Author Archives: amanda gill

Illumination and TGEM

Stephens and Clements (2015) discuss the importance of students having sufficient background foundational knowledge before exploring and utilizing simulations. Simulations help to motivate students and create excitement, but students need to understand that there is a difference between reality and simulation which was discussed by Srinivasan et al. (2006). This lesson will be using the T-GEM framework and an interactive activity from Illuminations. Using interactive manipulatives are helpful for learners as it allows these students to work at their own pace, self-discovery and exploration. The activities can be adapted to the individual learner with the support of the teacher if needed. Further using technology allows for an engaging and interactive learning experience for students. It’s also important for student to be able to connect curriculum to real life scenarios, and technology allows students to make these connections.

https://illuminations.nctm.org/Activity.aspx?id=3510

G-Generate:

Exploration is key for students. This will allow students to ask questions they may have, and connect previous knowledge with knowledge they are gaining through self-discovery. Students will be able to practice the relationships between equivalent fractions and match each fraction to its location on the number line.

Students will use the interactive activity to explore. They will select “Build Your Own” option. Here students will be able to explore creating equivalent fractions by dividing and shading either circles or squares.

With students, go over key terminology and foundational concepts.

What are fractions?

What is a number line?

What is the numerator and what is the denominator?

What are the various ways to represent fractions?

Where do we use and see fractions in our everyday lives?

Students will generate a hypothesis regarding the relationships between fractions and how to create equivalent fractions and the relationship on the number line.

E-Evaluate:

During this stage, the teacher can pose questions that may not follow students’ hypotheses as this will allow students to evaluate the relationship. Teacher will also use equivalent fractions and have students create additional equivalent fractions. Here, students will have to use their numeracy skills to solve these questions.

M-Modify:

Teachers will ask students to represent fractions in lowest terms. Here students will have to use their multiplication and division skills to determine this relationship and apply their knowledge. How will students use their foundational knowledge and apply it to this activity.

Questions for students:

Can all fractions be reduced to lowest terms? What are the main “benchmark” fractions?

Can one fraction have many equivalent fractions? How can you show this visually and numerically?

How does multiplication and division relate to fractions? How are number lines useful to describe fractions?

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

Srinivasan, S., Perez, L. C., Palmer,R., Brooks,D., Wilson,K., & Fowler. D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 137-141.

Stephens, A. & Clement, J. (2015). Use of physics simulations in whole class and small group settings: Comparative case studies. Computers & Education, 86, 137-156.

Making Math Meaningful

Speculate on how such networked communities could be embedded in the design of authentic learning experiences in a math or science classroom setting or at home. Elaborate with an illustrative example of an activity, taking care to consider the off-line activities as well.

