iPad technology Archive - Mathematics and Science in SD#38 (Richmond)

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professional learning from the summer of 2019

Posted on: September 2nd, 2019 by jnovakowski

Hi there,

It was a full and fun summer. I had lots of time to work on projects, read books, spend time with family and friends, tend to the garden, learn some new things and enjoy being outside where we live. I was also fortunate to travel a bit for work and build in some exploration time in the places I visited. All things that I like and bring my joy.

I receive and purchase a LOT of professional books. Books are a weakness for me and I often don’t have the time to read every new professional book I get. Because I often am asked to recommend books to schools, districts, etc my reading process is that I read the summary on the back cover or inside, I read through the tables of contents and then I skim through the whole book to get a sense of the flow of the book and to see how images, infographics etc are used. Finally, I choose one section or chapter of interest to read through completely. I feel okay about recommending books based on this process. Over the summer, I enjoy taking the time to read a selection of professional books cover to cover, usually about one a week in combination with my other reading for enjoyment. I received a new work iPads in June with an Apple pencil and my commitment this summer was to practice sketchnoting. The following are the sketch notes summarizing the professional books I read this summer.

In July I was invited to contribute to the updating of FNESC’s First Peoples Mathematics teaching resource. The existing resource was focused on grades 8&9 and can be found on the FNESC website here. The updated resource will focus on grades 5-9 and include adaptations for senior grades and K-5. It will be sent out to teachers to review this fall and will likely be ready spring 2020.

I attended a conference about early mathematics research in Portland, Oregon. The conference focused on current research and sessions were led be researchers and educators from across the USA. I learned about the DREME network from Stanford and the resources they offer and I was also fortunate to attend a session led by educators from the Boulder Journey School.

My husband rode his bike down to Portland and met me there so we made a little holiday out of it. It was my first time attending this conference and I hope to go again next year. More info can be found here.

I had less then 12 hours at home from our trip to Portland before I flew off to Chicago. I was honoured to be invite to a Public Math Gathering organized by the Public Math group. More info about their initiatives can be found here. There were educators from Minnesota, Wisconsin, Washington and Chicago as well as artists and museum folk from the Chicago area. We participated in a neighbourhood event on the Friday evening and then visited the “famous” Mr. Bubble laundromat where we observed how math initiatives (form the group as well as provided by the Chelsea Clinton Foundation) were being used by families in the space. We then spent the afternoon designing and prototyping new math installations for the laundromat. We went back to the laundromat Sunday morning to observe how our installations engaged the public. It was such an inspiriting experience to work with such a diverse group of people around math.

The summer always gifts me some sustained time to devote to writing projects. For many summers it was my academic writing but the last few summer I have been working on a book with a colleague, Misty Paterson. We finished off our edits in early July and sent things off to the printers. We held a book launch for Pop-Up Studio in Vancouver on August 28 – so great to be able to finally hold a book that took on a life of its own. More information about the book can by found on MIsty’s website here.

I am one of the members of the BC Numeracy Network (if you aren’t familiar, the website is here) and a subgroup of us met this summer to begin work on a resource to support professional learning in mathematics teaching and learning. It is always great to be able to work with colleagues that have become good friends. Look for our project coming out this fall!

And my final writing project of the summer was the first issue of our BC Reggio-Inspired Mathematics Project magazine. The first issue is called Thinking About Mathematics through materials. Teachers from eight Coast Metro districts contributed to this magazine which captures our collaborative professional inquiry focus from the last school year. More information about the magazine, including ordering information, can be found on our website HERE.

For the last couple of years my curiosity has been piqued by images I have seen of beautiful geometry art shared on twitter. With some investigation I found an online Islamic Geometry course that many math teachers on twitter have taken and I signed up with a commitment to do the first introductory/basic course this summer. I learned a lot, made lots of connections (was excited to visit the Islamic Art wing in The Art Institute of Chicago) and am inspired to find ways to embed my new learning in math studio experiences. Information about the course I took can be found here. Thank you to Samira Mian for her detailed explanations and lovely videos.

Another highlight of a very mathy summer was visiting the Numbers in Nature exhibit at Science World where I got some great ideas for projects and having our district’s Math Play Space at Richmond’s annual Garlic Festival. You can read more about that here.

Wishing you all a wonderful September,

Janice

April thinking together: communicate mathematical thinking in many ways

Posted on: April 30th, 2019 by jnovakowski

This month’s curricular competency focus is communicate mathematical thinking in many ways. This curricular competency is the same across grades K-9 and is included in the Grades 10-12 courses as “explain and justify mathematical ideas and decisions in many ways“.

