July 17

# Generalizing vs. Particularizing in Math

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.

July 15

# Impacting Engagement, Motivation and Success

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.

July 12

# Problem Solving and Math Talk

Reflect on the value of problem solving and consider what makes a rich and engaging question. Discuss how important it is for students to explore and use communication in consolidating mathematical understanding through ‘math talk’.

Problem solving questions, specifically in math, provide opportunities for students to practice their learned skills in applicable and relevant situations. They challenge the students to reflect on what they have learned theoretically and apply this knowledge in practical, thought-provoking applications. It is very important that we teach students to embrace problem solving, treating it like a puzzle to be solved rather than a brick wall preventing us from achieving success. When we adequately prepare students with the tools that they need during problem solving, they come to learn that they are able to problem solve and they can achieve success. This, in turn, develops a positive disposition towards problem solving for our students.

The Guide to Effective Instruction: Grades K to 6 – Volume 2 – Problem Solving and Communication teaches us that rich and engaging problem solving questions not only teach students through problem solving  (practicing conceptual understanding), but they also teach student about problem solving by learning applicable learning skills (Guide to Effective Instruction, pg. 6). By teaching student through and about problem solving, we are able to see if the student has grasped the concept while also exploring the strategy they used throughout the process. When we are able to see both aspects, we then know that we have created a rich mathematical question. It is also important that we ensure the questions are relevant to the students by using real-world situations that are linked to their specific interests.

Conversations around problem solving help to teach students to be cognitive about their own strategies, while also being able to learn from their peers and adopt new and perhaps more efficient strategies. As Marion Small says in the video Open Questions and Contexts, “[Different strategies] enrich the conversation; it does not detract from it.” Math talks and bansho consolidation presentations are great ways to verbally explore these strategies in a whole-class setting. Other ways to communicate their thinking could be in a math journal, in which the student explains the strategies they used throughout the day’s lesson, or by creating a video/voice recording of their verbal explanations (for those students less inclined to share with the class).

July 9

# Intentional Play-Based Learning

After spending time researching and exploring different teaching models, choose one to summarize, providing suggestions on how to incorporate this approach into your math class. Post your model along with a brief description of it and its application and usefulness in the primary/junior classroom.

Teaching Model

• Doug Clements: Intentional Play-based Learning

Brief Description

• Educators must stop choosing either a strictly “play-based” or strictly “academic” approach to teaching/learning mathematics
• Extreme play-based approaches to learning, where the teacher is completely removed from the learning and the students are in full control of their play, is not the essence of the best play-based curriculum
• Extreme academic approaches, where the students sit at desks and answer problem after problem, produce mechanical, uncreative thinkers
• The best type of learning including all kinds of learning experiences, including both play-based and guided learning
• Educators should prompt students and give creative challenges that develop high-caliber mathematical thinking and reasoning while the students are engaging in play-based learning

Application and Usefulness

• Kids develop higher levels of social skills, emotional skills, and self-regulation skills when they emerge in guided play-based learning
• Learning is enhanced when students can plan and established roles during their play, while in a guided environment
• Need to talk about the mathematic sand development the appropriate language to convey learning, which can be further assisted by an educator guiding the engaging in the student’s play

Suggestions for Integration

• Play-based learning should be purposeful with some pre-determined structure
• Challenges could be presented throughout the play-based learning to encourage further extensions of learning and tier the expectations for specific groupings or individuals
• Check-ins with students throughout the learning helps to reinforce mathematical language and develops the student’s ability to explain their processes and strategies
July 4

# Cross-Curricular Math Connections

Share a minimum of two connections that integrate math with other subjects. Post these two ideas along with an explanation as to why cross-curricular connections are beneficial to student learning, particularly as it relates to learning mathematics.

Coding is a great cross-curricular connection between Math, Science, and even Language. Coding has students create sequences of commands that lead to a specific action or outcome. When using robotics technology, such as a Sphero, students are able to code the robot to move a certain distance, rotate a specific way, and even travel at a certain speed. Robotics and coding would typically fall under the category of Science and Technology, however, there are many different and creative ways in which it can have a math focus. For example, students could use angles and rotations to maneuver the robot through a maze that the students create. There are also some valuable Language expectations met when coding, predominantly procedural writing. Coding and robotics are great ways to bring a math problem to life, while also teaching the students valuable and applicable 21st century skills.

There are many ways in which Math can also be cross-curricular with Geography. On way in particular that I was able to make a cross-curricular connection between these two subjects was when our class was learning about the environment and natural resources. Students used their data management skills to create and conduct a survey to other students within the school about the amount of waste that they brought in their lunches each day. The students were then able to use this data to calculate how much waste the school would produce each week, month, and school year, while also using different weight measurements. This proved to not only hit a number of different curriculum expectations in math, but it also helped the students to grasp the severity of their waste production from a geography mindset.

