Week 6: Summing it all up

This week our Webinars took over class, so I thought I would take this week's post to sum up my observations and reflect upon the presentations this week. But first of all, congrats to us for another semester down!

Just one more left.....

We began the presentations with implementing technology in the classroom. We went through the app "Explain Everything." I found this app to have incredible potential in the classroom, especially the way Group A presented their activity. We were given a handout of questions to answer through the app such as "what is a square root?" and kept adding new slides for each question, where we could draw and record ourselves explaining our process. I could see this being done in the classroom, or even, as suggested, the teacher using the app to post additional help for concepts. This type of app offers redefinition in the classroom. Teachers can use this to their benefit to keep track of student understanding. This also gives students a chance to prove their understanding in a new multimodal way. 

Our next presentation focused on teaching strategies with visual tools/aids. What I thought was an important feature this group honed in on was how visualization can help to improve student's understanding in math. A concept we watched Jo Boaler comment on in Lesson 5b, which emphasized that visualization (drawings, representations) help to enhance the way we understand ideas and retain ideas. Furthermore, Group B's implementation of the book Counting On Frank not only highlights the resources available in the IRC, but was an excellent way to make math applicable in new contexts. By engaging the class in a story and presenting new questions along the way, students will become invested in the problem, because they are invested in the book.

Clement, Rod. Counting on Frank.
Retrieved from: https://www.amazon.ca/Counting-Frank-Rod-Clement/dp/0836803582

Group C focused on Financial Literacy, it was very practical to go through other documents to find connections of how to directly relate financial literacy in other topics. This is a great way to make math cross curricular as well in some instances. For example, my partner and I made connections to the effects of smoking in grade four. Financial Literacy can be integrated by investigating the financial implications of being a smoker. You could ask questions such as "If someone smokes 2 packs a day worth $11.00 a pack, how much many are they spending a week, a year, over 5 years?" "If minimum wage is $11.40 an hour, how much of someone's work pay in a month goes into their amount of cigarettes bought in a month?" "What other items are of equal value and could be a better choice for your money?"

Group D discussed Differentiated Instruction and strategies for differentiating content, process, product and learning environment for students. Allowing students to have a lot of choice in the classroom is important, while also making sure to invest a lot of time in growth mindset, so that students are able to self-regulate and make the choices appropriate to them.

And the last group discussed how to implement technology in math and provided multiple apps and websites to explore that would be useful for students and teachers.

What I found common about the Webinar topics is that this information sets us up for 21st century learning. One of the articles from this week's reading, 21st Century Learning, 20th Century Learning by Zoe Branigan-Pipe, speaks towards how we as teaching professionals can better connect the concepts and practices of 21st century learning into our environment. She states, "In almost every country that values literacy for all its citizens, recognition has grown that students learn in different ways and at different paces, and as information and tools have become more accessible and equitable, we welcome and support a variety of media and strategies." As prospective teachers learning in the context of 21st century teaching practices we are at an advantage that we are able to delve into topics such as these, synthesize the information, and share with our peers. The purpose of the Webinar is to do exactly what Branigan-Pipe asks us in her article: How are we making connections between the concepts of 21st century learning to the classroom?

Resources:

Branigan-Pipe, Zoe. (2016) 21st Century Learning, 20th Century Learning. Education Canada. Retrieved from: http://www.cea-ace.ca/education-canada/article/21st-century-learning-20th-century-classroom

Week 5: Evaluating the Uses of Technology in the Classroom

This week in class we discussed blended learning and the benefits of implementing web tools as support for learning in the classroom. When selecting the appropriate tool for a class it is important to evaluate that tool and its usages. How will your students use this tool? Does this tool support students? How does this tool aid in problem solving? When assessing the properties of online tools and apps, one can refer to the SAMR Model developed by Dr. Reuben Peuntedura. SAMR (substitution, augmentation, modification and redefinition) model offers a method of seeing how computer technology might impact teaching and learning. The model also offers a progression that adopters of technology might follow as they progress through teaching and learning with technology (Technology is Learning).

Image from: The 4 Stages of EdTech - The SAMR Model for Technology Integration, 2015.

The above illustration demonstrates the continuum between the stages of SAMR. What I would like to highlight in the stages is the functional change that happens:

1. Substitution: 

Math playground offers a virtual Geoboard for students to use that helps them to calculate area and perimeter.

