Select one manipulative and describe how it could enhance the understanding of a mathematical concept or big idea. Align the tool to a grade and suggest a hands-on task. 

Tangram is a puzzle made from 7 differently-sized shapes that, when placed in a specific order, create an image. Tangrams are a great way to reinforce themes within geometry, such as shapes, sides, angles, and vertices. Additionally, through the continued use of tangrams, students are encouraged to recognize shapes and mathematical themes in their everyday life. The different sizes, shapes, and colours add to the sensory stimulation that engages students and keeps them attended to the activity at hand.

I have seen great success in using tangrams in grades as early as kindergarten. Students can be prompted to create an object using tangrams, contributing to their spatial awareness, creativity, and problem solving. Students can also be provided with silhouettes in which they must make their tangram pieces fit. This type of activity has now be enhanced through the use of the Osmo tangram application. The Osmo uses an iPad, tangram shapes, and a mirrored lens over the iPad’s camera to create a digital game that has students align their shapes on the table into the shape displayed on the iPad. The application then takes them through levels and different tangram puzzles using the same shapes. Here’s some more information about this engaging task:

Post 3 of the most important strategies or things a teacher is doing in the math classroom to support and/or create an inviting math environment. Describe and reflect on these high yield strategies.

Educators across the system are working towards creating positive, safe, and supportive learning environments in every subject matter. The Guide to Effective Instruction in Mathematics discusses the importance of developing a mathematical community, in which students can learn to support each other in their learning and build off of each other’s thinking. This is made possible when using strategies like Bansho or Number Talks. These strategies allow student to share their thought processes, while also learning from the strategies being shared by their peers. Intentionally teaching students how to be positive and respectful members of a learning community helps to add to the overall learning experience.

The using classroom resources is especially important with our new wave of teaching mathematics. Even a short 10 years ago, I was being taught mathematics in a learning environment that only used resources such as a textbook and worksheets. Nowadays, we provide experiential learning opportunities for our students in which they can touch, feel, and move throughout their learning. This involves using resources like manipulatives and technology (laptop, tablets, tools, etc.) to keep the learning engaging, while also teaching the students important 21^st Century learning skills.

Structure in the form of the three-part math lesson is an important strategy when creating an inviting math environment. The area in this type of lesson that is the first to be disregarded is the consolidation, typically because the class runs out of time. By being more structured with the timing of specific types and sections of lessons, educators can ensure that the consolidation is carried out for all lessons. This allows students to share their learning, use appropriate vocabulary, discuss strategies, and learn from their peers.

Feedback is often secondary to the grade or level received because it has been ingrained in the world for so long that the final grade is what counts. Educational research generally says that feedback without a mark is the most powerful for affecting change. 

How does this research impact your assessment practices? How do you use feedback to move student thinking forward? 

Even as a new teacher entering into the field of education, I have met a number of teachers who are going gradeless in their classrooms. This aligns with the educational research and their own experiences which tell them that students respond best to written or verbal feedback, rather than a letter or percentage grade. Too often, students look at the final grade and take it as the ‘be all and end all’, skipping over the descriptive feedback provided about their current performance and ways to improve. This cycle also leads students to “only want a C” or to achieve the letter grade that meets their parent’s expectations. This, however, actually takes away from the learning process in that final grades are the smallest form of feedback for students; it labels their current ability without providing ways or suggestions for improving.

The Assessment and Evaluation of Student Achievement portion of the Ontario mathematics curriculum states: “As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement” (Ontario Mathematics Curriculum, 2005). Education involves learning, trying, receiving feedback, and trying again. Written and/or oral feedback provides students with a personalized description of how to improve. This is why more and more teachers are moving away from overall grades and focusing on detailed feedback. However, I also acknowledge that much of our education system past the elementary grades revolves around percentages and final outcomes, especially because that determines the future of a student’s education (i.e., next course, university acceptance, etc.). I believe that it is our duty as Primary/Junior teachers to provide students with the understanding that feedback is important and that there is still something to learn when receiving feedback (learning about our process, as well as during the process).

Share your thoughts on whether you agree or disagree with Marion Small’s view of success criteria and “generalizing vs particularizing” in math. 

Marion Small makes a very interesting point when she discusses generalizing vs. particularizing in her video about success criteria. Marion spoke about how some educators identify the success of their students when they use the mathematic terminology that the researchers and textbooks provide. In these cases, there is a higher emphasis on ‘particularizing’, in that the students must learn to remember the name of a strategy rather than being able to explain how a strategy was used. ‘Generalizing’ involves having the students explain what method they used and how it was effective, without hyper-focusing on terminology.

I agree with Marion Small’s view of generalizing and particularizing in math, especially as it relates to success criteria. In my own practicum placements, I facilitated math number talks and explored many strategies to solve the same equation. Personally, I found it difficult to remember the various names given to each of the strategies used (i.e., double plus one, decomposing numbers, friendly numbers, etc.). I came to the realization that if it was difficult for me to remember the terminology, it was probably difficult for my students. Additionally, I had to consider what my true success criteria were for my students during the number talks: Was it to use the proper name of the strategy used, or to utilize multiple strategies and be able to explain what they did? For my group of students, the function was more important than the lingo, and I believe my students learned more from sharing strategies with their peers than from putting names to strategies. This does not dismiss the importance of the language used in math classes, but it shifts the focus from particularizing to generalizing.

What do you think will have the biggest impact on student engagement, motivation, and success in the elementary mathematics classroom?

In my opinion, the delivery of the mathematic content will have the largest impact on student engagement, motivation, and success. The best way that we can engage our students is by making the learning fun and interesting. We have a set curriculum that we must follow, so there isn’t much that we can change about what is being taught, but we can alter how it is being delivered. By using more play-based learning throughout the elementary grades, students will find consistency in how they learn mathematics while also associating a typically “difficult” subject with fun learning. It is also important that educators use visually stimulating tools to engage and motivate their students throughout their learning, including videos, books, and other texts (What Works? Research into Practice, pg. 2-3). When we are able to grasp our students attention and engage them in fun learning, students will be both intrinsically and extrinsically motivated to achieve success.

To ensure the success of all students in our elementary mathematics classrooms, we must ensure that the content being delivered is at an grade-appropriate and obtainable level. The lessons should be differentiated to meet the levels of all students in the classroom, as well as providing multiple entry points into the same learning opportunities. One thing that the Differentiating Mathematics Instruction Capacity Building Series suggests considering when differentiating our instruction are the students’ Zones of Proximal Development. This outlines the “distance between the actual developmental level” of the student and their “level of potential development” (Capacity Building Series, pg. 1). When we take this into account, we can determine where they are currently with their learning and provide them with learning opportunities that can challenge and extend this learning.