June 9

# Cash Cab: Accommodations vs. Modifications

Before the Activity

This activity will focus on differentiating between accommodations and modifications. Additionally, it will challenge the player to consider various ways the learning can be accommodated or modified for students with specific needs. It is important that the players are familiar with the terms “accommodation” and “modification” and their definitions. As per the document The Individual Education Plan (IEP): A Resource Guide:

• “The term accommodations is used to refer to the special teaching and assessment strategies, human supports, and/or individualized equipment required to enable a student to learn and to demonstrate learning. Accommodations do not alter the provincial curriculum expectations for the grade” (pg 25)
• Modifications are changes made in the age-appropriate grade-level expectations for a subject or course in order to meet a student’s learning needs. These changes may involve developing expectations that reflect knowledge and skills required in the curriculum for a different grade level and/or increasing or decreasing the number and/or complexity of the regular grade-level curriculum expectations” (pg. 25-26)

After these terms have been reviewed and a brief discussion around their importance in our inclusive classrooms has occurred, the group is ready to play “Cash Cab”. The facilitator can choose to have each individual play the game separately on their own devices, or as one large group.

Instructions to Play

1. Open the Cash Cab PowerPoint file.
2. Begin the game. It is recommended that the players are given a specified time to answer each question to ensure that the group stays on track.
3.  To check if an answer is correct, click the cursor inside the question box and the answer will appear. If the given answer is correct (meaning that it matches the answer that is displayed), click the green button on the bottom of the screen. If the given answer is incorrect, click red button on the bottom of the screen.  It will direct you to the correct slide, given the number of strikes accumulated. If a question is answered incorrectly, a strike will be given. The strikes will be displayed in the box on the left-hand side of the screen. Three strikes and you are out of the cab!
4. If 8 questions are answered correctly in a row, then the player can attempted the Red Light Challenge. Click the red box in the top right-hand corner to begin the timer. The player then has 30 seconds to answer the question by identifying the environmental accommodations present in the list. If the player answers correctly, click the green button on the bottom of the screen and award the player additional points.
5. At the end of the game, the player can either choose to take the points they have earned or go double-or-nothing on the video bonus question. Points being awarded are at the discretion of the facilitator.

After the Activity

This activity will provide a good opportunity to challenge individuals on their knowledge of accommodations and modifications. This challenge should spark a rich dialogue about how to identify when an accommodation or modification is required, what accommodations or modifications are effective in which situations, and which students in our own learning environment may require additional supports. It is important to remind the players that decision making around implementing accommodations and modifications are based on the child’s individual and unique needs. Additionally, it is important to mention that accommodations and modifications should consistently be evaluated after they have been implemented (Are they effective? Are more supports required? Does the student still require the supports being provided?).

References

Fisher, Stacy. “Free PowerPoint Game Templates for Teachers.” The Balance. N.p., n.d. Web. 02 June 2017.

The Individual Education Plan (IEP): A Resource Guide. Toronto: Ministry of Education, 2004. Print.

May 26

# Behavioural Exceptionality Case Study

In the case of Hannah on page 125 of Special Education in Ontario Schools, we learn about the continual behavioural incidences that occurred between nursery school and her current grade 4 year. Hannah always seemed to be on the move and would run until someone or something stopped her. She regularly blurts out anything on her mind. Hannah has a history of borrowing things without permission and failing to return the items until she is explicitly asked to do so. Hannah has a difficult time making connections with her classmates and often interferes with their learning during group work. This is becoming an increasing social issue, especially because Hannah seems to be unaware of how her actions are affecting (and annoying) her classmates. She has even been rejected from class fieldtrips for her past behaviour, even with her mother as a mentor. In grade 3, Hannah was diagnosed with ADHD, however, she is currently not medicated. With the untreated ADHD and subsequent behavioural issues, Hannah has been identified as lagging behind her peers academically. Hannah’s classmates and their parents have categorized her as a problem and refuse to accept her in social circles or group projects, which has led Hannah to become very emotional and distraught.

