looking at our world through a mathematical lens

On Tuesday at Grauer, I worked with Ms Poon and her class of grades 4 and 5 students. We began our session together with a short discussion about what math is…all the different areas of mathematics. We then explained that we were going to go outside of the school with the iPads and use the camera to see what mathematics we might notice. The students were a bit hesitant at first but soon began to see math in all sorts of places. The students worked in partners for this task.

When we got back to the classroom the students went through their photos and chose one that inspired them mathematically. We discussed what the photograph made them wonder about (and many of these questions had emerged when we were outside) and what kind of mathematical problem they could ask based on the photograph. During our discussion of problems we discussed how a problem really isn't a problem if you know how to solve it right away which helped students move on from the more standard word problem format (ie. There were 43 leaves on the ground and 26 blew away. How many leaves were left?).

How many pieces of garbage can fit in the garbage can?

How many squares are in this window?

How many triangles are there? How many lines are in the wheel? Is the shape symmetrical? 

As students posed their problems, they began to think about how they might solve them. Some students used the screencasting app ShowMe to share their photograph, state their problem and explain how they might start to figure it out.

The students emailed their photos and problems to me and during our next session together we are going to compile the photos and problems into a photo book, possibly using Book Creator on the iPads.

~Janice

place value constructions in grade 3

This week two grade 3 classes in Richmond played around with some place value concepts as they built animals using base ten blocks. At both Grauer in Mrs. Partridge's class and at Cook in Mrs. Verkade's class, the students shared with me what they knew about place value.

At Grauer, the students stated:
"We use ones, tens and hundreds."
"We use the 0-9 digits in each place."
"1-9 in the ones, 10-99 in the tens, 100-999 in the hundreds and 1000-9999 in the thousands."
"Each spot has a value. Each number goes ten times bigger each time."

The students were able to demonstrate with the base ten blocks that the ten-block was ten times bigger than the ones block and the hundred-block was ten times bigger than the ten-block. Understanding this ten-timesness is a big idea in understanding our place value/base ten system.

I provided the value of 257 and asked the students to create an animal worth that much. The students created all sorts of creatures!

The students were asked to discuss each part of their animal - what part showed the 200, what part showed the 50, what part showed the 7 and expanded notation was introduced. It was interesting that in both classes, all the students used 2 hundreds, 5 tens and 7 ones  for their materials, although both classes have been working on different ways to make large numbers. This made me wonder how I could have presented the task slightly different to make it a little more open so that students might have used different combinations of hundreds, tens and ones to make 257. Then again, it worked out well for  introducing expanded notation!

The students then could create their own animal or other construction, as long as they could figure out what the value was. They used the camera on the iPads to take a photo of their creation and then used the Skitch app (a first time for both these classes) to show two other ways to represent the number or value of their creation.

In both of the above examples the students had to problem-solve around how to record their values in expanded notation as in both cases, the students used more than 9 ones. Carlo's butterfly used 2 hundreds, 3 tens and 12 ones so he (and others) decided to regroup his 12 blocks into 1 ten and 2 ones for the purposes of expanded notation. 

~Janice

Math Catcher Outreach: seeing mathematics in our lives

This week I attended a session presented by the SFU Math Catcher Outreach Program to a group of Combined Studies students and some other invited students at Hugh Boyd. The main goal of the program is:
 to generally popularize mathematics and to increase students’ awareness about the presence and importance of mathematics in their lives. 

Dr. Veselin Jungic (Dr. J) is a mathematics professor at SFU and coordinates the program. He and two of his students shared their personal stories with mathematics, engaged the Boyd students in some mathematical thinking and presented some examples to help the students "see" the math in the world around them. We then were able to handle some amazing three-dimensional geometric models including some created by a three-d printer.

The students particularly enjoyed our opportunity to create our own geometric models.

More information about the program can be found HERE.

A big thank you to Leanne McColl, Teacher Consultant (Aboriginal Education) for organizing this event for our students.
~Janice

where is math in our classroom?

In September, I kind of got a little ahead of myself when working in Louesa Byrne's K/1 classroom at Thompson. Louesa has been investigating the use of Story Workshop with her young students and I said, hey, why don't we try a Math Story Workshop! We used Book Creator and the students created little scenes and then used the audio tools to record their voices telling their math stories.