This competency falls under the organizer of “Communicating and Representing” which includes the following related competencies:

Elaborations are suggestions for educators to consider as they plan for developing this curricular competency:

communicate using concrete, pictorial and symbolic forms
use spoken or written language to express, describe, explain, justify and apply mathematical ideas
use technology for communication purposes such as screencasting and digital photography and videography

There are clear connections between the Core Competency of Communication with this grouping of curricular competencies. A one-page table showing the language of both types of competencies can be downloaded here:

SD38 K-5 Math Communication_Avenir

An important part of communicating mathematical thinking in many ways is to be able to use different forms such as concrete (materials or math manipulatives), pictorial (drawings, diagrams, tallies) or symbolic forms (numerals and symbols).

An example from primary classrooms of how students may move from concrete to symbolic notations is with the use of materials such as base ten blocks. Students may communicate their understanding of numbers by creating that number with materials and then recording the symbolic notation. The following are some examples from a grades 2&3 classroom at Cook Elementary that show how children used concrete, pictorial and symbolic forms to help them solve and communicate their solutions for mathematical problems.

As students begin to understand a concept, such as multiplication, they usually construct a representation with materials to build understanding. These representation may then be recorded pictorially and then labels are added using symbolic notation. This fluency between forms is important and the connections between representations is essential to conceptual understanding. A student may be presented with a symbolic form (such as an equation) and asked to show a concrete form or pictorial form that “matches”. The following are examples from a grades 2&3 classroom at Tomsett Elementary.

For our intermediate and secondary students, it is still important to be using concrete materials, especially when students are developing their understanding of a new concept such as fractions, decimals, or integers. The following are examples from a grades 4&5 classroom at Homma Elementary

and also more fraction investigations with a grades 4&5 class at Steves.

In our curriculum, the terms “concrete, pictorial and symbolic” are used in ways for students to think about concepts but also to communicate and represent their thinking. In some other jurisdictions around the world, the term CRA is used to reference an instructional approach to concept development, standing for Concrete, Representational and Abstract. More information can be found HERE. There is some overlap between the the CRA framework and how our curriculum focuses on concrete, pictorial and symbolic communication of mathematical thinking and understanding.

Another area of focus in our district is using iPad technology for students to communicate their thinking and learning. One of the most common uses of the devices in math is to use screen casting apps such as doceri, ShowMe, Explain Everything or 30Hands. When students screencast, they can take a photograph or video of what they are doing and then annotate with arrows, words etc and then orally describe their problem-solving process or thinking. For example, in a grade 8 class at Hugh Boyd Secondary, students took images of number balances they used to develop their understanding of equivalence in algebraic equations and then communicated their thinking by orally explaining their understanding.

Some questions to consider as you plan for learning opportunities to develop the competency of communicating mathematical thinking in many ways:

How is the core competency of communication noticed, named and nurtured during the teaching and learning of mathematics?

What different materials are students learning to use, think through and represent with? What materials are mathematically structured and what other types of materials might we offer to students?

What opportunities are we providing for students to share their thinking in different ways? Are students provided with choices and is there a balance in the different ways students can communicate their mathematical thinking?

How might technology provide access for students or transform the way they are able to communicate their mathematical thinking?

~Janice

January thinking together: use technology to explore mathematics

Posted on: January 31st, 2019 by jnovakowski

This month’s focus is on the curricular competency: use technology to explore mathematics.

This is the language that is used from K-5 with the accompanying elaborations:

This is the language of the learning standard for grades 6-9:

And this is the language of the learning standard in grades 10-12, with elaborations that are more course-specific:

There are many questions that arise for educators and parents around the use of technology. In some contexts the use of personal devices becomes a management and liability concern for schools and in other contexts there are access and equity concerns around technology. In terms of pedagogy and appropriate use, there is always a professional judgement made as to the suitable use of technology and whether it is enhancing the learning experience in some way. Technology is not to be used just for the sake of using technology but instead, choices are made around technology use based on intention, context and purpose. In mathematics, there are many applications that allow for students to visualize and experience mathematics in ways they would not otherwise be able to (one example is the use of Desmos). Another aspect of using technology in mathematics teaching is as a tool to represent and share students’ learning. There are many accessibility features available on devices for students who may need different tools to support their communication or recording of ideas. Technology can be a powerful tool to support inclusive practices, choice and differentiation.

