Fractions

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Fractions by Mind Map: Fractions

1. Operations with fractions

1.1. adding

1.1.1. concretely

1.1.1.1. fraction blocks

1.1.2. pictorially

1.1.2.1. fraction circles

1.1.2.2. fraction strips

1.1.2.3. number lines

1.1.3. symbolically

1.1.3.1. find LCM

1.1.3.2. eg.

1.2. subtracting

1.2.1. concretely

1.2.1.1. fraction blocks

1.2.2. pictorially

1.2.2.1. fraction circles

1.2.2.2. fraction strips

1.2.2.3. number lines

1.2.3. symbolically

1.2.3.1. find LCM

1.2.3.2. eg.

1.3. multiplying

1.3.1. concretely

1.3.1.1. fraction blocks

1.3.2. pictorially

1.3.2.1. number lines

1.3.2.2. area model

1.3.3. symbolically

1.3.3.1. eg.

1.4. dividing

1.4.1. concretely

1.4.1.1. fraction blocks

1.4.2. symbolically

1.4.2.1. eg.

1.4.3. pictorially

1.4.3.1. fraction strips

1.4.3.2. number lines

2. types

2.1. proper

2.1.1. eg. 1/4

2.2. improper

2.2.1. eg. 5/4

2.3. mixed numbers

2.3.1. eg. 2 1/4

3. representing

3.1. modeling

3.1.1. concretely

3.1.1.1. fraction blocks

3.1.2. pictorially

3.1.2.1. fraction circles

3.1.2.2. fraction strips

3.1.3. symbolically

3.2. relationships between fractions

3.2.1. comparing

3.2.1.1. concretely

3.2.1.1.1. fraction blocks

3.2.1.2. pictorially

3.2.1.2.1. fractions circles

3.2.1.2.2. fraction strips

3.2.1.3. symbolically

3.2.1.3.1. eg. 1/2<3/4

3.2.2. ordering

3.2.2.1. concretely

3.2.2.1.1. fraction blocks

3.2.2.2. pictorially

3.2.2.2.1. fraction circles

3.2.2.2.2. fraction strips

3.2.2.3. symbolically

3.2.2.3.1. eg. 1/8< 1/5< 1/4<1/2

3.2.3. equivalent fractions

3.2.3.1. concretely

3.2.3.1.1. fraction blocks

3.2.3.2. pictorially

3.2.3.2.1. fraction circles

3.2.3.2.2. fraction strips

3.2.3.3. symbolically

3.2.3.3.1. eg. 3/4 = 6/8

3.2.4. simplifying

4. Using fractions

4.1. authentic tools used to work with fractions

4.1.1. clocks

4.1.2. cooking

4.1.3. measuring tapes

4.1.4. measuring spoons/cups

4.2. experts using fractions

4.2.1. carpenters

4.2.2. chefs

4.2.3. pharmacists

4.2.4. hairdressers

4.2.5. investors

4.2.6. STEM (science, technology, engineering, and mathematics)

4.3. future advantages in learning with an understanding of fractions

4.3.1. fractions are related to ratios, rates, percent, proportion

4.3.2. fractions are used in other math concepts: solving equations, finding volume and surface area, graphing equations, etc.

4.3.3. fractions are used in other subjects: biology, chemistry, physics, economics, cooking, business, etc.

4.3.4. fractional understanding builds on larger mathematics cognitive processes including proportional reasoning, spatial reasoning, probability, and algebraic reasoning (Bruce, Chang, Flynn, Yearly, 2013)

