Archive for September, 2018

September thinking together: mathematics curricular competencies

Posted on: September 28th, 2018 by jnovakowski No Comments

For the 2018-19 school year, the “thinking together” series of blog posts will focus on the curricular competencies in the mathematics curriculum.  The “thinking together” series is meant to support professional learning and provoke discussion and thinking. This month will provide an overview of the curricular competenecies and then each month we will zoom in and focus on one curricular competency and examine connections to K-12 curricular content, possible learning experiences and assessment.

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The curricular competencies are the “do” part of the know-do-understand (KDU) model of learning from BC’s redesigned curriculum.

The curricular competencies are intended to reflect the discipline of mathematics and highlight the practices, processes and competencies of mathematicians such as justifying, estimating, visualizing and explaining

The curricular competencies are connected the the Core Competencies of Communication, Thinking  and Personal & Social. More information about the Core Competencies can be found HERE.

 

Screen Shot 2018-09-28 at 9.45.26 PMThe curricular competencies along with the curricular content comprise the legally mandated part of the curriculum, now called learning standards. This means these competencies are required to be taught, assessed and learning achievement for these competencies is communicated to students and parents.

Something unique about the mathematics curricular competencies is that they are essentially the same from K-12. K-5 competencies are exactly the same with some slight additions in grades 6-9 and then building on what was created in K-9 for the grades 10-12 courses. Because they are the same at each grade level, to be assessed at “grade level” they need to be connected to curricular content. For example, one of the curricular competencies is “estimate reasonably” – for Kindergarten that will mean with quantities to 10, for grade 4 that could mean for quantities to 10 000 or for the measurement of perimeter using standard units and for grade 8 estimating reasonably could be practiced when operating with fractions or considering best buys when learning about financial literacy.

The new classroom assessment framework developed by BC teachers and the Ministry of Education focuses on assessing curricular competencies and can be found HERE.  A document outlining criteria categories, criteria and sample applications specific to K-9 Mathematics can be found HERE. The new four-point proficiency scale provides language to support teachers and students as they engage in classroom assessment.

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As we are begin a new school year and are thinking about year plans and overviews we might consider the following questions:

  • What opportunities do students have to learn about what it means to be a mathematician and what mathematicians do?
  • What opportunities can be created over the school year for students to name, be aware of, practice, develop and reflect on the core and curricular competencies in mathematics?
  • How can we make the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
  • As we are planning for instruction and assessment, how are we being intentional about weaving together both curricular competencies and content? What curricular content areas complement and are linking to specific curricular competencies?

~Janice

number glass gems

Posted on: September 18th, 2018 by jnovakowski No Comments

One of the elements of The Studio at Grauer that teachers often notice is the collection of numerals we have in baskets and trays on our shelves. I have collected these over the years and find them in craft and scrapbooking stores, thrift stores, Habitat for Humanity ReStore, and Urban Source on Main Street in Vancouver. I am always on the lookout for numerals. Students use them in their play and investigations, ordering them, using them to label/represent their collections or sets of materials or to use as purposeful numbers in their creations (addresses, phone numbers, parts of a story, etc).

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Just to clarify some terms…

Digit - A digit is a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in our number system to make numerals.

Numeral - A numeral is a symbol that stands for a number.

Number - A number is a count or measurement that represents an idea in our mind about a quantity.    Numerals are often used to represent a number.

It is how these materials are used that leads to them becoming called numbers – they are used to connect meaning to the symbols by matching the symbol to a set or quantity or are put in order/sequence which gives meaning to the symbols. They can also be used to represent the number in an expression or equation.

I chose to make my most recent set of glass gems using the digits 0-9. This way students can put them together to create different numerals/numbers to label their representations/sets/quantities.

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Materials needed: large glass gems (found at Michael’s and some dollar stores), foam paintbrush, Mod Podge and number stickers or cutouts

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Instructions: Using the flat side of the glass gem, apply a light coat of Mod Podge and lay a numeral upside down, centred on the back of the gem. Press down and smooth surface so that the numeral adheres and there are not air bubbles between the surfaces. Let dry for a couple of minutes and then apply a coat of Mod Lodge to the entire surface of the flat side of the glass gem. Let dry for 20-30 minutes and then apply a second coat. Let dry and then they are ready to be used.

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We have also created materials similar to this by adhering stickers to tree cookies/slices or to smooth stones. It’s just handy to have a collection of these and students find all sorts of ways to use them.

~Janice

making truchet tiles

Posted on: September 18th, 2018 by jnovakowski No Comments

What are truchet tiles?

Truchet tiles are square tiles cut across the diagonal into two triangles of contrasting colours.

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In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square. The tiles create patterns in grids of tiles. Since the original version was investigated, other variations have been created.