When we look at BC’s redesigned curriculum for information on the role of technology within a learning environment, the following is shared:

ICT-enabled learning environments

Students need opportunities to develop the competencies required to use current and emerging technologies effectively in all aspects of their learning and life. Technology can facilitate collaboration between students, educators, parents, and classrooms while also providing schools with rich online resources. Today’s technology enables classrooms, communities, and experts around the world to share digitally in a learning experience, wherever they may be.

source: https://curriculum.gov.bc.ca/curriculum/overview

E-Portfolios

Communication with families (and others) is an important part of our education system and in our district we are embracing e-portfolios and the use of technology to share and communicate student learning and progress with families. Students are able to take photographs or videos and upload them to their portfolios and annotate their posts with information or self-assessment about their learning. The teacher is also able to add descriptive feedback that is shared between teacher, student and family.

Screencasting

As a classroom and resource teacher and teacher-librarian, one of my favourite uses of technology was the use of screen casting apps. These apps allow students to take a photograph of the math they have been building, creating, diagramming or recording and then use annotation tools such as text labelling and arrows to explain their thinking as well as using audio tools to narrate their thinking. I found that many students were more confident and detailed in sharing their learning through these apps that what I might have found out about their understanding in other ways. There is also an honouring of students’ uniqueness in how they might see or think through the mathematics that can be shown through these types of apps. Some examples of screen casting apps we use in our district our: ShowMe, Educreations, Explain Everything, 30Hands and Doceri.

Math Apps

There are many apps that can support mathematics learning – some are mathematics specific and others are used to represent and share learning. A caution is the type of math apps that are essentially a worksheet and don’t include any sort of feedback to students, visual supports, problem-solving or mathematical thinking. Some locally produced apps include the TouchCounts from SFU that uses the research around gesturing to create an interactive app that focuses on counting and decomposition and composition of quantities. Another series of BC apps are the MathTappers apps developed through the University of Victoria. Each app has visual supports for students developing their understanding of a concept as well as symbolic or abstract notation. There are also choices as the number range that students can work with, allowing for differentiation. These apps are all on our district configured iPad devices. Some specific apps from this series include Find Sums, Multiples, and Equivalents.

The apps from the Math Learning Centre are also on our district configured iPad devices and allow for content creation and capturing students’ process and thinking. These apps are in web-based and iOS and Android formats. More information can be found HERE.

There are also so many apps that allow for students to share their thinking such as ShowMe, Educreations, Book Creator, PicCollage, 30Hands and Doceri.

Tracy Zager shares her ideas on evaluating math content apps HERE. Her non-negotiable criteria are:

1) no time pressure

2) conceptual basis for operations

3) mistakes are handled productively

Read through her blog post for explanation and examples.

The following is a link to some recommended apps and blog posts about students using them from #summertech15 and HERE is a blog post about using iPad technology and specific apps to support all students in mathematics.

Calculators

Although BC does not yet have a specific statement on calculator use, there is no intent that students will use calculators to complete calculations instead of learning the concepts and practice involved with operations (addition, subtraction, multiplication, division). In some cases, students that have specific learning needs and plans may use calculators as an adaptation. In some cases, teachers may choose to provide the choice of calculators when the focus of the lesson or assessment is not on calculation but on another area of the math curriculum such as problem-solving and calculators can be used for the necessary calculations so that students can focus on the other aspects of the task. Calculators can also be used to investigate patterns and relationships, support student reasoning or justification.

The NCTM has a research brief on calculator use in the classroom which can be found HERE as well as a position paper on calculator use in elementary grades which can be found HERE.

Virtual Manipulatives

The Math Learning Centre offers a variety of virtual manipulatives in web, iOS and Android formats. They can be accessed HERE.

desmos

Desmos is a free, online graphing calculator application that is used by teachers and students all over the world. There are both web-based and app platforms. Students are “able” to play with parameters in an equation and visually see how the graph changes as the parameters change. The desmos staff and teachers across the world have developed lessons and tasks that are open source and shared through the desmos teacher website at no cost HERE. There is also an activity builder so that teachers can create their own tasks.

I attended a math conference a few years ago where Eli Luberoff, CEO of desmos, shared his passion for the teaching and learning enabled and enhanced by this tool. In particular, I was captivated by the marble slides task he shared and the authentic learning that we witnessed happening for students in the video he shared.

More information about Desmos and access to many classroom activities can be found HERE.

Coding and Computational Thinking

There are many links between coding and computational thinking. Two new senior math courses – Computer Science 11 and 12 have been added to our BC curriculum framework and these courses focus on coding, programming and computational thinking. I will be sharing a blog post specific to coding and math in the next few months.

