Sequence: Introduction to Vectors

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Sequence: Introduction to Vectors
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Description:

Keywords:vectors, scalars, physics, introduction, senior physics, high school, educ261

Subject: Introduction to Vectors

Audience: Senior high school

Run time: 40-45 minutes

Delivery Mode: Online

Resources: Access to YouTube required

Outline of Activities: A recap quiz on assumed knowledge followed by 3 short video tutorials interspersed with quick quizzes.

This learning sequence is based on the NSW Board of Studies Stage 6 Physics syllabus section 8; “Moving About” (NSW Board of Studies [NSWBoS], 2002/9, p. 30) which introduces a fundamental concept; vectors.

The focus of "Moving About" is to engage students using familiar concepts in transportation (distance, speed, acceleration, road design, car safety features) and then introduce more complex ideas such as displacement, velocity, momentum, summation-of-forces and the difference between instantaneous and average values for these quantities.

The primary tool used to examine these ideas is the vector so it is important for students to obtain a good grasp of this concept.

On completing this sequence students should be able to:

•    distinguish between scalar and vector quantities with a good conceptual grasp of the properties of vectors,
•    add vectors to find a Resultant,
•    use vector diagrams to solve simple problems.

These goals include conceptual (distinguishing between vector and scalar quantities) and procedural (addition of vectors) knowledge (Anderson, Krathwohl et al. 2001, p. 27).

Content:

The introduction and development of key concepts throughout the sequence closely follows the suggested learning model detailed in the syllabus (NSWBoS, p. 30).

It may have been many months since students dealt with Newton’s Laws so a quick recap of assumed knowledge is presented as a multiple-choice quiz with feedback.

Differences between scalars and 1-dimensional vectors are discussed in the first video from the Khan Academy, (khanacademy, 2011, “Introduction to Vectors and Scalars”) chosen to reflect core requirements of the syllabus (NSWBoS, p. 30) by comparing concepts such as distance/displacement and speed/velocity. A quick quiz follows to reinforce these concepts.

A second video (Naray, 2013, "Introduction to vectors part 1") expands on these basics, introducing 2-dimensional vectors, again focussing on transportation. The author produced this video as the follow-up Khan Academy video (khanacademy, 2011, “Visualising Vectors in 2 Dimensions.”) did not satisfy the syllabus’ criteria: It leapt into a more mathematical treatment of 2D vectors rather than conceptually linking them to the established framework of transportation.

Following this video is a group activity where students use active/collaborative learning (Jonassen, Howland, Marra, Crismond, 2007, pp. 2-5) to discover the concept of commutative addition of vectors.

The third video, also self-produced, (Naray, 2013, "Introduction to vectors part 2") continues to build on previous concepts by introducing vectors at any angle in 2D space, and the trigonometric technique of adding vectors. This is meant to be a 40min lesson plan, so due to the complexity of the material, the following assessment has only one question. Further practice problem solving should be done by assignment or in class with educator guidance where needed.

Links to further material are provided at the conclusion to spur the interest of learners and provide bridging to subsequent lessons. One link is to another self-produced video (Naray, 2013, "Introduction to vectors part 3") introducing vector subtraction and vectors as forces. Originally intended to be part of this sequence it was relegated to “further reading” due to time constraints of the 40min lesson plan.

Pedagogy:

Elements were chosen specifically to provide a good understanding of the concept of vectors and the procedures used in their manipulation. Additionally, it was important that the sequence follow the guidelines set out in the syllabus (NSWBoS, p. 30) requiring that vectors be introduced as a tool to facilitate visualising and solving problems about motion, based on intentional/authentic learning models (Jonassen, et al., 2007, pp. 2-5).

The videos were carefully chosen/produced to fulfil the criteria espoused by Mayer for effective multimedia learning (Mayer, 2005, p. 6) guided by the principles of split-attention, modality, redundancy, coherence, and personalisation. The principle of segmentation (Mayer, 2005, p. 6) is also emphasised in the shortness of the videos and adherence to a well defined goal, introducing basic concepts within a consistent framework. Principle affordances (Bower, 2008, p. 6) of video media (rewind-ability, pause-ability, view-/listen-ability) make this method of presentation of material ideal for such a self-paced learning exercise. Note that rather than simple linking, a Google-Gadget gives access to the first video to encourage students to explore further material.