4.4. Real -life uses/Authentic Scenerios where fraction knowledge would be important

4.4.1. construction

4.4.2. telling time

4.4.3. money/sales/investments

5. Misconceptions

5.1. The largest denominator is the largest fraction

5.2. Adding denominators when adding and subtracting fractions

5.3. You need a common denominator when multiplying and dividing fractions

6. Constructivist MultiMedia Teaching Ideas

6.1. Constructivist critical criteria for interactive multimedia (Herrington and Standen, 2000 )

6.1.1. 1. authentic context that reflects use in real-life

6.1.2. 2. ill defined authentic activities

6.1.2.1. Solve a problem, fix something that isn't working, develop a creative solution

6.1.2.1.1. choose a site that does a poor job of teacher a particular math concept - students analyze the site and provide creative solutions to improve the site. Site should teach the specific concept better. Concept was used in this paper http://www.ascilite.org.au/ajet/ajet17/neo.html

6.1.3. 3. access to expert performance andmodelling

6.1.4. 4. Multiple roles and perspectives

6.1.5. 5. Reflection

6.1.6. 6. Collaborative construction of Knowledge

6.1.6.1. Student created knowledge and sharing of fractions understnading

6.1.6.2. group project possibilities

6.1.7. 7. Articulation - learn to speak the language

6.1.8. 8. Coaching and Scaffolding

6.1.9. 9. Authentic Assessment

6.2. 10 critical elements for effective multimedia instructional design (Mayer, 2008)

6.2.1. Five principles for reducing extraneous processing

6.2.1.1. 1. Coherence

6.2.1.2. 2. Signaling

6.2.1.3. 3. Redundancy

6.2.1.4. 4. Spatial Contiguity

6.2.1.5. 5. Temporal Contiguity

6.2.2. Three principles for managing essential processing

6.2.2.1. 1. Segmenting

6.2.2.2. 2. Pretraining

6.2.2.3. 3. Modality

6.2.3. Two principles for fostering generative processing

6.2.3.1. 1. Multimedia

6.2.3.2. 2. Personalization

6.3. The math curriculum should: engage students in problems that require extended effort, allow for collaboration and discussion, make connections with other subjects, support the use of technologies for solving problems and exploring relationships (NCTM, 2014)

6.3.1. SCANS report identified collaborative activity, problem solving, communication, self-assessment, and competence and confidence with technology as critical to success in the 21st century (US Dept. of Labor, 1992)

6.4. Constructivist Learning Environments on the web (Jonassen, 1999)

6.4.1. 1. Question/Case/Problem/Project - learners solve or resolve (this is the goal)

6.4.1.1. Problem is represented in an appealing way (video/audio clip, narrative - this link has a great example of a math problem represented in a visual video format - coool way to lead off a lesson and engage students in the problem

6.4.1.2. students should be able to manipulate the problem in some way in order to engage with it.

6.4.2. 2. Related Cases -

6.4.2.1. similar problems and their solutions or non-solutions help scaffold memory

6.4.3. 3. information Resources

6.4.3.1. Information learners may need to solve the problem

6.4.4. 4. Cognitive (Knowledge Construction) Tools

6.4.4.1. eg. visualization tools

6.4.5. 5. conversation and collaboration tools

6.4.6. 6. social/Contextual Supports

6.4.6.1. eg coaching, scaffolding

7. References Used

7.1. Herrington, J., & Standen, P. (2000). Moving from an instructivist to a constructivist multimedia learning environment. Journal of Educational Multimedia and Hypermedia, 9(3), 195-205.

7.2. Mayer, R. E. (2008). Applying the science of learning: evidence-based principles for the design of multimedia instruction. American Psychologist, 63(8), 760.

7.3. National Council of Teachers of Mathematics (2014). Principles to actions: Executive summary. Retrieved May 27, 2014 from http://www.nctm.org/uploadedFiles/Standards_and_Focal_Points/Principles_to_Action/PtAExecutiveSummary.pdf

7.4. Goldman, S.R., Hasselbring, T.S., (1997). Achieving meaningful mathematics literacy for students with learning disabilities. Journal of Learning Disabilities, 30 (2), 198-208.

7.5. U.S. Department of Labor (1992). Secretary's commission of achieving necessary skills report for America 2000. Washington, DC.