There is no real functional change in teaching and learning. There is no real gain in using computer technology, rather it substitutes the use of using a real Geoboard. This stage is usually teacher directed.

2. Augmentation

Arcademics Skiller Builders provides online games for all subjects, which you can narrow down to grade and also strand of mathematics.

This tool takes problem solving and transforms it into a game. This tool acts with functional improvement because students are problem solving but they are engaged because of they are playing a game. Students also receive immediate feedback from the game. This stages moves into teacher/student focus.

3. Modification

Kahoot! is a way to create online quizzes, which students can join using an electronic device. I used Kahoot! in my placement and the feedback was incredible. For math I used Kahoot! to create unit reviews, the students wanted to play again and again because of how fun they found the experience.

This tool acts as significant task redesign for what could have been a paper-pencil review. Students are able to receive immediate feedback as well as the teacher is able to view students' answers and see where students are at and where areas of need are. Students are also more engaged in learning. Students reflect on own learning.

4. Redefinition

Educreations is an interactive whiteboard app with a screen casting tool. Students can draw or write out their concept, problem or solution and annotate, animate or narrate along and share their screen cast with the class.

This tool allows for creation of new tasks that were, before, inconceivable. Every student is able to screen cast their problem and share with the class, and the teacher is able to have a recording of each students' screen cast to assess learning. When using whiteboards in the classroom, sometimes only a few students get to share their ideas, and ideas get to be erased later on. With Educreations, sharing is immediate, long lasting, and each student is accountable. The benefit is that now the teacher is able to gather more valuable evidence of learning.


The SAMR Model is extremely helpful when it comes to assessing the value of apps, tools and implementing technology into your classrooms. The model provides a basis of evaluation for teachers to follow to assess the benefits of the choices they will make when planning for blended learning.


Resources:

SAMR Model - Technology Is Learning. (n.d.). Retrieved October 15, 2016, from https://sites.google.com/a/msad60.org/technology-is-learning/samr-model 

 (2015). The 4 Stages of EdTech – The SAMR Model for Technology Integration. Retrieved October 15, 2016, from http://lingomedia.com/stages-of-edtech-the-samr-model-for-technology-integration/ 

Week 4: Interleaved Practice

This week was all about learning how to implement rich tasks for mathematics. First, we discussed interleaved vs blocked practice. Blocked practice/study (or block learning) is an accustomed practice. This is where concepts or skills are introduced and taught explicitly until they become mastered, once mastered, the next concept or skill is taught. In interleaved learning, new material is taught while at the same time reviewing past material, this style proves that students hold on to information for a longer period of time. The diagram below shows the differences between the two methods:

Chamberlain, 2016. [Information from lecture]

In blocked study concepts are taught in blocks, as shown as above, and not reviewed through out, but are completed when mastered. In interleaved learning concepts are shown to be revisited. For example, a teacher would spend quite some time with Concept A, since that is where fundamental skills would be developed. The teacher would transition to Concept B, but continue with Concept B while equally reviewing Concept A. Afterwards, Concept C would be introduced, and at the end of the unit the teacher would spend a little amount of time with Concept A, some time with Concept B, and most time with Concept C. This type of balance between concepts allows for students to see the relevance of concepts throughout the unit. It also allows students to go back and review skills that they have already mastered and put them to new usage as they engage in further tasks. As stated in the Concepts video in this weeks forum, all math concepts are connected to each other, and the curriculum scaffolds information in a way that builds a basis for the next subject to be taught. Seeing how concepts are connected builds a new respect for each respective concept. It makes the concepts more relevant and more applicable, knowing that they will be needed to build towards another.

Dr. Doug Rohrer in his video The Benefits of Interleaved Practice provides a relevant analogy between blocked practice and interleaved practice. He compares the two to a baseball study, where batters were given types of pitches in blocks of 15, in this the batters knew what to expect when at bat because of the repetition. In interleaved practice, batters were given different pitches mixed up, not knowing what was coming next. Later they took a test, which was like an actual baseball game where the batters did not know what to expect, and the batters that received interleaved practice did far better than those who received blocked practice. Interleaved practice gives opportunity to do exactly what would need to be done during a test.

