## creating double bar graphs to compare winter olympics medal counts

Posted on: March 2nd, 2014 by jnovakowski

The grades 5 and 6 class at Garden City has been learning about bar graphs. As part of a collaborative inquiry amongst a small group of teachers at the school, we have been looking at how iPad technology can enhance mathematical communication and engagement.

This week we provided the students with the medal counts charts from the 2010 and 2014 Winter Olympics. The students were welcome to use another data set or quickly create their own survey to collect some data, but the focus was on the creation of graphs using the iPads so I think all of the students just used the medal counts for their data set.

The students used the screencasting app doceri to create the graphs, after a short discussion about when and why you would use a double bar graphs. We reviewed the parts of a graph and then students worked in small groups to create their graphs. There was some frustration in labelling the axes and the students wished there was a typing/text feature that was easy to use.

The students’ explanations in the following screencasts reveal a few things – misuse of mathematical vocabulary in labelling axes, understanding of the components of a graph to convey information clearly and a hint at the purpose of bar graphs. We didn’t provide specific criteria about what the screencasts needed to have and if we had, we might have received more consistent information included in all the screencasts. The students seemed to have a good sense about what information they should try and convey though, without our explicit guidance.

And yes, the students could have just as easily created these graphs using paper and written out their analyses instead of using a screencasting app. After introducing apps like doceri, they become part of a student’s repertoire and hopefully, they will be given choices in how they might represent and share their learning, and those who want to use paper and pencil can and those who want to use a screencasting app can do so or there might also be an option 3!

When we are assessing mathematical understanding, does it matter how students show us what they know? I don’t think so. I think our role as teachers is to make sure students have many opportunities to show what they know about something, in ways that work for them. We want all our students to be successful and screencasting apps like doceri allow students who may have difficulties writing their thinking down on paper a way to show what they know, using visual supports and diagrams to enhance their explanations.
~Janice

## assessing mathematical communication

Posted on: February 16th, 2014 by jnovakowski

I made my monthly visit to Quilchena Elementary on Wednesday and the intermediate teachers and I worked together around assessing communicating about mathematics.

Una recorded some language prompts on the whiteboard such as angles, parallel, perpendicular, congruent, etc to support students’ questioning. The students took a photo of their quadrilateral with the iPad and then inserted it into the ShowMe app and then recorded their question and answer session, with the grade five student trying to determine the size and shape of the quadrilateral.

What we quickly noticed is that although the grade 4 students could all create quadrilaterals, they didn’t actually have the language for and understand the questions their classmates were asking them about the attributes. I listened with interest as a grade 4 student confidently say “yes” that there were parallel sides in her shape when there clearly was not. I pointed this out to the students and of course the grade 5 student was frustrated because it had thrown him off in trying to figure out the shape.

Una and I agreed that the task itself was excellent for assessing students’ use of mathematical vocabulary and to assess understanding of attributes of shapes, but that students needed to be paired with students who had the same instruction and background knowledge for the task to be successful. So when teaching a combined class, if you do not expose all students to both sets of learning outcomes, you would need to separate this task by grade levels. The grade 4s could have easily have done a similar task but using prisms (using three dimensional blocks in the classroom) instead of the quadrilaterals.

*****

In Andrew Livingstone’s grade 7 class, the students are accustomed to using self-assessments in other curricular areas, using a four point scale in line with our BC Performance Standards language. The intermediate teachers worked together to create a self-assessment scale to use with math journals, specifically focusing on communicating mathematical thinking. When we discussed it, we realized it could also be used with screencasting that the students have been doing with the iPads.

The students had already completed individual ShowMes using a practice question from the Grade 7 Numeracy FSA. A few students volunteered to share their ShowMes up on the big screen in front of the class so that we could use the self-assessment tool with them. I spent some time going through each level of criteria and what that might look and sound like in a ShowMe. We then shared the first ShowMe, with the students having the assessment tool in front of them. It was interesting to note that none of the students recorded anything on the assessment tool until after the ShowMe was over. I shared how I took notes during the ShowMe, so that I had “evidence” for my assessment for each level of criteria. The students soon realized that this would have been helpful. We discussed how they “scored” the ShowMe and asked for specific examples of why they chose “fully” or whatever level they chose.

