draft of the math lesson plan we’re have to complete. I actually had a lot of fun doing it, and have ideas for how to create follow up lessons to start creating a unit. It was not without its difficulties though. I decided to make my lesson as practical as possible, so I tailored it for the students in my placement (a grade 4/5 split). I was initially stumped because I wasn’t sure how to create activities that didn’t dumb things down for the grade 5s but wouldn’t be alienating for the grade 4s. Luckily the topic of my lesson (introduction to telling time) has associated learning expectations that are similar. The only difference between the time expectations for grade 4 and 5 is that grade 4s need to identify time on a clock down to a minute, and grade 5s need to be able to identify seconds as well. Within the direct instruction portion of the lesson, I can still teach all the students the same things, but then ask the grade 5 students of the class some more complicated questions about calculating time. Grade 4s can feel free to answer but precedence is on a grade 5 answering the question correctly. We’ll see how that actually works in practice, but in theory it should turn out alright!

I can tell that 8P29 is rubbing off on me because during my lesson plan, I automatically started thinking of multiple strategies students could use to work on their homework problems, which is not a level of reflection I had at the start of the year. Visual aids and manipulatives never really helped me that much in math when I was a child, so I wasn’t in the habit of thinking about using or talking about those methods, but now it is becoming part of my automatic brainstorming about activities to try to incorporate those elements into lessons **when possible**.

On the topic of manipulatives and visual aids in math, one suggestion from the textbook I enjoyed the most this week was using balance scales and paper bags to help students visualize balancing equations in the patterning and algebra unit. Using this method, I feel like students of many ages and abilities could grasp how approach finding x in a problem because it shows the direct consequence of what happens when you don’t balance the equation (literally!).

I wouldn’t mind testing out this method on my friend’s 8-year-old daughter, as the last time she was over, once she finished her place value homework, she expressed an interest in figuring out linear algebra problems (isn’t it amazing how children natural want to know things and challenge themselves?). She was able to grasp a fairly straightforward question (n +5 = 7) by counting that 7 is 2 more than 5, so n is 2. But when she asked for a harder one, I gave her n + 4 =11-3, and she was having a bit of trouble understanding balancing. I think with the scales and paper bags this would be much more evident for her.

There’s so much more I want to talk about; I’ve found this course inspired my creativity, something I honestly didn’t think would happen with teaching math, but I’ll leave it at this for now.

Part of the In-Crowd: Multilevel Reading so Everyone Can Join In

Eletu, Olu. "Alphabet, Children." March 17, 2015.
Retrieved from https://stocksnap.io/photo/Q5FJUK9OFH

No one likes to feel left out. And for children, many of who want nothing more than to achieve the status of “fitting in”, this is an especially concerning matter. You want to wear what your friends are wearing, have the same toys and gadgets that your friends have. So what do you do as a self-conscious child when for whatever reason, be it giftedness, a learning disability, whatever, you find yourself ahead or behind the pack? You feel awkward, like something is wrong with you. As educators, we can help with that. No, we probably can’t convince a student’s parents to get them those Nike shoes that everyone else in the class has, or those special edition, holographic Pokemon cards, but what we can do is help students feel included in classroom activities, even if the student might be reading at a grade or two below or above the rest of the class.

How do we do this?

By introducing multilevel reading in the classroom.

Catherine Cornford at University of Ottawa wrote a brief, but helpful research monograph about multilevel reading called “What Works? Using Multilevel Texts—Supporting Literacy in the Inclusive Classroom.” In it, she argues that one of the reasons for lack of student engagement in reading is that the text is either too easy or difficult and provides some useful suggestions to how educators can incorporate multilevel texts or scaffolding into the classroom so students can read and learn together, regardless of reading level. You can download the PDF here.

So how could multilevel fiction help?

Multilevel fiction may be written at different levels of complexity, so students can all be reading the same story. They may also use multiple genres or writing styles to communicate information, for example, one version of the text is in verse and another version is in prose. Some texts may even use fiction and non-fiction, for example incorporating a narrative and informational text. The Ontario curriculum’s Reading strand expects students read and understand a variety of texts, literary, graphic, and information, and to understand how different text forms and stylistic elements help communicate meaning. Studying a multilevel text exposes students to multiple writing genres and styles, thus giving them versatility in their reading comprehension.

Can I still be inclusive even if the text isn’t designed to be multilevel?

Even if a text isn’t specifically multilevel, teachers can still be inclusive with reading in the classroom. One of the ways to do that is through reading buddies, where a teacher would pair up students of different reading levels and abilities to participate in a shared reading activity. This can give a student of a lower reading level exposure to a more challenging text, but with some guidance along the way. The student of the higher reading level still benefits, because one consolidates knowledge through explaining it to others.