Another benefit of interleaved practice is that it provides further support for students to develop reasoning. Since skills are introduced and revisited, interleaved practice allows for relevance of older concepts to be used in new problems. It is a way of making concepts applicable to one another and students can make decisions and justify problem solving pathways by seeing relevance of the fundamental skills taught at the beginning of the unit.

Resources:
Flick, Michael Harry. Learn Better: Interleaved vs Blocked Learning. September 4, 2013. URL: http://www.personal.psu.edu/afr3/blogs/siowfa13/2013/09/learn-better-interleaved-vs-blocked-learning.html

Lasting Learning. The Benefits of Interleaved Practice, Dr. Doug Rohrer. December 31, 2015. URL: https://www.youtube.com/watch?time_continue=88&v=4wJEB0cEUok

Lesson 4f. June 12, 2014. URL: https://www.youtube.com/watch?v=q8hzzv4a_8Y&feature=youtu.be

Week 3: A Thinking Classroom

This week in class we discussed the article Building Thinking Classrooms. The article defines a "Thinking Classroom" as a space inhabited by thinking individuals, where students are working collectively, learning together, constructing knowledge and understanding through activity and discussion. (Liljedahl, 2016) A thinking classroom is one based on inquiry, where the teacher is not only delivering content and transmitting knowledge, but students have questions and use problem solving skills and collaboration to work through problems. A thinking classroom also deals with a good amount of struggles. If students are working together and thinking out loud about problems they are discussing how to work through them, through this students meet struggle. Struggle takes on a new term though, in allowing struggle and mistakes happen when problem solving helps to make your brain grow (Mistakes and Research, 2016). This weeks forum video Mistakes and Research discussed how mistakes allow for synapses in the brain to fire and growth is made, but getting an answer correct, no growth is made. It is because struggle and hard thinking is when the brain grows the most (Mistakes and Research, 2016). A thinking classroom is therefore a critical environment to cultivate that would allow students to work together, make mistakes and practice tasks to develop their learning.

In class we had our own example of a thinking classroom. We were given a variety of problems to work out with our table groups such as Tax Man or the Collatz Conjecture. During these tasks we did reach some struggles, or at least I did. But working collectively allowed for different perspectives to be encountered, and problem solving to become less difficult. The teacher walked around as a facilitator of discussion and when we thought we were done with beating the Tax Man, asked us to see if we could beat him in a better way. With more thought, we were able to beat the Tax Man better. We also used vertical non-permanent surfaces (whiteboard) to show our work. The benefit of using white boards or other non-permanent surfaces is that it gives students an opportunity to show their work to an audience. It also allows students to look around the room and visibly compare the problem solving strategies done by their peers. It allows students to get out of their seat and actively participate and be contributors of knowledge.

EDBE 8P54 Week 3 Slideshow. Teaching Mathematics for all learners.

These types of implementations in the classroom not only successfully build knowledge, but they are ways to trigger engagement. A thinking classroom is a meaningful experience that gives students responsibility to contribute to learning. A thinking classroom also allows for multimodal problem solving, activity, and collaboration which varies drastically from a traditional classroom. Just even these few simple differences make all the difference in engaging students and diverse learners. Diverse learners have so much more to benefit from this type of environment; they are able to collect strategies from their peers, visualize problems, ask questions openly and build confidence in their math skills while being a part of a solution team. In a thinking classroom worry over making mistakes does not exist so much, since it is an open environment to discuss strategies and work through problems collectively.

Sources:
Lesson 3a 360p. (2016). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=kGV0HQujmKs

Liljedahl, P. Building Thinking Classrooms: Conditions for Problem Solving. Simon Fraser University (June 2016). Retrieved: September 23, 2016

Week 2: Adaptive Reasoning

In this past weeks class we participated in a variety of highly engaging activities.

The first warm up activity asked us to find out how many owls were laid out throughout the blocks. Most students had to visualize this in a different way and went to take the snap cubes to start building a 3d model of the image, while some students drew out the image from a surface view.

Image from: In Class Activities Slideshow. EDBE 8N54 J/I Mathematics II Retrieved: September 19, 2016 

Another activity we participated in was the finger counting problem. We were asked which finger we would land on if counting to 1,000 and then again if we were counting to 12,345,789. Students were very engaged at this point and were up at the board problem solving and writing down their strategies that proved their answer. There were agreements and disagreements, but there was also a ton of communication involved while retrieving a general consensus. 