Reinforcement is provided by brief quizzes. Students are encouraged to discuss the questions and answers with their neighbours and collaborative/discovery based learning (Jonassen, et al., 2007, pp. 2-5) is emphasised in the “Treasure Map” activity for commutative addition. Scaffolding – through feedback, direct instruction and collaborative exercises – is provided throughout from the recap of assumed knowledge, within the video tutorials and in all assessment tasks.

Michael Naray 2013-04-09
43183395

References

Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., Raths, J., Wittrock, M. C. (2001). A Taxonomy for Teaching, Learning and Assessing. New York: Longman.

Bower, M. (2008). Affordance analysis – matching learning tasks with learning technologies. Educational Media International, 45(1), 3-15.

Jonassen, D., Howland, J., Marra, R., Crismond, D. (2007). Meaningful Learning With Technology. Upper Saddle River, New Jersey: Prentice Hall.

khanacademy. (2011, June 11). Introduction to Vectors and Scalars. Retrieved from http://www.youtube.com/watch?v=ihNZlp7iUHE

khanacademy. (2011, June 16). Visualising Vectors in 2 Dimensions. Retrieved from http://www.youtube.com/watch?v=xp6ibuI8UuQ

Mayer, R. E. (Ed.) (2005). The Cambridge Handbook of Multimedia Learning. Cambridge: Cambridge University Press.

Naray, Michael. (2013). Introduction to vectors part 1; 2D vectors. Retrieved from http://youtu.be/ZTfFGHSuUaA

Naray, Michael. (2013). Introduction to vectors part 2; geometric addition. Retrieved from http://youtu.be/o6AhoysBMaY

Naray, Michael. (2013). Introduction to vectors part 3; subtraction and forces. Retrieved from http://youtu.be/IceUOR6dAYQ

NSW Board of Studies. (2002 – revised 2009). Physics Stage 6 Syllabus. Sydney, NSW: Author.

NB: Quiz questions were written by the author and are CC: Free to Use.
Author view:

Audience:

Subjects:

Language: English

LAMS Version: 2.4.1.

License: Attribution-Noncommercial-ShareAlike

Support Files: No files

Sharing with: Everyone in Public

Status: Active

Average Rating: Not rated yet!

Number of downloads: 3 times

Number of previews: 37 times

Authored By: mike naray

Date: 08 April 2013 07:32 PM

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Add comments to Introduction to Vectors sequence

