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For some of you in my group you may have heard me make reference to Desmos in some of my posts during our course. I wanted to make sure this was one of the first pieces of software that I introduced for this learning centre. For those that are now aware of what Desmos is, it is an online graphic calulator that your students can use to manipulate a wide range of linear and non-linear equations.

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Providing students to software like Desmos is an innovative way for teachers to encourage student interest in mathematics, which for the intermediate student is usually rigid. Desmos is also a great way of delivering course content while allowing student the freedom to explore and interact with mathematic concepts. The range of concepts that one could use Desmos for include: “Graphing equations... [Generating] lists, plots, regressions, graph restriction, and simultaneous graphing tasks” (King, 2017) to name a few.

In addition, Desmos is a browser-based application which means that students can interact with this software on a computer or a mobile device. For those that are familiar with an older model graphing calculator, they could be cumbersome and hard to see due to the small screen. Desmos on the other hand is simple for students to interact with and takes on the screen size of the technology that it is accessed from. (King, 2017)

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By reviewing and interacting with the software I have highlighted in my learning station, teachers will see just how effective modern technology can be in transforming thier practice and providing a greater level of support for the development of their students' learning of mathematics.

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1. Become aware of the ease of implementing technology into your classroom to support student learning.
2. Learn more about the evidence based research surrounding these technologies to foster deeper learning.
3. Recognize how these tools could be used throughout the intermediate mathematics curriculum.

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Here's Why... Augmenting your teaching practices!

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Here's Why... Augmenting your teaching practices!

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Technology can have an amazing impact on our teaching when it is used in a way that helps to augment already well established and evidence based pedagogical strategies. Research has found that the greatest challenge to technology in the classroom is actually the adoption of technology by the teacher. It is my goal today that you will see just how effective some of the technologies and tools are for enhancing the things that you are already doing well in your teaching practice. Using technology in the mathematics classroom allows students to construct and interact with multimodal learning environments and manipulatives to deepen learning. Also,  these technologies also allow for interactive visualizations that support mathematical thinking skills and problem-solving capabilities towards a range of topics and ages. (Misfeldt, Andresen, & Lee, 2014)

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Reference List Based on Order in Which They Appear

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Reference List Based on Order in Which They Appear

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1. Misfeldt, M., Andresen, M., & Lee, N. H. (2014). Technology and mathematics teaching. Electronic Journal of Mathematics and Technology, 8(2), 66+. https://link.gale.com/apps/doc/A368472068/AONE?u=lond95336&sid=bookmark-AONE&xid=29a3ee83

2. King, A. (2017). Using Desmos to draw in mathematics. Australian Mathematics Teacher, 73(2), 33+. https://link.gale.com/apps/doc/A498845403/AONE?u=lond95336&sid=bookmark-AONE&xid=ba7f64e9

3. Martinovic, D., & Manizade, A. G. (2014). Technology as a partner in geometry classrooms. Electronic Journal of Mathematics and Technology, 8(2), 69+. https://link.gale.com/apps/doc/A368472069/AONE?u=lond95336&sid=bookmark-AONE&xid=d2eee1fd

4. Ministry of Education. (2012). Technology in the Mathematics Classroom. Student Achievement Division. http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/ww_technology.pdf

5. Radović, S., Radojičić, M., Veljković, K., & Marić, M. (2020). Examining the effects of Geogebra applets on mathematics learning using interactive mathematics textbook. Interactive Learning Environments, 28(1), 32–49. https://doi.org/10.1080/10494820.2018.1512001

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Desmos offers students the ability to explore math concepts, check their understanding/answers, reason through experimentation, and interact with content through the use of problem solving activies in the form of class games/challenges.

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C2.1 Variables and Expressions
add and subtract monomials with a degree of 1 that involve whole numbers, using tools

C2.4 Equalities and Inequalities solve inequalities that involve multiple terms and whole numbers, and verify and graph the solutions

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C1.1 Patterns identify and compare a variety of repeating, growing, and shrinking patterns, including patterns...