Carraher et. al’s (1985) article Mathematics in the Streets and in Schools discuss that “there are informal ways of doing mathematical calculations which have little do with the procedures taught in school”(p.21). The researchers suggest that students apply their mathematical abilities correctly in real world scenarios than with context-free paper and pencil problems. Context seems to play an important role when solving mathematical problem based questions. The researchers found that “in that natural situations children tended to reason by using what can be termed a ‘convenient group’ while in the formal test school-taught routines were more frequently, although not exclusively, observed” (p.25). This shows that as educators we need to provide opportunities for students to connect to real world situations as we want the skills taught in skill actually be used outside of the classroom. As a learning support specialist teacher teaching students who struggle with numeracy, I always think about how I can relate situations to a real world situations. Providing a meaningful context is essential for my students. Students need to be involved in the learning process as they are better able to retain the information. The newly reformed BC curriculum incorporates many inquiry based opportunities for students and also reinforces that students need to learn at their own pace. This is the key for the students that I specifically teach as they are working at their own level. Measurement was a difficult unit for my students. We did work on the basic concepts but they really didn’t understand the differences between centimeters, meters, and kilometers for example. So to help understand the differences between kilometers and centimeters, we went outside and went for a walk and walked 1km around the school grounds. Only after experiencing this themselves they truly understood the magnitude of 1km. Another favourite math activity students enjoy working on is converting our classroom into a “floor plan”. This covers area and perimeter which students have a hard time understanding. After go over the basics, each group of students are responsible for a certain area of the “house” (ie. kitchen, bedroom, bathroom etc.). They are given dimensions and need to recreate this space in the classroom using meter sticks and masking tape. Students have to work together to correctly measure the perimeter and area of their space. By working together they are working on their critical thinking and problem solving abilities. We could also use technology to support our mathematics curriculum as sometimes it is not feasible to always go out to explore math concepts in real world situations. For example, the use of VR has becoming extremely powerful as it allows students to achieve real life like situations. I always remind my students during our “money unit” to practice using money when they go out shopping with their families. The reality is many of my students don’t spend much time going out with their families, so they don’t get to experience it. Using VR would help bring real life situations into the classroom as we could go the grocery store to purchase items and practice giving and receiving change. This could also be done in the classroom, by turning the classroom into a store and students using money manipulatives to purchase items. An article by Furner & Marinas, discuss how “today the emphasis is on using technology to teach math and getting students interested in STEM” (p. 209). They suggest using interactive technology such as GeoGebra and connecting them to photography to allow students to make deep connections. As educators we need to find unique opportunities where learning opportunities connect to student interests, allow for experiences, and will connect with their future.

Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British journal of developmental psychology, 3(1), 21-29.

Chapter 3. Making a Real-World Connection (n.d.). Retrieved March 23, 2018, from http://www.ascd.org/publications/books/102112/chapters/Making_a_Real-World_Connection.aspx

Furner, J & Marinas, C. (n.d.) Learning Math Concepts In Your Environment Using Photography and Geogebra. ICTCM. Retrieved from: http://archives.math.utk.edu/ICTCM/VOL25/S125/paper.pdf

Math and Embodied Learning

Winn’s (2003) article was an interesting read. Winn (2003) describes embodiment as, “the physical dimension of cognition” (p.7) and discusses how there is a real connection between cognitive activity and the environment. Winn (2003) also discusses how the three concepts, “embodiment, embeddedness and adaptations form a viable theoretical framework” (p. 6). When reading the article this part stood out for me, “To say cognition is embodied is to say that it involves our entire bodies not just our brains” (p. 8). This means that our bodies and movement contribute to learning and understanding of concepts.

Thinking about my practice as a learning support specialist teacher in Mathematics I incorporate collaborative activities and use hands-on on manipulatives regularly, as the movements and physical presence of objects help my students understand concepts. Roschelle & Singleton’s (2008) article describes the benefits of graphic calculators. The benefits of using graphic calculators include “chang[ing] how students learn by reducing the cognitive load, increasing opportunities for complex and multi-step problem solving and enabling teachers to emphasize mathematical reasoning, not just calculation” (p. 951). This is an area that I have been working on with my students this past term. Even though we are not at that level of using graphing calculators, we do use regular calculators to help with multi-step word problems and application so students don’t need to focus on computation. Roschelle & Singleton (2008) state that “40% of high school mathematics classrooms use graphing calculators, whereas only 11% of mathematics classroom use computers” (p. 952). This shows that graphing calculators are a powerful handheld tool that support student learning. Further, Roschelle & Singleton (2008) mention that school districts are providing professional development opportunities around the use of graphing calculators to enhance teaching and learning. Another affordance discussed in the article includes allowing students to check their work and to help justify their answers. I encourage this in my classroom as it gives students responsibility and ownership of their learning. Roschelle et al. (2010) discuss using TechPALS, a small handheld device that provides feedback to students working together in small groups when solving fractions. This was compared to students using a desktop application which provided feedback to the student individually as the student works on tasks independently. The study showed that when students worked together and collaborated using TechPALS, this enhanced student learning vs when students worked independently. This emphasizes the importance of repeated practice in activities where students learn by exploring and discussing in a collaborative form.