7.6. Jonassen, D. H. (1999). Constructivist learning environments on the web: Engaging students in meaningful learning. In The Educational Technology Conference and Exhibition, Singapore.. Retrieved May 29 from http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A7008CD7F83B63719C7087DCD2B4E7A1?doi=10.1.1.137.618&rep=rep1&type=pdf

7.7. Bruce, Chang, Flynn & Yearly, 2013. Foundations to learning and teaching fractions: Addition and subtraction. Retrieved May 29, 2014 from http://www.edugains.ca/resources/ProfessionalLearning/FoundationstoLearningandTeachingFractions.pdf

7.8. Groff, P. (1996). Is teaching fractions a waste of time? Clearing House, 69(3), 177- 179.

8. Student Challenges

8.1. Students do well with number computations, but have difficulty with fractions, decimals, percentages, and multi-step word problems (Goldman & Hasselbring, 1997)

8.2. Harel, Post & Lesh (1993), insisted that “learning fractions is probably one of the most serious obstacles to the mathematical maturation of children” (in Charalambous & Pitta-Pantazi, 2007, p. 293).

8.3. Mathematics education literature suggests that understanding fractions is a challenging area of mathematics for North American students (National Assessment of Educational Progress, 2005).

8.4. Not only do students have trouble grasping concepts related to fractions, they have difficulty retaining fraction concepts (Groff, 1996).

9. Assessment and Evaluation

9.1. How are students assessed? How will they demonstrate a mastery of the curriculum expectations?

9.1.1. Assessment For Learning

9.1.1.1. frequent self-assessment opportunities

9.1.1.1.1. how will students be able to use this to improve?

9.1.2. Assessment As Learning

9.1.2.1. scaffolding opportunities built in to mm - preferably linked to the formative assessment results

9.1.3. Assessment of Learning

9.1.3.1. summative assessment - will this be a project, test or other?

9.2. How will students be evaluated? How will their work be judged?

9.2.1. Grading

10. Learners

10.1. Who are they? Grade level, age, etc.

10.1.1. Cultural background

10.2. What is the learning environment? Online? Bricks and Mortar? Blended environment?

10.2.1. I always like to consider students are in the online environment then we can be sure to include the instructional elements or "teacher voice" into the mm

10.2.2. or does the environment matter?

10.3. Previous math experience?

10.4. Previous experience with fractions?

10.4.1. Are we using this as a remedial piece - send a student to use this multimedia piece if they are having issues with this topic....or is this something where we introduce the topic for the first time. I think the later is easier to develop for plus can be multipurpose

10.5. Learning accommodations or special needs?

10.5.1. ensure audio component on each page of mm

10.5.2. videos contain captions and controls to stop/pause ect.

10.5.3. avoid flash if possible to increase accessiblility

11. The Lesson Plan

11.1. Three Part lesson

11.1.1. Minds-On

11.1.1.1. How will we activate students' prior knowledge?

11.1.2. Action

11.1.2.1. Engage students in active and authentic learning tasks

11.1.3. Consolidation

11.1.3.1. Student reflection on their learning

11.2. Overall and Specific Expectations

12. Multimedia Tools

12.1. How will we build and deliver this content?

12.1.1. Website?

12.1.1.1. Weebly, Google Sites?

12.1.2. Videos?

12.1.2.1. Youtube, other?

12.1.3. Learning Objects?

12.1.3.1. Adobe Captivate

12.2. Assessment Tools

12.2.1. Google Forms

12.2.2. Moodle Quiz

12.2.3. Existing mm

12.2.4. Discussion Forums

12.2.4.1. Google+

12.2.4.2. Moodle

12.3. Collaboration Tools?

12.3.1. Google docs

12.3.2. Wikis

12.3.3. MindMeister

13. General points to consider when developing mm

13.1. simple conversational language

13.2. consistant naming structure

13.3. clear procedures

13.4. reference external sources

13.5. consistant font

13.6. minimalist ideas around text

13.7. short pages - little scrolling