virtual manipulatives

Posted on: June 19th, 2020 by jnovakowski

updated September 3 2020

Although I believe nothing replaces the physical and sensory interaction with materials such as math manipulatives, in this time of COVID-19 and its many health and safety precautions and protocols, we are turning to the use of virtual manipulatives or e-manipulatives more then ever. Students can use them on their computers or devices at home or in-school so that students do not need to physically share and use materials that would need to be regularly sanitized.

The use of widely-used commercial mathematically structured manipulatives originated with the design and creation of Cuisenaire Rods in the early 1950s , although many other math materials, such as Froebel’s gifts and some Montessori math materials had been in use before this. Unifix Cubes were developed soon after this in 1953, by a family of educational suppliers who had worked with both Froebel and Montessori. Over time there have been “overhead projector” and magnetic versions of these manipulatives and since the 1990s virtual manipulatives have been developed using flash or java apps or applets.

One of the first collections of virtual manipulatives was the National Library of Virtual Manipulatives hosted by Utah State University, launched in 1999. You can find manipulatives sorted by math topic and grade band. The site can be accessed HERE.

A book sharing ways to teach mathematics with the manipulatives from the NLVM was published in 2010. I found it still available for purchases HERE.

The following are suites of free, accessible virtual manipulatives:

(please note that all image below are screenshots from the websites and do not link to the apps/sites. there is a link for each website embedded in the description)

The Math Learning Center

The Math Learning Center provides a suite of virtual manipulatives that are available as web-based apps, iOS apps and are also available in the Chrome Store. The Math Learning Center iOS apps have been loaded to our district-configured sets of iPad devices. Some of the apps have a new sharing features that allows teachers to pose problems or design investigations specific to their class of students. The pages hosting the apps and more information about them can be found HERE. Some of the apps available are pictured below.

Didax Education

Didax Education has created virtual manipulatives of their widely used physical manipulatives such as Unifix Cubes. The manipulatives, instructions, learning activities, and ways to embed the manipulatives in online platforms can be found HERE. Some of the virtual manipulatives that can be found on the Didax site are pictured below.

Mathies

Mathies Learning Tools have been developed in Ontario, including Canadian money manipulatives. Information is available in English and French and the tools are available for different platforms. The pages hosting their virtual manipulatives and other tools can be found HERE.

Mathigon

Mathigon hosts a “polypad” which is like a web-based whiteboard screen that their suite of virtual manipulatives can be used on. The page can be accessed HERE.

Toy Theater

Toy Theater hosts a page of virtual manipulatives. The site also includes a range of number charts like 100 and 120 chart and Canadian money manipulatives. The page of virtual manipulatives can be found HERE.

The following suites of virtual manipulative are added from Twitter suggestions. With thanks to Karla Pearce, Alistair Carratt and Sean K for their suggestions.

Mathsbot Manipulatives

Mathsbot hosts a page of virtual manipulatives within their site found HERE. There are standard math manipulatives like tangrams, pattern blocks and Cuisenaire rods but also tools like discs, dice, counters, a visual fraction wall, geoboards and many other visual supports for learning, doing and thinking about mathematics. It is the only suite that I have found that includes prime factor tiles, number frames and Hungarian frames.

Geogebra

Geogebra create a specific page to host tools to support remote learning, including an array of whiteboards (dots, grids, isometric, etc) as well as virtual manipulatives such as algebra tiles, protractors, fraction circles, prism creators, and many others that can be used across the grades. This page can be found HERE.

The Geogebra home page also takes you to several math apps, tasks, simulations, games and other classroom resources.

Some online resources on the research and use of virtual manipulatives:

As part of the NCTM 100 Days of Learning series, Chrissy Newell presented a webinar, sharing different ways to use virtual manipulatives. The recorded webinar can be accessed HERE. And the presentation slides can be downloaded here:

What are Virtual Manipulatives? article published in Teaching Children Mathematics, NCTM, 2002

A meta-analysis of the effects of virtual manipulatives on student achievement and mathematics learning, 2013

~Janice

Big Math Ideas in Grades 3-5: professional learning series 2020

Posted on: June 16th, 2020 by jnovakowski

This year’s Big Math Ideas for Grades 3-5 series used Tracy Zager’s book, Being The Math Teacher you Wished You’d Had, as our core resource. Teachers read chapters between our sessions and we shared our highlights at the beginning of each session along with exploring some of the resources, websites and math tasks from the book.

The publisher’s companion website for the book, with supporting materials, can be found HERE.

In our first session, we explored the idea of what mathematicians do and shared some of the picture books that Tracy highlights in her book along with some others from my collection. We watched a video “How to Snakes” by mathematician/artist Vi Hart, in which she exemplifies the playful, curious nature of doing mathematics. You can find the video HERE.

Other areas of focus during the series included computational fluency and using math games for purposeful practice.

In our second session, we looked at the big idea of spatial relationships.

And introduced the instructional routine of Same but Different.

In our third session together, we looked at the big ideas of number, specifically around fractions and also the big ideas around data analysis.