In summary

We all have different skill sets and aptitudes and in the inclusive classroom, there’s no reason why we have to segregate students based on their reading level. Providing a narrative that scales according to reading level makes all students feel like they’re part of the group and can increase reading engagement. I get so excited when I see students interested in what they’re reading and eager to share what they’ve read with their peers. I think everyone should have that opportunity, whether they’re reading Seuss or Shakespeare. 

8P29 Week 6 Post

This was the week I did my learning activity assignment, which consists of a 10-minute presentation where you lead your peers through an activity you could do with students and the different strategies for solving the problem. It went surprisingly better than I thought it would; I had had nightmares about it the night before, and usually presentations don’t faze me. This week’s theme was on proportional reasoning and includes questions on ratio, rate, and percent. Proportional reasoning can be a trick thing to teach students because it relies on students being able to change the way they think from multiplicative to additive thinking, and also relies on a firm understanding and snap knowledge of multiplication, division, and factors. Considering how many students (and adults!) rely on calculators to do even basic math, this can be a bit of a challenge. But with the proper practise and scaffolding through the use of charts, manipulatives and hundreds grids anything is possible.

Pythagoras and the Ratios book cover. Retrieved from
http://www.amazon.com/Pythagoras-Ratios-A-Math-Adventure/dp/1570917760

I liked exploring the different children’s books recommended at the end of the proportional thinking chapter of Small’s Making Math Meaningful. Pythagoras and the Ratios by Julie Ellis is a fun way to introduce children to mathematical history and the idea of ratios. The book deals more with ratios in musical chords than it does with other types of ratios, but I think that’s still acceptable because it can show the student that math doesn’t exist in a vacuum, but actually shows up in all parts of their life. Something I’m learning through my placement is that it’s often hard for teachers to fit everything they want to teach into a day, because activities inevitably almost always take longer than estimated. That is why it’s a good idea to integrate subjects as much as possible. Have students read about book about science or math, that way you kill two birds with one stone.

The activity I used in my ratio presentation had to do with adjusting recipes based on serving size, but I brainstormed a couple other ideas I think students might find fun. Having seen the movie Antman a few months ago, it got me thinking about how an ant’s relative strength is much much higher compared to its mass than a human’s strength is. It might be fun to learn about different animals and ratios by finding other animals and insects with “superpowers” like the ants and figuring out how that strength scales if that animal was the size of a human. I haven’t fleshed out this idea though, so it may be too complicated to put into practice in a classroom, we’ll see.  This year is going to be full of trial and error, but I don’t mind. No one ever learned anything doing the same thing every day.  

8P29 Week 5 Post

This week the focus was on integers. Integers aren’t too bad once you learn the rules. The trick is to understand the logic behind the rules, otherwise they become harder to remember and you can mix them up depending on what operation you’re completing (for example, thinking two negatives make a positive when you’re subtracting, rather than multiplying or dividing integers). But once students understand the rules, it becomes simple computation, something students would have been doing for years already.

I may have mentioned this before, but I have to say that Marian Small’s book Making Math Meaningful is a tremendous resource for pre-service teachers. Everything in the book is laid out clearly and there are plenty of class activity ideas within each chapter. If you’re a pre- or in-service teacher looking to improve their skills teaching math concepts, go out and buy this book, you won’t regret it.  Small’s chapter on integers is no exception to the rule. She suggests a fun card game called Integro to help students practice adding and subtracting integers. Have an Integro tournament in your class to see who will reign supreme as Imperator Integro (that’s a working title for the winner of the tournament, message me if you think of a cool one).

Making Math Meaningful by Marian Small p. 327

It’s easier to teach if you can get students to connect the concepts to something in the “real world”. Small suggests temperature, altitude, and sea level, but I think the real world example I like the best is debt. One, it’s good in general to teach students that debt is an awful hole that makes you think you have money, but really you don’t, and two, you can apply the debt situation to any of the operations. Here’s a quick example:

If I’m broke and I borrow 5 from Tony and 3 from Pauly, how much total debt do I have?

(-5) + (-3) = (-8)

Here you can see adding together two negatives puts you deeper in the hole, because I start at 0 and now I owe money I don’t have. Now let’s say I have a windfall:

Tony, in his magnanimity, has forgiven my debt, but Pauly still wants me to deliver. However, Silvio also gave me $4 birthday money as a gift. Now what’s my total debt?

(-8) – (-5) + (+4) = (+1)

See, I paid back Pauly, because he was starting to scare me a little (his eyes get all buggy when he’s angry), which makes me debt free, and also not broke anymore (thanks Silvio!). Putting it in a story like this makes it make a lot more sense than trying to memorize a set of rules. Add in some manipulatives and a number line (number line is key), and your lesson would hit a lot of bases.

What this is teaching me about teaching math is that there’s a lot more to students learning rules than them just learning the rules to certain concepts. Without the “why” there is very little retention, or common mistakes and mix-ups can occur. The “why” doesn’t have to be tremendously complex, but without context math is meaningless punching in figures like computers, and we aren't trying to make students into automatons, but autonomous, curious, problem-solving individuals.