A question emerged from a little five year old...What is math? Wow. Big question! This was the "getting ahead of myself" part and I realized it right away. It was September in a classroom with many students who had no formal school experience. Part of me thought it was great they really didn't know what math was...should we be compartmentalizing everything anyways? Couldn't we just look at everything as learning?

So last week we backtracked a bit and did a class brainstorm about makes up mathematics. Many students were able to contribute ideas to the class chart and I could tell some students were still unsure.

Louesa set the students up in partners with an iPad to share. Two days before I came in, Louesa had introduced the Haiku Deck app to the class and they learned how to start a new slide show, search for an image and add text. I popped into the class at the end of the day and tweeted out that the students were working with Haiku Deck. Within seconds, the good folks at Haiku Deck tweeted back! So fun for the students to see there are lots of people interested in what they are doing!

The students worked together and took two photographs each, using the iPad. They walked around their classroom looking for math and I followed along with my iPad, amazed at the different things they found and created. The students added their text and then we had a little sharing circle so we could see everyone's Haiku Decks.

And here is the collaborative one that I created with the students on my iPad:

exploring ways to represent learning in intermediate math classes

The Quilchena intermediate teachers are engaging in a collaborative professional inquiry this school year, looking at ways for students to represent their learning in mathematics. Alongside this, is looking at forms of assessment that are authentic and honour the different ways that students are representing what they know.

The teachers are beginning to use math journals as a way for their students to record mathematical thinking and today during our team meeting, I suggested the importance of opportunities for oral rehearsal before students record their thinking in writing and diagramming. I shared some examples of screencasting using the iPad as a way to capture mathematical thinking and to have "evidence" of this for assessment purposes.

I spent the last block of the day in Ms Simpson's grades 4 and 5 class. This week, the students had been working on using benchmarks to help them estimate when adding large numbers. They were doing a game from their textbook aimed at practicing specific skills. As the adults circulated in the classroom, they asked the students to explain their approaches to estimating the sums of a pair of numbers.

I pulled out my iPad to use the ShowMe screencasting app with one grade 5 student and captured his thinking in the ShowMe below:

We shared the student's ShowMe with the rest of the class and the students and teachers were intrigued by the use of technology in this way. I think this oral and visual capture is a great way for students to sort out their thinking and show what they know. I'm looking forward to continued work on this inquiry project this year.
~Janice

counting on fall: math stories

This week I visited Ms Teramura's and Ms McKenzie's Kindergarten classes at Errington Elementary.

We read the first few pages of Counting on Fall by Lizann Flatt and then I role played a math story using a bear and an eagle puppet along with some acorns the bear had gathered for a snack.

The students were then asked to tell their own math stories, using materials set up on tables around the classroom.

 

 

Although many of the students did not specifically tell math-related stories, they enjoyed creating stories with the materials, and the adults in the rooms had the opportunity to ask students to count the different materials they were working with to assess one-to-one correspondence and general number sense. The two videos below were created using the Vine app:


note: click off the red X by the speaker icon in the top left hand corner of each video in order to hear the audio
~Janice

looking closely: finding treasures

The kindergarten students in Mrs. Grisdale's class at General Currie went outside on a beautiful, crisp autumn day to spend over an hour looking closely at nature's treasures. We had all sorts of amazing finds - chestnuts, acorns, leaves of all sorts, special tree bark, mushrooms and dandelions seeds.

This class spread their wings and travelled a little farther than they usually do when they go outside. General Currie has a huge park area and many older trees. The children found many many treasures and I noticed an acorn or too being quietly placed in pockets. The students were on a treasure hunt looking for acorn "hats".

This class has been working on observing using their five senses and you could really tell by the types of comments the students made - they had so many great descriptive words and great connections!

"It's like a belly button on the tree."

"English Bay" (ESL level 1 student connecting white birch bark to tree she saw at English Bay!)

"Leaves are falling from the sky."

"It is prickly."

"There was red transparent stuff stuck to the tree."

"The bark is smooth and bumpy. It's white like in the book."

"I found a rainbow of leaves."

The kindergarten students were excited to be scientists and took pride in the special tools they were given to look closely when they were outside. One little guy asked if he could use the Olloclip on my iPod Touch and after taking a few photos exclaimed, "That's like a magnifying glass for your camera!" 