~Janice

2019-2020 primary teachers study group: continuity of learning during term three

Posted on: June 16th, 2020 by jnovakowski

Much like our students, teachers learned “at-home” during term three, during our province’s continuity of learning during the global COVID-19 pandemic. We joined together on Zoom for our next scheduled session in April and the group decided it would like to continue to connect every two weeks.

We shared and collected resources to provide to families during this new way of teaching and learning and have posted some of them on a page at the top of this blog, called PTSG Outdoor Learning Opportunities. A direct link can be found HERE.

An area we focused on during our Zoom discussions with communication with families. We compiled the different ways teachers in the group were successfully communicating with students and their families.

In June, the teachers in the group completed an online survey to provide feedback on this year and to plan for next year. Areas of interest include teaching and learning through the First Peoples Principles of Learning, the core competencies, student agency and a continued focus on outdoor learning.

Take care and have a wonderful summer,

Janice

2019-2020 primary teachers study group: session four

Posted on: June 16th, 2020 by jnovakowski

For our fourth (and what turned out to be our final in-person time together) session, the primary teachers study group met at Anderson Elementary.

We began our time together by investigating the materials included in the Bog Ecology Kit, available through our district resource centre (DRC).

Inspired by some cards in the kit, the group decided it wanted to create plant cards on a ring that teachers could take outside with their students. Each teacher in the group will take on a local plant to photograph and research with their students.

The teachers from Anderson took us out to visit their outdoor learning area and garden and then we walked over to Garden City Park, where we used Anne-Marie Fenn’s nature finding list to observe the area.

Thank you to the Anderson teachers for hosting us!

~Janice

2019-2020 primary teachers study group: session three

Posted on: June 16th, 2020 by jnovakowski

For our third session of our primary teachers study group, we came together at Spul’u’kwuks Elementary to think together about land-based art and the connection to language.

We chose to intersect creating land-based art with the idea of exploring landscape – sky, land, water. January is also often a tumultuous time of year for weather, so we extended the idea of landscape to connect to ideas of weather through the language of place. Jess created weather word cards using vocabulary from the Online Musqueam Teaching Kit.

The weather word cards can be downloaded here:

We walked from the school down to the edge of the river, where the river meets the ocean. Small groups of teachers created landscapes with materials they found on the land and some added the weather word cards to their landscapes.

Some of the resources shared during our session:

Musqueam Place Name Map
https://www.musqueam.bc.ca/our-story/musqueam-territory/place-names-map/
The Origin of the Name Musqueam http://www2.moa.ubc.ca/musqueamteachingkit/video22.php

Musqueam Language and Culture Department Online Book Collection

http://www2.moa.ubc.ca/musqueamteachingkit/stories.php
Teacher resource guide below virtual books

Virtual hən̓q̓əmin̓əm̓ Alphabet Cards

http://www2.moa.ubc.ca/musqueamteachingkit/alphabet.php

Teacher resource guide below virtual books

Water Words (2014) Public Art
By: Joanne Arnott and Spul’u’kwuks Elementary School

https://www.richmond.ca/culture/publicart/collection/PublicArt.aspx?ID=443

Online Musqueam Teacher’s Kit: Musqueam: giving information about our teachings

http://www2.moa.ubc.ca/musqueamteachingkit/teachers.php
The kit can be booked through the Museum of Anthropology or through our SD38 District Resource Center 

Our current Aboriginal Education Enhancement Agreement:
https://www.sd38.bc.ca/programs/secondary/Documents/SD38-AEEA-2017-2022.pdf

Many teachers were interested in further development of their understanding of the hən̓q̓əmin̓əm̓ language. If you are a SD38 teacher and would like the keyboard for the hən̓q̓əmin̓əm̓ language, you need to fill in a tech work order and ask for the North American Phonetic Alphabet keyboard to be installed.

Thank you to the teachers at Spul’u’kwuks for hosting us for this inspiring session.

~Janice

tessellating tiles indoors and outdoors

Posted on: June 10th, 2020 by jnovakowski

As we have moved to a blended model of teaching and learning in June 2020, I had the pleasure of spending time with two small groups of grades 1&2 students at Grauer while they were at the school for in-school instruction. To connect to the different online math studio projects we had been doing this spring, I wanted to do something that connected math and art. The classroom teachers and I decided to explore tessellations with sidewalk chalk.

With the first class, it was raining quite heavily so we decided to stay indoors and practice create tessellating tiles from old library cards. The students drew a line from corner to corner on the bottom of the card, cut along the line and then “slide” that piece to the top of the card. Then using masking tape, the student taped the two pieces together. They were asked to imagine what that new shapes could be? What had they transformed the rectangle into?

Each student was given a large piece of paper to trace and tessellate their tiles and add details, patterns or character or animal features.

Later in the week, I visited the second class on a dry day outside. I demonstrated how to create a tessellating tile and the students were given a letter-size piece of manilla tag/cardstock. I had prepared individual bags of sidewalk chalk that students would use and then keep in their personal tote boxes for the rest of the month.

We headed outside and found an area of concrete where students could physically distance themselves. One student drew a circle around her space. The students traced and tessellated their tiles using sidewalk chalk and then added character features.