Osmo

Osmo is an interactive accessory for iPad technology that uses the camera to create Reflective Artificial Intelligence. The red camera clip and white base are used with free apps and game materials that can be purchased online or at the Apple Store. Two of its earliest games focused on mathematics – the Tangram game focuses on spatial reasoning and the Numbers games focuses on decomposition and composition of numbers. Osmo is always developing new games including a Pizza game that focuses on financial literacy and a series of coding games.

More information about Osmo can be found in a blog post here and on their website here. The SD38 DRC has five Osmo kits available to borrow. Note that one iPad device is needed for each kit.

Augmented Reality (AR)

Augmented reality (AR) is an interactive experience of a real-world environment where the objects that reside in the real-world are “augmented” by computer-generated perceptual information, sometimes across multiple sensory modalities (from Wikipedia). There is an interplay in AR between digital and real-world environments whereas in Virtual Reality (VR) you engage with a simulated environment. A few years ago we had a Google Expeditions team visit Homma school and share their Google cardboard virtual reality devices with the students. A blog post about that experience can be found HERE. This was a first foray into thinking about ways this kind of technology could support teaching and learning. My first experience with AR was a few years ago when the colAR app created a special event to go along with Dot Day (inspired by the book by Peter Reynolds). The information about this can be found HERE and is a great starting point to use AR with students.

Our new technology integration teacher consultant Ellen Reid has been exploring AR with the iPad app AR Maker . We talked about the mathematical possibilities for using AR and along with the development of spatial reasoning, the following concepts came to mind: surface area, volume, transformational geometry, scale, proportion, ratio, 2D and 3D geometry, and composition and decomposition of shapes. The following are some photos Ellen captured as she created AR WODBs (Which One Doesn’t Belong?):

WODB_AR (movie file)

For Richmond teachers, please also check out the Integrating Technology for Teachers page, curated by Chris Loat, on our district portal linked HERE.

Some questions to consider as you plan for learning opportunities to develop the competency of using technology to explore mathematics:

How can technology enhance students’ mathematical experience and see and think about mathematics in different ways?

What specific curricular content and competencies at your grade level could be explored and investigated through technology, including the use of calculators?

How can technology be used to support students’ collaboration and communication in mathematics?

What opportunities are we creating for sharing and communication with families through the use of technology? How are we communicating with parents how forms of technology are being used in our schools to support learning in mathematics?

~Janice

creating spaces for playful inquiry: thinking about reflection – January 2018

Posted on: May 11th, 2018 by jnovakowski

On January 25, Richmond educators gathered at Grauer for our second dinner session of our Creating Spaces for Playful Inquiry professional learning series. This month our focus was on reflection and time. Educators shared their experiences engaging in playful inquiry with their students and considering the role of reflection in documentation and making both students’ and our professional learning visible.

After dinner together, teachers participated in interest groups facilitated by our playful inquiry mentors.

A handout with curricular connections to the idea of reflection can be found here: Reflections_Provocations_Jan25_2018

~Janice

looking for math outdoors

Posted on: January 4th, 2017 by jnovakowski

During my last visit of the year to the Kindergarten classes at General Currie Elementary, it was a snowy and icy day so we decided to venture outdoors with some iPads to capture images of things that inspired our mathematical thinking. We had a quick talk with the students about how to look for math outdoors – looking up, looking down, looking all around. We talked about what math might look like outdoors – the counting of items, the shape of things, patterns in the environment, as well as sources of inspiration for thinking about math.

One of the first mathematical ideas we played with was shadows – how does your position affect your shadow? what determines the height of your shadow? what do we need to think about if we wanted to put our shadows in height order?

As with the case of all our school sites…there is a story that lives there. General Currie was one of the first one room school houses on what was originally called Lulu Island. We stopped briefly at the historic building that is still on the new school’s site and talked about the time elapsed – what school might have been like, what the neighbourhood might have looked like, etc.

We ventured on to the field and took photos as we walking along noticing nests in trees, tracks in the snow, all sorts of ice and frozen leaves.

The ice was a source of fascination and many questions for the students. They were also very interested in some footprints they found and wondered about the size of different footprints or tracks.

We came back into the classroom and the students used the app Skitch with one of the photographs they took. They labelled, circled or used arrows to show where they noticed math or what inspired a mathematical problem or question.

Classroom teacher Kelly Shuto then showed some of the students “skitches” to the class to inspire further questions.

The following week Kelly tweeted out about the class photo book they had created, based on the idea “What math lives here?”