For the second ShowMe we watched, the students took notes as they watched and had a better sense of what kinds of things they should be watching and listening for. They agreed the second time was easier than the first and that it would get easier the more they did it.

Here’s a short little video from our session together:

http://animoto.com/play/qGT0q9bBqVJv60951Sv9Kg

With both examples, we had long discussions about the difference between “Show your work” and “Explain your thinking” building on previous discussion we have had with this class about descriptive vs explanatory thinking. For these tasks, the show your work was really about showing what you did to complete the task/how you did the calculations whereas the explain your thinking was the metacognitive part, the explaining the “why” you chose to solve it the way you did and your reasoning involved in completing the task. We are finding that we are really needed to pull this out of students, that they just do the reasoning part but aren’t used to articulating it. We are going to make a few revisions to the assessment tool to help students understand these differences more clearly.

~Janice

## using mathematical language at Garden City

Posted on: February 6th, 2014 by jnovakowski

I am spending some time with a small group of teachers at Garden City this term, extending the work they are doing around their school goal of math to a collaborative inquiry project. The teachers are looking at ways that math journals might help students to represent their mathematical thinking. After a lunch hour meeting during which discussed different ways students could add to their recordings in their journals by using photographs, speech and thought bubbles and diagrams created on the iPad, I was able to spend time in two of the classrooms last week.

In Jenna Loewen’s grade one class, the students have been investigating measurement and building understanding of comparison, using specific math language to explain their comparisons. Jenna created an anchor chart to support her students.

The students were excited to use the iPads for a measurement task. They worked in small groups and were asked to choose an item in the classroom and then find two other items and compare their measurements. They learned how to use the camera on the school’s iPads and then used the app, PicCollage to fit their photographs into a template and add text. Although most students focused on shorter than and longer than, some students explored taller than as well as heavier and lighter than.

The grade one students particularly enjoyed seeing their PicCollages posted up on the big screen, by connecting the iPads to the projector.

In Paula Zack’s grades 5 and 6 class, the students have been learning about the relationship between multiplication and division using arrays as a model. The students worked in groups and used materials to create arrays and then used a screencasting app called Doceri to explain their understanding.

The following is a Doceri movie created by a small group of students. As the teacher and I discussed, these screencasts are a great “assessment for learning” tool, as misconceptions are captured. For example, in this little movie, the students do a great job of listing the multiplication and division facts represented by the array and acknowledge that if the array was rotated, their equations wouldn’t change. The students (in odd chipmunk voices…) explain that 4×5 is the same as 5×4 by saying the order doesn’t matter and then generalize this to division, where the order actually does matter (20 divided by 4 and 4 divided by 20 are not the same thing). The other generalization the students make is that for both multiplication and division, equal groups are used. This is the case when we use arrays as a model, but when we divide in real life, there are often those dreaded remainders! Again, something to take into consideration when planning the next set of learning experiences for these students.

Lots to learn from listening to students explain their mathematical thinking!
~Janice

## descriptive vs explanatory thinking in mathematics

Posted on: February 2nd, 2014 by jnovakowski

On Wednesday morning, I made my monthly visit to Quilchena to take part in a collaborative inquiry with the intermediate teachers looking at alternative ways to assess students’ mathematical thinking.

In Una Simpson’s grades 4 and 5 class, the students had been studying various aspects of geometry. The day before I visited, Una listed a series of geometry-related topics on the board and pairs of students were assigned a topic to highlight in a “ShowMe” screencast. Students were asked to both describe the shapes they were using by their attributes and to explain the concepts involved such as what makes a prism a prism, what is a polygon, what is the relationship between two and three-dimensional shapes?