The following week, when it was dry outside the classroom teacher from the first class made larger tiles with them and they took them outside to tessellate using sidewalk chalk.

Usually with tessellating with primary students, we focus on collaborative tessellating with materials like pattern blocks but in this time of physical distancing and not using shared materials, this was a great task to focus on transformational geometry, positional language and spatial reasoning in our lead up to World Tessellation Day on June 17!

~Janice

BC Continuity of Learning 2020

Posted on: April 28th, 2020 by jnovakowski

During this post-spring break phase of the school year, we are providing continuity of educational opportunities and learning experiences for our students. We are planning these opportunities through the lenses of learning priorities, equity, access and compassion. Every student’s context will be unique and we are responding with choices and options that are manageable for families at this time. A collection of resources to support the teaching and learning of mathematics and numeracy during this time have been created and curated on a page on this blog, which can be found above.

You can link directly to it HERE.

creating spaces for playful inquiry: encounters with fibres and fabrics

Posted on: December 14th, 2019 by jnovakowski

We launched our ongoing Creating Spaces for Playful Inquiry professional learning community this year with a dinner event out at IDC for 50 Richmond teachers on October 22.

After time with materials, playful inquiry mentors Briana Adams and Jess Equia shared their investigation into fibres, sewing and natural dyes with Briana’s class. After dinner together, we broke into interest groups to engage in conversation with playful inquiry mentors.

The handout for the session can be downloaded here:

Follow up Studio Series sessions have been held in The Studio at Grauer. Our first session looked at the language of wool roving and what affordances it has. Teachers considered the story of wool from sheep to sweater and considered concepts such as texture and transformation that are developed as students work with this material.

Teachers had the opportunity to touch, transform and use wool roving in different ways to help deepen their understanding of this material and how they might use it in the classroom.

Our second Studio Series session looked at the language of cotton and what possibilities it offers us as a material. We considered the story of cotton from plant to t-shirt and also discussed the social and environmental implications of the cotton industry.

Teachers used cotton in different forms – fabric, rope, embroidery floss and thread – to create with.

Our third Studio Series session looked at fabrics, textiles and clothing and how fabric can be transformed to reflect identity, culture and place. Briana and Jess both shared families stories connected to textiles.

Our fourth and final Studio Series session looked at printmaking practices and examples of printmaking on fabrics from different parts of the world.

As we were unable to gather together in the spring to share and celebrate our learning from the year, Jess, Briana and I collected some ideas to share to continue our encounters with fibres and fabrics in both at-home and in-school contexts for June.

This document can be downloaded here:

Thank you to all the playful inquiry mentors for continuing to grow this community in our district and a special thank you to Briana and Jess for all their contributions!

~Janice

intermediate numeracy project: global issues infographic creation

Posted on: December 12th, 2019 by jnovakowski

For our session together in December the grades 5&6&7 class at Quilchena examined two infographics about environmental issues and discussed how infographics use numbers and data in different ways to convey information, provoke thinking and to be persuasive. The students shared how they noticed how the infographics made some numbers large or highlighted them with colour to draw attention to them and how different types of charts or graphs can help the reader understand the information.

The students in the class have each selected a global issue that they are passionate about and have found an article in the National Geographic database to read and take notes on about their topic. They referred back to the article and their notes to find mathematical information that they could use in their own visual image that could become part of an infographic for their global issue project.

The students used apps (Pages, Paper or PicCollage) or online platforms (Canva, Piktograph) to create a visual for their project.

Through the process of creating their own visuals to share information, the teachers and I think the students will become more fluent at interpreting and analyzing infographics and other media.

~Janice

Big Math Ideas in K-2: professional learning series, fall 2019

Posted on: December 12th, 2019 by jnovakowski 1 Comment

For another year, we have held this three-part after school series with primary teachers to think together about the big math ideas in mathematics. For this series we focused on counting, number sense and place value understanding. Each teacher was provided with the teacher resource book Choral Counting and Counting Collections by Megan Franke, Elham Kazemi and Angela Turrou-Chan.

At our first session, we reviewed the different aspects of counting (see pedagogical content knowledge paper on counting available at the bottom of this post) and discussed ideas for both choral counting and counting collections. Teachers worked together in small groups to plan and lead a choral count that they would use with their students.

Stenhouse Publishers have an online choral counting tool you can use to plan out choral counts with your students. You can access it HERE.

Teachers were also asked to use the new SD38 Early Numeracy Assessment with some students in their classes and provide feedback on its usage and findings. This tool will be available publicly soon after this last round of trials and feedback.

At our second session, teachers shared what routines and innovations they tried with their classes and then we did counting collections together, considering ways to extend the counting collection experience by recording both the process of counting and the final count as well as recording equations that describe the count.

At our third session, we focused on place value concept development through tasks and games. Teachers had the opportunity to make some numeral materials. Its always handy to have sets of numerals available in the primary classroom for students to make connections between concrete rerpesentations of quantity with symbolic forms.

Some of the text slides from the sessions can be downloaded here:

Some other resources shared during the series are available here:

I have been fortunate to collaborate and co-teach with some of the teachers in this series as we continue to think together about developing number sense through counting and place value tasks.

~Janice