Questions:

Winn (2003) suggests that cognition involves our entire bodies not just our brains. How can the use of technology such as personal devices be used to involve our entire bodies?

Roschelle & Singleton (2008) show how powerful graphing calculators are to student learning. If this is the case, why at the elementary level are calculators looked down upon by many educators?

Roschelle, J., & Singleton, C. (2008). Graphing calculators: Enhancing math learning for all students. (pp. 951-959). Boston, MA: Springer US.10.1007/978-0-387-73315-9_60

Roschelle, J., Rafanan, K., Bhanot, R., Estrella, G., Penuel, B., Nussbaum, M., & Claro, S. (2010). Scaffolding group explanation and feedback with handheld technology: Impact on students’ mathematics learning. Educational Technology Research and Development, 58(4), 399-419. 10.1007/s11423-009-9142-9

Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114. Full-text document retrieved on January 17, 2013, from: http://www.hitl.washington.edu/people/tfurness/courses/inde543/READINGS-03/WINN/winnpaper2.pdf

Module B Synthesis

Synthesis 533

Learning about the four technology-enhanced learning environments was eye opening as each technology has something to offer to my students and I would need to tailor it to meet the needs of elementary aged intermediate students. There was a common theme of exploring and inquiry with each technology. Learning should be engaging for students so they can make meaningful connections.

The Jasper series emphasizes the importance of helping students. The series “affords generative and cooperative learning activities in way that traditional mathematics problem-solving materials do not” (p. 65). I think it is important to create a community of inquiry that includes students and teachers as students are actively involved in the learning process. Collaborative learning is powerful as students all have their specific strengths and when they work together they each learn from one another.

Web-based Inquiry Science Environment (WISE) is highly beneficial as it offers students a different style and approach to learning. WISE allows students to work in a step by step fashion while working at their own pace.

Learning for Use model “is a description of the learning process that can be used to support the design of content-intensive, inquiry-based science learning activities” (p.355). The Learning Cycle is an “inquiry based pedagogy” where content knowledge and process learning are combined. Edelson (2000) discusses how inquiry learning fosters deep learning among students. Using technology is engaging for students, technology and computers are able to store large amounts of information (ie. data), and technology bring change to the classroom as it is evolving. Constructivists believe that knowledge is built from exploration and experimentation. Further, new experiences are connected with pre-existing knowledge and knowledge is gained. Here, learning is active and students are engaged. The newly BC reformed curriculum falls more with a constructivist approach as inquiry learning has become increasingly popular as it allows students to gain critical thinking and problem-solving skills.

The Lfu model stood out for me and also learning about how others used PhET simulations within their practices. Last week I already had the chance to introduce the simulations to my students. We really focused on exploration of area and perimeter as that was a hard concept for some of them. The learning was active and engaging and the students responded well. My goal is to try and incorporate the four TELEs in my math lessons over the next few months and do some exploring of my own!

Cognition and Technology Group at Vanderbilt (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology, Research and Development, 40(1), 65-80

Edelson, D. (2001). Learning-for-Use: a framework for the design of technology supported inquiry activities. Journal of Research in Science Teaching, 38(3), 355-385.

Slotta, J. D., & Linn, M. C. (2009). WISE science: Web-based inquiry in the classroom. Teachers College Press.

TGEM: Fractions, Percents and Decimals

As a learning support specialist teacher, my intermediate students struggle with many mathematical concepts. My students currently are struggling with understanding the relationships between fractions, percents and decimals. Fractions are introduced in the younger grades but as they move onto the next grade without the key foundational skills, the gap increasingly grows. I use many hands on manipulatives and last year discovered a free online interactive tool (visnos.com). I had hoped to use this interactive tool more, but didn’t have time to properly integrate in within my teaching practice as I was trying other methods and intervention programs. Thinking about the T-GEM approach, using this interactive math resource will fit well within my current unit. Using interactive manipulatives are helpful for struggling learners as it allows these students to work at their own pace and activities can be adapted to the individual learner. Further using technology allows for an engaging and interactive learning experience for my students. It’s also important for student to be able to connect curriculum to real life scenarios, and technology allows students to make these connections.