More information about truchet tiles can be found HERE and HERE and HERE

Once again, I have been inspired by Christopher Danielson and his lovely math materials. His version of truchet tiles can be found HERE.

I have made a simple version for an upcoming make and take afternoon with teachers in The Studio. You need square tiles, paint and a brush. I painted the tops and edges of the tiles in colour first. You could leave them naturally coloured. Once the paint was dry, I used a piece of tape to “mask” off one side, lining up the tape from corner to corner along the diagonal. Press firmly along the edge of the tape so you don’t get any paint seepage under the tape. Paint the exposed side of the tile black or other high contrasting colour. Depending on your paint, you might need a second coat. I left the tape on as it was handy to hold onto as I turned the tile over to paint the back (once the first side is dry). I chose to paint the second side all black but you could also leave it natural, or paint it a colour or paint it the same way you painted the first side. Let completely dry and then carefully peel off the tape.

Note: I used a “value” paint for this project and I didn’t like the feel of the tiles in my hands so I added a coat of Mod Podge and they are much smoother to the touch now.

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Each tile has four orientations:

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Combining two tiles together and then using these in different orientations allows for many different patterns and designs. How many permutations of two tile combinations are there? ( a great spatial reasoning investigation)

These tiles are great for thinking about spatial reasoning, orientation and transformation as well as composing and decomposing shapes.

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Finding lots of square tiles in bulk isn’t easy. I ended up ordering 400 from a craftsperson on etsy. I used 1-inch tiles but you could make them in any size. I think you need at least 25 (5×5 grid) to create patterns using the different shape compositions you can create. They could also easily be made with construction paper or cardstock but the wood is more durable and I am not a fan of laminating (reasoning – make the materials more slippery and hard to tessellate and takes hundreds of years to decompose).

I am looking forward to seeing how students across the grades in Richmond investigate and create with these tiles.

~Janice

the new playground at Grauer: where’s the math?

Posted on: September 18th, 2018 by jnovakowski 1 Comment

IMG_1946 Last year the families, staff and community fundraised for a new playground for Grauer Elementary. Grauer is a small school with only five, six or seven divisions (depending on the year) and it is hard work for a small school to raise $60 000! It was very exciting when the school reached their goal and is such a good example of an authentic numeracy experience for students to think about. In the BC curriculum, numeracy is defined as an application of mathematics to solve or interpret an issue or problem in context.

 

 

Last Saturday, I joined staff, parents and community members coming together to install the playground (self-installation with staff support from the playground company saves thousands of dollars). As Ms Partidge and I helped to read the specifications for the installation of one of the fire poles, we commented to a couple of parents around us how much mathematics was involved in the process.

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I shared some of the photos from the installation day with the two grades 1 & 2 classes. All of these students had been to The Studio last year with me and had spent some times exploring the idea of “what is math?” so I framed this investigation as “where is the math?” I knew for some students this would create some dissonance as even young children can sometimes already have a very narrow view of what mathematics is and think that it is about counting, numbers and “plussing”. Part of this investigation was to disrupt this thinking. Of course counting, numbers and arithmetic operations are important content areas of mathematics, but they are not the only content. This investigation was one avenue to create meaning for learning mathematics, having students make connections to math beyond the walls of the classroom. The students came up with some initial ideas and we will continue to add to our thinking over the next couple of weeks.

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The students were invited to design and create playgrounds and to consider where, when and how mathematics would be applied/used. One group of students followed the kit diagrams to create a Playmobil playground set – there was lots of math talk during that collaboration! Some students chose to draw and paint a playground from their imagination and some built playgrounds with blocks and loose parts, including a playground for animals.

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After our first time together, I noticed the students were very interested in the photographs of adults using the levels and measuring tapes so I ordered some (not toy) tools to add to the construction area of The Studio. It was great to watch the students use these tools in authentic ways.

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One of the classes had gone outside to look closely at the playground twice, creating detailed labelled diagrams or maps of the playground.

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We extended this experience in The Studio by asking the students to create “math maps” indicating “where’s the math?” on recordings of their playground creations.

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And what are are we assessing in terms of mathematics? These types of investigations and explorations lend themselves to informal formative assessment and gives us a sense of mathematical language the students have and where students are along a learning trajectory around different concepts and skills such as spatial reasoning, comparison of size and quantities and measuring. This type of assessment, that focuses on observing and listening to the students’ play and math talk is so important at this time of year and informs our instructional plans and focus for the fall.

When students engage in this type of learning through materials we make their learning visible through a sharing session at the end of our time together and capturing photographs, videos and students’ thinking so that we can revisit and reflect on the experiences, make connections to new learning experiences and consider questions for further investigation. The following are examples of documentation panels that we create to post in The Studio to help make our learning visible.

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I’m looking forward to seeing where the students take us next on this investigation.

~Janice