Hannah seems to be in a much better position to be successful in school, having learned some successful self-control skills at a camp specifically designed for individuals with ADHD. However, Hannah has a reputation now, and her classmates and the school community have an expectation of her negative behaviour. Given the information outlined above regarding Hannah’s behavioural issues, there are a number of supports and accommodations that must be put into place in order for Hannah to be successful:

### Instructional Accommodations

It is important that classroom instruction is differentiated to meet Hannah’s current level of subject matter comprehension, ensuring that the work is not too advanced or unachievable given her current academic struggles. In an effort to capture and maintain Hannah’s attention throughout instructional periods, various forms of media (Chromebooks, magazines, YouTube videos) and visual aids (anchor charts, drawings, images) should be incorporated into lessons. Providing step-by-step instructions that are manageable and achievable within Hannah’s threshold of attention will ensure that she does not wander or become disengaged in her learning (Bennett et al, p. 126). It is also important to provide extra assistance at the beginning of a new activity so that she has goals and objectives outlined that she needs to achieve. Classroom instructions should be delivered in close proximity to Hannah so that the audio and visual distractions are limited and the focus is solely on the educator (Bennett et al, p. 126). Additionally, it is important that Hannah is provided with regular reinforcement and celebrations to motivate her, acknowledge her progress and achievements, and to show the other students that she is a valued member of the classroom community.

### Environmental Accommodations

A suggested way that Hannah could appropriately channel her energy, especially during quiet work periods, is by having an exercise bike in the classroom or replacing her chair with a yoga ball. An important consideration when placing Hannah in the classroom is to ensure that windows or other highly stimulating areas in the classroom are considered and/or altered if distractions occur. It is also important that Hannah is placed in a location within the classroom in which she can stay focused at be successful, such as away from the classroom door and other areas of high traffic. However, it is also important that Hannah is not isolated from her peers in a study carrel or “solo” desk, given that she doesn’t have strong peer relationships as it is. It may even be of benefit to Hannah’s social connections to establish a peer mentor/buddy that Hannah could sit with. This student would naturally be a liaison between Hannah and the rest of her classmates, helping to reduce negative stigmas attached to her and to establish positive peer relationships. Following a discussion with Hannah about positive self-regulation strategies, an image of the Zones of Regulation could be taped to the corner of her desk so that she is consistently aware of her behaviour and is reminded of appropriate strategies (http://www.zonesofregulation.com). Hannah should also be allowed to listen to music during work periods in an attempt to keep her focused and avoid potential opportunities to distract her peers.

### Assessment Accommodations

In direct correlation with the instructional accommodations, it is important to differentiate pieces of assessment to meet Hannah’s current level of comprehension. It is important to outline step-by-step instructions on all pieces of assessment so that Hannah has an outlined process that she must follow and items that she can check off once completed. In addition to the step-by-step instruction, the educator can create goals with Hannah in respect to deadlines and success criteria. A way to focus Hannah on the task at hand would be to assist her with organizing her work and thoughts at the beginning of the assessment (Bennett et al, p. 126). Frequent check-ins throughout the assessment process would ensure that Hannah is on task and understanding the content being explored. Incorporating visual aids would help to spark Hannah’s interest in the assessment and, ideally, engage her throughout the process.

There are a few other foreseen issues that Hannah may experience if these supports are not put into place. If a stable routine is not put into place, then the coping strategies that Hannah is working on may become difficult to utilize in unpredictable situations. However, once a classroom routine is established, Hannah will know when it is appropriate to do what (i.e. listen to music). It is almost important that while the educator must be flexible and adaptable given Hannah’s varying behaviours, firm expectations about appropriate classroom behaviour should be created and discussed with Hannah. This will allow her to become more self-aware of her behaviour and its ramifications, especially if teacher prompts have become exhausted.

This is a crucial time in Hannah’s academic development. It is imperative that her distractions are limited so that her academic achievement increases to a grade-appropriate level. Perhaps even more pressing is Hannah’s social development. As previously mentioned, she has established a negative reputation among her classmates and their parents. This can be very damaging for Hannah’s self-esteem and overall self-image. It is very important that the classroom teacher works with Hannah and her peers, through restorative justice and community building initiatives to mend Hannah’s relationships with her peers and provide her with a supportive and accepting social circle (Ministry of Education, p. 36). I believe that through the implementation of the suggested accommodations and considerations, Hannah can be set up for a successful academic and social development.

### References

A Concept to Foster Self-Regulation & Emotional Control – Welcome. (n.d.). Retrieved May 19, 2017, from http://www.zonesofregulation.com/index.html

Bennett, S., Weber, K. J., Dworet, D., & Weber, K. J. (2008). Special education in Ontario schools. Niagara-on-the-Lake, Ont.: Highland Press.

Ontario Ministry of Education (2010). Caring and safe schools in Ontario: supporting students with special education needs through progressive discipline, kindergarten to grade 12. Toronto: Queens Printer for Ontario.