G-Generate:

Exploration is key for students. This will allow students to ask questions they may have, and connect previous knowledge with knowledge they are gaining through self-discovery. Students will be able to practice the relationships between fractions, percents and decimals. Students will also be able to practice and explore the relationship between equivalent fractions and develop strategies for converting fractions to decimals.

Students will use “Starter Calculate Percent Fraction Decimal” and “Percentage Fraction Decimal Grid” interactive activity to explore.

With students, go over key terminology and foundational concepts.

What are fractions?

What is the numerator and what is the denominator?

What are the various ways to represent fractions?

Where do we use and see fractions, decimals and percentages in our everyday lives?

Students will generate a hypothesis regarding the relationships between fractions, variables and decimals.

E-Evaluate:

During this stage, the teacher can pose questions that may not follow students’ hypotheses as this will allow students to evaluate the relationship. Teacher will also use equivalent fractions and have students determine the fractions, percentages and decimals. Here, students will have to use their numeracy skills to solve these questions.

M-Modify:

Questions for students:

Can all fractions be reduced to lowest terms? What are the main “benchmark” fractions?

Can one fraction have many equivalent fractions? How can you show this visually and numerically?

How does multiplication and division relate to fractions, decimals and percent?

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

Numeracy and LfU

In what ways would you teach an LfI-based activity to explore a concept in math or science? Draw on LfU and My World scholarship to support your pedagogical directions. Given its social and cognitive affordances, extend the discussion by describing how the activity and roles of the teacher and students are aligned with LfU principles.

Many see traditional teaching as “memorization of recitation of facts” (p. 356). The main goal of the Learning for Use model is to make learning and knowledge meaningful for the learner so they are able to apply it. The LfU model is based on 4 principles:

-Learning occurs through construction of knowledge

-Knowledge construction is a goal-directed process

-Knowledge construction will be used for future use

-Knowledge is constructed in a form that supports use before application

Edelson (2000) discusses how the first principle is related to constructivism. Constructivists believe that knowledge is built from exploration and experimentation. Further, new experiences are connected with pre-existing knowledge and knowledge is gained. Here, learning is active and students are engaged. The newly BC reformed curriculum falls more with a constructivist approach as inquiry learning has become increasingly popular as it allows students to gain critical thinking and problem-solving skills.

As a teacher who specializes in Numeracy instruction for students who struggle with math, I began thinking how I could apply principles of LfU to explore a mathematical concept. My students often struggle with money and applying it to real world situations. I would use LfU principles to teach a lesson on budgeting. To motivate my students (upper intermediates), I would show them $100 bill. This would be a hook to get students excited about money. This would also give them an opportunity to think about what they could possibly purchase for $100 and what value it holds. They would be assigned a project where they are planning a party and inviting three friends over and they have budget of $100 for food, decorations and activities. They each would be given an iPad and can use online shopping (ie. Save on Foods) to “purchase items” for the party they are hosting. This brings in the real-world element and most students use technology for online shopping. This also provides them with visuals to enhance learning. Here they would investigate, explore and determine if it’s better to buy single items or in bulk. Here they would build upon their problem solving abilities. The students would devise a plan, share their purchases and all discuss if the $100 budget was realistic or not and this would create a discussion among the students. After, they will reflect whether they effectively used $100 effectively and if they stayed on budget. This activity follows the four principles of the LfU.

Edelson, D. (2001). Learning-for-Use: a framework for the design of technology supported inquiry activities. Journal of Research in Science Teaching, 38(3), 355-385.