I'm looking forward to working with this group of young scientists again!
~Janice

looking closely in one small spot

This week, I returned to Blair to spend some time with the two grade one classes. First, we showed a few pages from the book One Small Square: Backyard by Donald Silver. There are also Woods, Pond, Tundra, Seashore and many other versions in this series.
Next, Mrs. Sato, Mrs. Quan and I took the students out into the Blair park to look closely at one small space/rectangle. The teachers had made simple frames out of manilla tag but more permanent frames could also be used - made out of twigs or popsicle sticks, framing mats or actual empty picture frames.

The frames really helped the students to pause and focus their observations. I suggested they act like detectives and see what clues they can find about what living things might have been in their small space. Although we didn't see any animal tracks that day, we did see some tracks from a tractor! A student commented that "When I look closely, I can see square in the tracks, from the tires."

The students walked around with their frames, looking up and looking down and then taking time to look closely at what they could see.

One student, who took her time noted that she noticed all these things in her small space: mushrooms, leaves, grass, twigs, chewed clover and moss.

The mushrooms were an exciting find. Comments from the students included:
"It's a family of mushrooms!"
"There's spikes on there."
"The mushrooms are golden."

For the next visit, we hope to take some clipboards outdoors to record our looking closely observations.
~Janice

graphing rational functions in Pre-Calc 12

Last week I visited Ms Wagner's Pre-Calculus 12 class at McMath Secondary. The students were using their graphing calculators to graph rational functions and then compare them. Ms Wagner provided the prompts: How are they the same? How are they different? These same prompts are used in mathematics from Kindergarten-Grade 12 to frame students' comparisons and analysis. In Grade 1, students might compare how a square and a rectangle are the same and different and then fast forward to Grade 12 and the same open-ended questions lead to strong mathematical thinking about rational functions.

Knowing that the math department at McMath would soon be getting a set of iPads, I pulled out my iPad and asked a student if he would like to try something out. We used the ShowMe screencasting app and he took a photo of the screen on his graphing calculator and then recorded his thinking about the two graphs.

We shared his short screencast via projector and speakers and the rest of the class clapped...not what I was expecting in a grade 12 class! I think the students were already thinking of the possibilities for this technology in math and I am looking forward to working with them again.
~Janice

looking closely at trees

Primary students all across Richmond are Looking Closely as they observe natural items outdoors.

Kindergarten and Grade 1 students in Ms Lo's class at Anderson were read the book Picture a Tree by Barbara Reid and then we took the students outside to look closely at different trees - the shape, the bark, the leaves. The students matched up the fallen leaves on the ground with the trees they came from, sometimes having to look a little closely at the trees as it had been quite windy and the leaves were all over the place! The students worked in partners and chose an interesting leaf or a tree to draw, noticing and recording details.

One kindergarten student was particularly interested in the olloclip on my iPod Touch and he enjoyed taking some macro photographs of the leaves he was looking closely at.

Amazing photo from a five year old!
~Janice

math screencasting in intermediate EFI classes

On Tuesday, I visited Mme. Bird's Grades 4/5 Early French Immersion class and Mme. Trewin's Grades 6/7 Early French Immersion class at Bridge Elementary. Both classes had been learning about algebraic thinking and we used math materials and the Doceri app on the school's iPads for students to communicate their mathematical thinking en francais.

The Grades 4 & 5 students thought of a pattern rule (ie. + 5) and the Grades 6 & 7 students thought of an algebraic expression (ie. 2n + 3) and then represented their increasing patterns using math materials. They then took a photograph of their patterns and opened the photo in the Doceri app. Using the app the students explained their pattern and created a chart or table using both the drawing features and the audio recording features of the app. The students were then able to play back their screencast to check it  over and then save it to the camera roll on the iPad.

Screencasting in mathematics is an excellent way to capture students oral explanations of their mathematical thinking, an essential element of our mathematics curriculum in BC.

Below is a short Animoto video of some of the students from these two classes:


I also used the Vine app to capture the students' french language use while they were screencasting and posted these clips to Twitter. If you go to twitter.com and search the hashtag #sd38mathandscience you will be able to view the Vine video clips we shared with the world!
~Janice