8P29 Post 11

I like to hope my tests will be more reasonable than that.
"Math Test Joke on Professor's Door." Retrieved from
http://www.mirror.co.uk/news/weird-news/hilarious-note-posted-maths-teachers-4565393

The more I spend time in the classroom, and attend the math course at Brock, the more I realize how different math class is now from when I was a child, and it is definitely a change for the better. There are far more activities and collaborative work compared to just sitting at your seat and answering textbook questions and there seems to be a greater focus on finding different ways to assess student learning than merely taking tests.

Of course, doing practice questions in the textbook or taking quizzes and tests still have their place in the classroom, and they will still be a reality in my own math class, but those don’t have to be a teacher’s only options anymore. Students should have opportunities to explain their thinking and to develop their metacognition, so that they can start to think about and even refine their problem solving process and figure out what strategies work best for them while problem solving. Students should have opportunities to work on math that is appropriate to their grade level, but also problems that could be applied to multiple grade levels and challenge their reasoning and math skills.

Lucky for educators, we have the internet, and there are a ton of cool resources to help us out with this endeavour. Dr. Khan showed us an example (Challenge 03 Finger Counting) from www.collaborativemath.org, which has a variety of challenge questions posed, but that is only one of many other places that you can find riddles and math problems that will engage and challenge students. Students could work on a difficult question like the Finger Counting over the period of a week or more, and then record their solution and reasoning in a brief video using the app Show Me. This is a way to assess students without having to rely on the traditional test-taking method. I don’t think this should be the main source of assessment material, but it is certainly a way to differentiate based on student interests, skill sets, etc.

 The main form of assessment will be observational notes, which makes a lot of sense. As I’m circulating my placement class and looking over student work, I’m making tabs on who seems to be getting it right out the gates, and who seems to need more practice. It’s important to have those moments so you can help the student build their knowledge before the test or quiz where there’s an achievement level associated with it. As an example from my own experience, I noticed one of the students (we’ll call him Abdul), was mixing up some of the steps when it came to multiplication and regrouping. I spent extra time walking him through the process and in my absence, my associate teacher sent home some additional practice problems for him to work on. When I saw him on my next observation day, there was such a difference! Abdul was solving problems quickly, often figuring out the answer well before many of his classmates and his work was free of error. If that had not been caught in my initial informal assessment, his mistakes may have adversely affected his test scores, and all over errors easily fixed through some addition instruction.

This first math course is nearing completion and I’m starting my practicum within a few weeks. I’ve learned a lot, but I’m sure I will make twenty-five million mistakes and when I think I’m finally getting the hang of it, I’ll make another mistake. But that’s teaching and that’s life. It’s best I just get in there and start trying.    

Here is a link to my digital portfolio, which is a "greatest hits" if you will of math resources compiled over the term: http://8p29digitalmathportfolio.blogspot.ca/

8P29 Post 10

We’re coming to the end of the year in our first math course of teacher’s college and this week we worked on what I’m pretty sure is the last unit we’ll be working on: data management and probability. The next few weeks will be on assessment and lesson/unit planning, or at least that’s my prediction based on what I’ve looked at in the syllabus.

Data management and probability is a relatively short unit compared to some of the other ones, such as number sense and numeration. I think the intention in my placement is for the data management unit to only be 2-3 weeks. Nevertheless, this unit is a great opportunity for your class to let loose and have a little fun, because there are many games you can play to help demonstrate probability concepts.

One such game we did in class on Friday was the horse race game to show the most likely dice rolls when rolling 2 dice. Students have to set up a racetrack (graph) numbering all the possible dice outcomes from 2 to 12. Each number represents a different horse. To make things interesting, have students pick a “horse” they think will win. Students than have to roll the dice and the result is the horse that moves forward e.g. roll an 8, then horse 8 gets a tick on the racetrack. The first horse to get to 7 (or some other agreed-upon number) is the winner. Students will notice that most of the time, 7 will be the winner, or very close to it. From there, you can launch into a lesson demonstrating why this is the case. I am definitely going to use this activity in my placement classroom because I think the students will get really into it.

Anthony92931. "Suffolk Downs Horse Race." August 1 2007.
Retrieved from https://en.wikipedia.org/wiki/Horse_racing#/media/File:Suffolk_Downs_horse_racing.JPG

 Another reason data management and probability is fun is because students get to do surveys and record their collected data. Students can be creative in these activities and make up a survey on anything they’d like to ask their schoolmates about e.g. music tastes, video game, eye colour. It gets them up and moving, which is a welcome reprieve from sitting still in their seats all day.