More Photos in Photosynthesis

As a learning support specialist teacher, I teach students with varying abilities and learning designations. Using Web-based Inquiry Science Environment (WISE) will be highly beneficial as it offers students a different style and approach to learning. I often incorporate visuals and videos when teaching my students and also ensure I provide a break down and step by step instructions. Using WISE will allow for this while working at their own pace. My students would appreciate the breakdown of questions and prompts as it allows them to focus on the specific task. Slotta & Lonn (2009) describe WISE has having many types of activities which “promotes autonomous learning.”

Looking at the Photosynthesis Project (ID: 9932), there seemed to be lack of autonomous learning to enhance student learning. Some changes I made were I added in videos to the introductory activities and added in additional images to activities that were mainly text based. Thinking about my students who are visual learners and require visuals to make connections to text, this was an important change because the content was mainly all text. Further, for my English Language Learners (ELL) they rely heavily on visuals to learn concepts and to make connections.

I made changes to the Quiz by removing the “only three chances to complete this quiz” component, as this will cause stress for some students and would not enhance learning. I did like how with some questions, there was immediate feedback for the learner and if the student made an incorrect error, they were redirected to the section that needed to be reviewed as it wouldn’t let the student move forward. This is essential as with some programs, students just click through and going through the motions without gaining knowledge. This way, students go back to review concepts they don’t understand and can spend more time in those areas.

Further, I added some collaboration components for some of the activities as this was lacking in this unit. Overall I believe the WISE can have place within the classroom as supplementary support to enhance learning, but it will be important that the WISE activities are tailored to the students’ needs.

Linn, M. C., Clark, D., & Slotta, J. D. (2003). WISE design for knowledge integration. Science education, 87(4), 517-538.

Slotta, J. D., & Linn, M. C. (2009). WISE science: Web-based inquiry in the classroom. Teachers College Press.

Jasper Series: Anchored Instruction

The Jasper series emphasizes the importance of helping students. Furthermore the series “affords generative and cooperative learning activities in way that traditional mathematics problem-solving materials do not” (p. 65). The videos encourage students to become independent thinkers and learners rather than just solve basic computational questions. It is emphasized that as educators we need to “help students engage in generative rather than passive learning activities” (p. 67). The article discusses the importance of generative learning which includes having a cooperative learning environment along with a cooperative problem solving setting as this way students can work collaboratively together brainstorming ideas, the students can monitor each other ensuring that everyone is on the right track. The articles discusses the NCTM’s suggestions regarding the emphasis on giving students more open-ended math questions that are related to real world problems where students have to work together and use their critical thinking skills to solve these problems. For students who have learning difficulties and even for new English Language Learners, the Jasper series in appealing as the videos can compensate for reading difficulties and also it provides a great visual (p. 69). “An overall goal of the Jasper series is to establish a community of inquiry that includes students, teachers and other as well” (p. 76). I think it is important to create a community of inquiry that includes students and teachers as students are actively involved in the learning process. The Jasper series falls under a constructivist perspective, in that students have to merge a new experience (the problem to be solved) with existing information. Further the Jasper series allows students to explore and make sense of new information through inquiry based activities. As educators, we would take the facilitator role and guide students. This is powerful for students as they are fully involved in the learning process and are not passive learners, they can work collectively and collaboratively and it requires students to use higher-order thinking skills (applying, analyzing, evaluating).

Thinking about my class and instruction, I try to use similar methods outlined in Hasselbring, Lott & Zydney (2006) article such as the “7-step strategy” for students who have learning difficulties. It would be ideal to actually have the program as students would be able to work through each step independently using a computer program. Rather I use similar strategies and use a graphic organizer to help students work through problems. The article further discusses the effectiveness of using calculators within their classroom during problem solving activities, and this is something that I promote in my class. I find my students are hesitant though to use calculators as they view it as “cheating”. However, they soon realize that the calculator is just a tool to assist them with their mathematical calculations and realize the significance of using it. Additionally, my students enjoy watching Khan Academy videos to help with understanding ideas and concepts they require further explanation and clarification with. They enjoy how visual it is and how clear the instructions are. If they don’t understand a part, they can simply rewind and watch again until they understand it. Even though Khan Academy has isolated videos on certain mathematical strands, and it is not very interactive, many of my students find it highly beneficial as it has helped them “close the gap” and they can see their improvement in their learning. My students have also used IXL math to help reinforce skills and enjoy it as students can collect points for awards so find it highly motivating. What do others use in their classroom?