C2.3 Equalities and Inequalities
solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions

C2.4 Equalities and Inequalities
solve inequalities that involve integers, and verify and graph the solutions

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C1. Algebraic Expressions and Equations demonstrate an understanding of the development and use of algebraic concepts...

C3. Application of Relations
represent and compare linear and non-linear relations...

C4. Characteristics of Relations
demonstrate an understanding of the characteristics of various representations of linear and non-linear relations...

D2. Mathematical Modelling
apply the process of mathematical modelling, using data and mathematical concepts from other strands

E1. Geometric and Measurement Relationships demonstrate an understanding of the development and use of geometric and measurement relationship...

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1. Quadratic Relations of the Form y ax2 = + bx + c Unit
2. Analytic Geometry Unit

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Here is the LINK to Desmos! Please make sure to click on the 3 horizontal bars in the top left corner to experiment with this software
Also click here https://www.desmos.com/ for the full website! Lots of great tools

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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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https://www.mathlearningcenter.org/apps

Please make sure to check out this amazing resource! There are applications avaliable to teachers and student that allow for the ability to manipulate geometric figures, fractions, place values, financial literacy, and even a white board application.

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Manipulatives have long been an effective tool in supporting the mathematical knowledge of our students and many of us use manipulatives in our own practice. The Math Learning Center is a particularly useful example of how we can take those same type of manipulatives and transfer them to a virtual setting that allows for greater interaction with knowledge, and the ability to bring in more diverse manipulative opportunities.

Through these applications, teachers can use this software to deepen the feedback that students receive that can alert them to inaccuracies in their thinking or scaffold their learning quite effectively. Often, we can use these technologies to help students with the mathematical thinking by providing them with the environment and tool necessary for interacting with their conjectures and examine their thinking and validity. Together the Math Learning Center provides us exploratory tools that would not be as readily available or accessible  if they were placed into their physical form. Unlike what you had experienced through Desmos, this software will require carefully designed tasks for students to interact with this software in a meaningful way.
(Martinovic & Manizade, 2014)

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Applications of The Math Learning Center

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Applications of The Math Learning Center

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As mentioned earlier, the software that this website offers is extremely easy to use and delivers a high level of interactions and manipulation for students, but it is not as structured as a software as Desmos so it will require more rigorous planning for activities to run smoothly. I would recommend that you provide an example or model the way that you want your students to interact with the software to avoid confusion.

With high structured activities the areas that this software can be used is up to your imagination as a teacher. Below you will see some general connections to intermediate math curriculum with a specific focus on the number sense and geometry strands

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B1. Number Sense demonstrate an understanding of numbers and make connections...
B1.4-7 Fractions, Decimals, and Percents use equivalent fractions to simplify fractions
B2.2 Math Facts understand and recall commonly used percents, fractions, and decimal equivalents
B2.4-10 Addition and Subtraction, Multiplication and Division
use objects, diagrams, and equations to represent, describe, and solve situations...
C1. Patterns and Relationships identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

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B1. Number Sense
demonstrate an understanding of numbers and make connections...
B2. Operations use knowledge of numbers and operations to solve mathematical problems...
C1.1-3 Patterns
C4. Mathematical Modelling

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B1. Development of Numbers and Number Sets
B3. Number Sense and Operations
C1. Algebraic Expressions and Equations
D2. Mathematical Modelling
E1. Geometric and Measurement Relationships
F1. Financial Decisions

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1. Using Analytic Geometry to Verify Geometric Properties
2.  Investigating Similarity and Solving Problems Involving Similar Triangles

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Take a look through the applications that I identified at the start of the this collumn. I know when I was getting myself oriented with this software that is when I started to see all of the amazing applications of this tool.
https://www.mathlearningcenter.org/home

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Interactive Whiteboards and SMART Board Technology

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Interactive Whiteboards and SMART Board Technology

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When discussing these tools, it is important to know that there is a wide range of whiteboard technologies available for teachers. During this past year with most of us having to teach online at some point, online whiteboards became more accessible to students through google classroom, microsoft OneNote, Microsoft Teams, and other online avenues. This is not to take away from the actaul use of physical whiteboards in your classroom as well, both ones positioned around the classroom but also personal whiteboards for your students to engage with math content through.