Chamberlain, 2016.

Chamberlain, 2016.

The reason I chose to discuss these activities was because they embody the building blocks to mathematical proficiency. According to the article The 4 Strands of Mathematical Proficiency, proficiency develops over time. Students need enough time to engage in specific mathematical activities in order to develop that skill. Only one or two experiences with a procedure will likely not help them succeed, but practicing over sustained periods will help make connections between previous knowledge and new knowledge. (137)

Practice with mathematical concepts is hidden within these brain teaser activities. Students want to solve the problem and without being told begin to find resources to solve that problem (i.e. snap blocks, visual pictures). They get up and start to explain the justification of their strategies and communicate with others around them and form adaptive reasoning. They start to think logically about the relationships among concepts and situations, justify their procedures and give sufficient reasoning. (130) 

Adaptive reasoning is the overarching goal for mathematics, it is the last step towards mathematical proficiency. It goes back to the video we watching for our online modules Messages about Math, when students are praised for giving the correct solution they are more likely to choose easier paths that do not challenge them, where students who are praised for their hard work will continue to challenge themselves and be more confident in mathematics. Students need to be acknowledge for the effort they put into deriving the answer, for their ability to get up and explain their thinking, regardless if it is right or wrong, if they can express what they are trying to do and we can correct it together. Students minds need to shift from the end answer as the goal and the classroom should practice the pathway to adaptive reasoning. A shift in focus will allow for students to be more engaged, more confident in themselves, less worried about making mistakes, and more literate in math.

Sources:
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Chapter 4: The 4 strands of Mathematical Proficiency in Adding it up: Helping children learn mathematics. [pp. 115-135] Washington, DC: National Academy Press.

Lesson 2c 360p. (2016). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=_9q0paQoZa8

Week 1: Establishing Confidence

This week's online activities really established a mindset that teachers and students should have prior to engaging in mathematics. By addressing stereotypes, reflecting on myths we have heard about math, and looking for instances where stereotypes are broken allows us to confront and reflect upon our own math experiences, successful or unsuccessful, and uncover those experiences.

Being aware of how math is portrayed through media, fashion etc. shows us as teachers why young people may be so hesitant towards the subject. The overall big idea we uncovered this week was that

everybody can do math.

So, knowing this as teachers, why should we not have our students know this as well? In my forum post I addressed the myth that some people are left-brained (logical) and some are right-brained (creative) and there is no crossover. This means that if you are good at math you cannot do well in the arts, or if you excelled in arts, you could not do well in math. This seems as though a heavy weight excuse for those who do not want to try at the "opposing" discipline. If anything it allows students to give up much more easily because they are going in with the mindset that they cannot accomplish much because it is not their strength. And as students go further into their education they follow their strengths. As educators, especially in junior intermediate, where students are becoming more eager to identify themselves, we should be showing and encouraging students to see disciplines as integrated subjects that make up our world. Because they are. We should be insisting that you are whole-brained and as said in the video The Brain science on Growth Mindset mistakes help to grow your brain.

EpilepsyUni. August 16 2013. epilepsyu.com

It is absolutely crucial to establish an environment that encourages students to have an open mind, mistakes are welcome, and have them know they are capable of being successful at math. Doing this will be a stepping stone towards confidence and student success. 

Starting in September we have the opportunity to debunk any stereotypes in our classroom. We could have students do the exact thing we are doing in class. We could be asking them about their personal math story and have them address stereotypes and myths they may have, and smash the stereotypes for them. We could show students Hollywood Hates Math  (appropriate clips) and challenge students to become aware of any time math negatively comes up when they are watching television or movies, and have them bring those instances to the classroom.

We could also have them look for instances where stereotypes are being altered. One particular scene that came to mind for this was from the movie Stand and Deliver:

In this scene the teacher, Escalante, shatters his students' own ideas of what they can accomplish in math. He challenges them with something new and difficult, algebra, and proves to them that math is in their blood. You can see after the student correctly answers 0 the look of satisfaction on his face. It takes a teacher to come in and drive confidence into students. Establishing confidence from the start will put students on a pathway to success.

Sources:

Jo Boaler: The Brain Science On Growth Mindset. (2015). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=s4xqzgBy-lM 

Stand and Deliver (1988) scene. (2013). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=Q3a-bXXN9Xc