In this crisp wintery weather, what will your students notice outdoors? What math lives in the frozen puddles and tracks through the snow? How far do animals need to travel to find food? What might your students wonder about?

~Janice

thinking about measurement in kindergarten

Posted on: May 24th, 2016 by jnovakowski

I was invited into Denise Tong Vargas’ kindergarten class at Dixon Elementary to look at ways to present mathematical provocations to students at this age level as well as how to integrate technology use as a way to document learning.

For our first time together, I asked the students to share what they knew about measuring. I then did a little demonstration with matryoshka dolls which the students were fascinate with. We compared their height and ordered them from tallest to shortest. We talked about the importance of using specific mathematical language like long, tall, short instead of a general term like “big”. We talked about how when we are comparing two objects directly that we need to “line them up” or use a baseline for accurate comparison. The students were then challenged to find something in the classroom and compare and measure it in different ways.

As we came together at the end of their investigation time, as a way to share the students’ experiences and consolidate students’ thinking, we co-created two pic-collages using photographs I had taken using iPad technology, focusing on the concepts of baseline and units.

On my second visit to the class, Denise and the students settled in with their regular morning routine and then I talked to the students for a short time about the big idea that we were going to focus on – comparing and ordering objects and how we might use mathematical ideas and measuring tools to help us investigate this. I had set up three provocations on tables, adding to the one that Denise and her students had been investigating already.

And I added another onto the carpet area involving containers and cylinders to provoke students’ thinking about measuring curved surfaces and measuring capacity/volume.

There was high engagement amongst the students and many of the children stuck with one set of materials or provocations while others moved around. It was interesting listening to them play with the language – second tallest, “mediumest”, third shortest, etc., play with the materials and play with mathematical ideas.

I must say that there is something to be said for unique and “fresh” materials that engages students and helps bridge school and the world outside of the classroom. By using toys and materials (like ribbons and pinecones) that they might find outside or at home, the students can see that they can be measuring wherever they are – not only if they have a ruler or Unifix cubes!

Some new pic collages were created to help consolidate the students’ learning and to focus on the big ideas involved with measuring.

I am looking forward to checking in on Mrs. TV’s classroom blog to see what other measuring experiences the students have.

~Janice

Richmond’s first IGNITE event – #sd38ignite 2016

Posted on: May 10th, 2016 by jnovakowski

The Richmond School District hosted its first IGNITE event on Monday, May 9th at the Big River Brew Pub. The first IGNITE took place in Seattle in 2006 and is now a movement that is international in scope. An IGNITE talk is a five minute presentation consisting of 20 slides, auto-advancing after 15 seconds whether the speaker is ready or not. The IGNITE tagline is….”Enlighten us, but make it quick!” More information about the IGNITE movement can be found here.

Having presented a few ignite talks and experiencing the inspiration and fun that goes along with these social events, I really wanted to be able to bring this professional learning format to our district and my colleagues Rosalind Poon and Lorraine Minosky were on board and we ran with it. Chris Loat created our logo for us…

And both Chris and Lisa Schwartz agreed to be our technical support for the event. We found a site and had a meeting at the Big River Brew Pub to see where attendees would sit and how the technology and food service would play out.

We invited Richmond educators representative of primary, intermediate and secondary as well as a balance of teachers and administrators to share a story about something they are passionate about. We also invited two out of district colleagues to add to our Richmond stories.

Two weeks before the event, we hosted a rehearsal especially for educators who were new to the ignite format. It gave them a chance to meet other igniters and to practice their presentation in front of an audience. By seeing and discussing what we appreciate about others’ presentations, I think it also gave presenters some ideas for their own ignites. And its always great to have sushi…and pens.

As we were setting up on May 9th, we were all so excited to see everything fall into place. The venue was great and it was a beautiful day so the patio was open, the technology was cooperating and the tables were set with programs and sweet treats from Sinfully the Best for our guests.The burger bar was a hit and the company was great. Unfortunately two of our igniters (Neil Stephenson and Sarah Garr) had to pull out due to personal reasons.

Some of the guests…

And then the talks began! I was live streaming the talks using the Periscope app and people that weren’t able to attend the event could still watch the talks live. Between each “set” there was a 15-minute break for guests to chat about the talks, etc.

Twitter was alive with #sd38ignite…we were trending!

It was such a positive, passionate event and such a great way to build community amongst colleagues. All our igniters shared their own personal narratives within their professional narratives and these stories are what connect us and make us better together.

We will be releasing the IGNITE talks on youtube soon…watch twitter for announcements!

A HUGE thank you to our igniters…you are what made the event the success it was!

~Janice