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As we continue to imagine what the classroom will look like as we return from a year and a half of uncertainty related to the classroom environment, many of those who taught high school had to deal with the constant exchange of physical textbooks. For some the ability to put their textbook online was a welcomed tool. Now as we return your staff may be considering if you purchase new physical textbooks, but you may also want to consider investing in an eTextbook to better support your learners.

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A study by Radović, Radojičić, Veljković & Marić (2020) investigated the effectiveness of eTextbook technology on mathematics achievement. They found:

A) That the use of an eTextbook increased student motivation and classroom engagement.

B) eTextbooks provided teachers with increased opportunities to vary/differentiate their instructional practices.

C) Increased a student's ability to perceive mathematical patterns, relationships, and objects.

D) Students also identified that the access to immediate feedback through the e-text also helped to increase their engagement while working from home and on their own time.

E) Students who used the eTextbook demonstrated greater knowledge, and improved retention of learned material.

(pp. 45-46)

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The uses of an eTextbook extend themselves beyond the normal uses of a textbook which is used to facilitate and provide an anchor to student learning. eTextbooks provide features that a physical text cannot like allows you as an educator to check in and see how your students are interacting with their text on an individual basis. This can be useful to see where students have highlighted material, what questions they have struggled with, and even how often they are accessing their text. Also, most eTextbooks come with the ability for teachers to make notes on pages of the text to remind students of conversations or examples that they used in class.
(Pearson .com, has some great ideas of how to use these resources)

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Extend learning beyond the classroom

Affordable and easy to use, Pearson eText helps students keep on learning no matter where their day takes them. The mobile app lets students read and study, even when they are offline. They can also add highlights, bookmarks, and notes in their Pearson eText to study how they like.

There are two ways you can use Pearson eText in your class: as a digital version of the Pearson title you're using that students purchase on their own, or as an assignable course that lets you interact with students directly in the eText.

Begin by browsing available Pearson eText titles in your discipline (click "eText" at the top of the page) and selecting the title you would like to use.

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Learn how Pearson's engaging, affordable eTextbooks help instructors connect with and motivate students - in and out of class.

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As you may expect, these tools are able to be applied to each strand of curriculum for grade 7-10. The key is that this resource provides students with access to the content regularly covered in your class, but through a medium that incorporates new methods of interaction.

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I would recommend that you take a look at some of the textbook providers that you use at your school to see if they offer the text you currently use in a digital format. Also conversations with a Department Head or Principal about these resources may spark some purchasing power in the future. As you move closer to the start of the next year, also consider how these features could support the diversity of learners in your classroom and students with learning exceptionalities.

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The Ministry of Education published a great resource on the usefullness of interactive whiteboards in the classroom back in 2012. Click the LINK for access to that document.
I have also hear rumours that some school boards are not longer funding SMART Board etchnology unless a teacher outright asks for it, so make sure you are having a conversation with your Department Head and Principal about getting these resources for your class.

Resources for Interactive Whiteboards:
https://crm.org/news/best-online-whiteboard
- https://tmerc.ca/

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Advantages of Interactive Whiteboards and SMART tech. 

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Advantages of Interactive Whiteboards and SMART tech. 

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One amazing advantage of interactive whiteboards and SMARTboard type technology is that they allow the teacher to become an active participant in student learning. Findings have shown that interactive whiteboards are effective tools to bridge the gap between student mental representations and mathematic conceptualization.

These tools are also fantastic for whole class discussions and group work due to the increased level of manipulation and flexibility of student contributions which is relatively unavailable from traditional chalk boards.

Please check out this image from the Ministry's interactive whiteboard publication for ways of shifting your pedagogy to include this technology  (Ministry of Education, 2012)

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An interactive whiteboard can be used for each strand of curriculum at any age. The key to this use is to focus on establishing a more significant interaction between students and curriculum, teachers and students, and students with one another as you facilitate their learning.