Something that is important as a mathematics teacher is varying the activities that you do in the classroom. There is a time and place for students to sit and answer practice questions at their desk individually, but there is also a time to see math in action, though games and tasks like the ones mentioned above. I feel very lucky in my placement because the students seem pretty pumped to do math problems each day. I’m not sure if that is unique to this class, or if 9 and 10-year-olds are always this excitable. I really don’t remember cheering after completing math problems as a class, but now I wish that we had done that every year of math, even in high school! That enthusiasm gives me flexibility in what I can do in the classroom.  

"Yay math!"
"Children Cheering." Retrieved from http://goo.gl/DqRu5i

Listen to your Heart (and the Teacher): Developing Student Listening Skills

"Listening to Instructions." Retrieved from
https://www.pinterest.com/pin/276619602089214994/

The above teacher meme is facetious, but nonetheless an accurate portrayal of what happens in many classrooms. Listening is a vital life skill and unfortunately, large amounts of students for a variety of reasons are not strong listeners.  Now I’m not here to speculate about why students may be poor listeners, and I’m certainly not going to give the cop-out excuse of the prevalence of technology because let’s not kid ourselves here, children have been getting distracted long before tablets and smartphones came on the scene. What I am here to do is discuss some suggestions of what we can do to help students become better listeners, and thus better communicators and citizens.

            The article “Let’s Talk about Listening” from The Literacy and Numeracy Secretariat on EduGains has some great ideas on activities to help students listening comprehension and ways a teacher can create a listening classroom. I’ve summarized some of the important points below and added some thoughts of my own.

Listening is a Full Body Experience

            It’s not just your student’s ears and mind that should be at work when listening, but their whole body. Teachers mainly in the younger grades (although it is no less important in the higher grades) talk about the concept of “listening bodies,” that is the way your body should look when you’re actually listening to someone. If you’re listening, you usually turned to face the speaker, looking at the speaker, not talking, and if you are moving, you’re making signs that you are hearing the speaker e.g. nodding your head, adjusting your facial expression. Students need to know that this is what they should be doing to help them listen better.

Demonstrate to students what a listening body looks like. Feel free to even get a little silly if that’s what it takes! Ask a student what they did on the weekend, and when he or she starts to talk, turn around and go stare into the corner, Blair Witch style. It’s goofy and exaggerated, but hopefully it will show your students the absurdity of incorrect listening body language.

Pictured: A poor active listener
End of The Blair Witch Project movie still. Retrieved from
http://www.mtv.com/news/1869809/blair-witch-project-15-anniversary/

Mental Checklists

            It takes practice to become good at listening, and it’s an ongoing process. Even the most focused of people sometimes need to check wandering attention if they’re not engaged. Imagine then what it’s like for a student with issues with distractibility or central auditory processing. This is why all listening needs to be taught as a meta-cognitive process. Students should have mental checklists to make sure they’re understand what the speaker is saying. I find with some students who get distracted easily, even a physical checklist can be helpful. If they catch their attention wandering, they put a checkmark down in their notebook.

            Students should also be asking themselves if they understand what’s being said and if they don’t understand, they need to feel free to ask a question. This part is highly dependent on the teacher, because if a teacher shows impatience for questions, then the students will be less encouraged to clarify information with the teacher. What is not acceptable is having to teach the entire lesson all over again because the student wasn’t listening the first time around, but on the whole, questions should not be discouraged. Make sure you establish with your class that you should feel free to ask questions to double-check what they need to do, or to inquire further into a topic they’re interested in.

Model Behaviour

 

"Storybook active listening bodies." Retrieved from
http://www.cwtherapy.com/wp-content/uploads/2012/11/cw19.jpg

           Lead by example. Show students how to be a good listener by listening to them. It doesn’t just have to be through remembering a story they told, or what console they play, but responding to their learning needs in the classroom. Students can be extremely perceptive and they can usually tell right away if you’re someone who cares.

            Listen with your eyes and ears to ensure student understanding of concepts, to figure out if they’re perhaps holding something back or feigning understanding to avoid embarrassment. A teacher who is a good listener will see that and respond accordingly. Little things like that can mean a lot to a struggling student, or any student!

Listening is part of the Oral Communication strand of Literacy in Ontario, but listening skills transfer over into any subject in the classroom, or any interaction the student will have throughout the day. Feel free to do listening activities that are cross-curricular, assessing student listening skills even if what they’re listening to is a social studies podcast.

Apart from the article I mentioned earlier in the post, I also recommend Julian Treasure’s TED talk “5 ways to listen better” if you have 8 minutes to spare (of course you do, don’t lie!). It is an entertaining and direct speech on listening and you can definitely try some of the techniques he suggests with your class.  Learning to listen is a big task, try to have students work on it as much as they can and they will quickly notice the benefits of being more present in the classroom.

             

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!