Hasselbring, T.S., Lott, A.C., and Zydney, J.M. (2006). Technology-Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development. Washington, DC: CITEd, Center for Implementing Technology in Education

Place Value in Grade 3

I first learned about TPCK and PCK frameworks in my very first MET course. These frameworks are something I always think about as I integrate technology within my instruction. From the reading, this part stood out for me, “Newer technologies often disrupt the status quo, requiring teachers to reconfigure not just their understanding of technology but of all three components” (pg. 1030). I’ve taught for 6 years and currently in my 7^th and so every year the way I teach has changed as newer technologies emerge and I need to adapt and change they way I teach. Some of my colleagues haven’t adapted to the 21^st century way of learning and teaching and still are very traditional with their teaching practice. This brings up the notion again of why teachers need good quality professional development and training so they are able to learn and apply newer technologies with confidence for example.

I specifically teach Math as a Learning Support Specialist Teacher. When teaching new math concepts, I ensure that I activate prior knowledge and make connections to material learned prior to the new unit, as this is essential for my students. One of the very first units I always teach and review is Place Value. I use various materials to teach Place Value. I use visuals, hands on manipulatives and virtual manipulatives on iPads for example.

For example, for my Grade 3 class block as an introduction I will put up a number on the whiteboard and leave out manipulatives and let the students use manipulatives (base-ten blocks) to represent the number. After exploring for a few minutes, the students share their responses and collaborate. During this time, I can assess which students understand and are connecting the Place Value with the correct Base-Ten Block and where further instruction is needed.

Next, I thoroughly go through each place value spot with the corresponding manipulative to ensure students are making the connection. Students first listen and watch, and then they work together with their group to demonstrate their understanding. Once student understand the value of each place value position, we focus on representing the place value of numerals in three notations: Standard, Expanded and Written and focus only until the thousands position until everyone has a good understanding. Students can demonstrate their knowledge by using manipulatives, using whiteboard place value mats, or recording their thoughts on paper or digitally. For students who struggle and require another explanation, they can watch the tutorial videos on Khan Academy, which they always find very useful.

Once the students have “mastered” each place value spot and can represent it various ways (standard, expanded and written), we move onto the next until of addition with regrouping. Since I have just been teaching math the past few years, I have become very specialized in this area and have received training in specific programs and concepts.

Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054.

Virtual Reality

The definition of technology that stood out for me was Jonassen (2000) definition. Specifically, these parts:

” [S]tudents learn from thinking in meaningful ways. Thinking is engaged by activities, which can be fostered by computers or teachers. He believes that technology can support meaning making by students and that this happens when students learn with rather than from technology.”

“Mindtools include digital tools that support knowledge construction, exploration, learning by doing, learning by conversing, and learning by reflecting.”

I believe that students need to collaborate and explore to construct meaning. Experiences should be connected to real world issues and be meaningful to the students. I also see technology being used a tool to assist students with their learning and it should enhance their overall learning experience. Science can be explored through using virtual reality (VR) environments to learn about various units. For example, if the Science unit was on Body Systems, students would be able to virtually explore the systems and have real-life experiences by using a VR system. This enhances the students overall learning experience rather than looking at the body systems in a textbook. It provides them with a visual learning experience where they can explore, inquire and ask questions, which is great for all learners as sometimes opportunities of going into a lab is not available at elementary level. It’s also important to provide students opportunities to explore their own inquiries and collaborate with their peers. Passion-based learning would be part of this as it allows students to be critical thinkers, engage with one another and ask questions.

Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63-85. doi:10.1007/BF02300500