The students took several photographs that could be used to explain their topic.

And then used the ShowMe screencasting app to record their descriptions and explanations.

In Tanya Blumel’s grades 5 and 6 class, we looked at the two types of division (sharing/partitive and grouping) and then the students worked through some three digit divided by one digit questions using the grouping method. As students shared their work, we focused on how they explained their thinking and the mathematical language they used to support their reasoning.

In Andrew Livingston’s grade 7 class, the student have been learning about the relationship between fractions, decimal numbers and percentages. He gave the students a task from their textbook but instead of writing their responses in their math journals, the students were asked to explain their reasoning orally using the ShowMe app. The students coloured in the various shapes on the grid and then had to determine the fraction, decimal equivalent and percentage of the total grid for each space. The students’ reasoning for the triangular shapes was the most interesting to listen to.

This is ongoing work and we hope to see the benefits of focusing on oral explanations when we ask students to write about their thinking…hoping that the metacognitive writing will be easier for them with these background experiences.
~Janice

## little bits pilot inquiry project: day five

Posted on: January 11th, 2014 by jnovakowski 2 Comments

For the final day working with littlebits, the students refined one of their projects and documented their design and project using the district iPads. The students were asked to record the materials for their project and how the steps in putting the project together. The students set up “photo shoots” and used the iPad to take photos. They were reminded to show enough detail so that others could replicate their projects.

The students could choose from a variety of apps to document their littlebits projects. Some students used Skitch to create labeled diagrams.

Some students used Haiku Deck to create a slideshow on the iPad.

Created with Haiku Deck, the free presentation app for iPad  Others used screencasting apps such as ShowMe to use photos and record their voices.

And here is the fluttery butterfly in action:

Rick asked the students to write a short reflection on their week working with littlebits. Overall, the students really enjoyed the experience. One student said it all seemed kind of “bad” at the beginning because he wasn’t sure what the littlebits were able to do but realized their potential as the week went on and mentioned how “fun” school had been. Another student commented how she really liked how the littlebits forced her to think and be creative.

The littlebits will be going to our District Resource Centre now to be processed as a district kit so that teachers around our district can request it and use it in their classrooms. We have been using two Deluxe Kits this week and I will be recommending investing in more power bit packs (power bit, battery and cable) and a few individual bits from other kits (like the fan and pressure sensor and long wired LED lights) to extend the possibilities of the Deluxe Kits.

I loved watching the students’ confidence with the bits grow as the week went on and seeing their imaginations open up to the creative possibilities with the littlebits. So much creative and innovative use of technology!
~Janice

## looking closely: what do we notice and wonder in the woods

Posted on: January 8th, 2014 by jnovakowski

The three grades 2 and 3 classes at McNeely have been learning all about plants. Near the end of November two of the classes took the school’s iPads on a little field trip to the wooded area near the school and the afternoon class had treasures from the wooded area into their class for the afternoon (it started raining at lunch and rain and iPads do not mix!). The students were asked to look closely at the plants and their different parts, noticing colour, shape, size, textures and details.  What students observed then inspired many questions.

The students took photos of plants or parts of plants, using the iPad. Many students took pictures of both moss and mushrooms although they were not sure they were plants (but were more sure about the moss because it was green!). Great openings for future inquiries!
Two apps were introduced to the students.
They used Skitch to create labeled diagrams with the photos they took.

The students also used the ShowMe screencasting app to record what they noticed and wondered about their plants.

It was a great day working with natural materials and technology side by side.
~Janice

## exploring ways to represent learning in intermediate math classes

Posted on: October 24th, 2013 by jnovakowski

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

## graphing rational functions in Pre-Calc 12

Posted on: October 13th, 2013 by jnovakowski

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

## math screencasting in intermediate EFI classes

Posted on: October 2nd, 2013 by jnovakowski

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.

Linked HERE  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