Sequence Information
Sequence:	Introduction to Vectors Preview \| Open LessonLAMS \| Download
Description:	Keywords:vectors, scalars, physics, introduction, senior physics, high school, educ261 Subject: Introduction to Vectors Audience: Senior high school Run time: 40-45 minutes Delivery Mode: Online Resources: Access to YouTube required Outline of Activities: A recap quiz on assumed knowledge followed by 3 short video tutorials interspersed with quick quizzes. This learning sequence is based on the NSW Board of Studies Stage 6 Physics syllabus section 8; “Moving About” (NSW Board of Studies [NSWBoS], 2002/9, p. 30) which introduces a fundamental concept; vectors. The focus of "Moving About" is to engage students using familiar concepts in transportation (distance, speed, acceleration, road design, car safety features) and then introduce more complex ideas such as displacement, velocity, momentum, summation-of-forces and the difference between instantaneous and average values for these quantities. The primary tool used to examine these ideas is the vector so it is important for students to obtain a good grasp of this concept. On completing this sequence students should be able to: • distinguish between scalar and vector quantities with a good conceptual grasp of the properties of vectors, • add vectors to find a Resultant, • use vector diagrams to solve simple problems. These goals include conceptual (distinguishing between vector and scalar quantities) and procedural (addition of vectors) knowledge (Anderson, Krathwohl et al. 2001, p. 27). Content: The introduction and development of key concepts throughout the sequence closely follows the suggested learning model detailed in the syllabus (NSWBoS, p. 30). It may have been many months since students dealt with Newton’s Laws so a quick recap of assumed knowledge is presented as a multiple-choice quiz with feedback. Differences between scalars and 1-dimensional vectors are discussed in the first video from the Khan Academy, (khanacademy, 2011, “Introduction to Vectors and Scalars”) chosen to reflect core requirements of the syllabus (NSWBoS, p. 30) by comparing concepts such as distance/displacement and speed/velocity. A quick quiz follows to reinforce these concepts. A second video (Naray, 2013, "Introduction to vectors part 1") expands on these basics, introducing 2-dimensional vectors, again focussing on transportation. The author produced this video as the follow-up Khan Academy video (khanacademy, 2011, “Visualising Vectors in 2 Dimensions.”) did not satisfy the syllabus’ criteria: It leapt into a more mathematical treatment of 2D vectors rather than conceptually linking them to the established framework of transportation. Following this video is a group activity where students use active/collaborative learning (Jonassen, Howland, Marra, Crismond, 2007, pp. 2-5) to discover the concept of commutative addition of vectors. The third video, also self-produced, (Naray, 2013, "Introduction to vectors part 2") continues to build on previous concepts by introducing vectors at any angle in 2D space, and the trigonometric technique of adding vectors. This is meant to be a 40min lesson plan, so due to the complexity of the material, the following assessment has only one question. Further practice problem solving should be done by assignment or in class with educator guidance where needed. Links to further material are provided at the conclusion to spur the interest of learners and provide bridging to subsequent lessons. One link is to another self-produced video (Naray, 2013, "Introduction to vectors part 3") introducing vector subtraction and vectors as forces. Originally intended to be part of this sequence it was relegated to “further reading” due to time constraints of the 40min lesson plan. Pedagogy: Elements were chosen specifically to provide a good understanding of the concept of vectors and the procedures used in their manipulation. Additionally, it was important that the sequence follow the guidelines set out in the syllabus (NSWBoS, p. 30) requiring that vectors be introduced as a tool to facilitate visualising and solving problems about motion, based on intentional/authentic learning models (Jonassen, et al., 2007, pp. 2-5). The videos were carefully chosen/produced to fulfil the criteria espoused by Mayer for effective multimedia learning (Mayer, 2005, p. 6) guided by the principles of split-attention, modality, redundancy, coherence, and personalisation. The principle of segmentation (Mayer, 2005, p. 6) is also emphasised in the shortness of the videos and adherence to a well defined goal, introducing basic concepts within a consistent framework. Principle affordances (Bower, 2008, p. 6) of video media (rewind-ability, pause-ability, view-/listen-ability) make this method of presentation of material ideal for such a self-paced learning exercise. Note that rather than simple linking, a Google-Gadget gives access to the first video to encourage students to explore further material. Reinforcement is provided by brief quizzes. Students are encouraged to discuss the questions and answers with their neighbours and collaborative/discovery based learning (Jonassen, et al., 2007, pp. 2-5) is emphasised in the “Treasure Map” activity for commutative addition. Scaffolding – through feedback, direct instruction and collaborative exercises – is provided throughout from the recap of assumed knowledge, within the video tutorials and in all assessment tasks. Michael Naray 2013-04-09 43183395 References Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., Raths, J., Wittrock, M. C. (2001). A Taxonomy for Teaching, Learning and Assessing. New York: Longman. Bower, M. (2008). Affordance analysis – matching learning tasks with learning technologies. Educational Media International, 45(1), 3-15. Jonassen, D., Howland, J., Marra, R., Crismond, D. (2007). Meaningful Learning With Technology. Upper Saddle River, New Jersey: Prentice Hall. khanacademy. (2011, June 11). Introduction to Vectors and Scalars. Retrieved from http://www.youtube.com/watch?v=ihNZlp7iUHE khanacademy. (2011, June 16). Visualising Vectors in 2 Dimensions. Retrieved from http://www.youtube.com/watch?v=xp6ibuI8UuQ Mayer, R. E. (Ed.) (2005). The Cambridge Handbook of Multimedia Learning. Cambridge: Cambridge University Press. Naray, Michael. (2013). Introduction to vectors part 1; 2D vectors. Retrieved from http://youtu.be/ZTfFGHSuUaA Naray, Michael. (2013). Introduction to vectors part 2; geometric addition. Retrieved from http://youtu.be/o6AhoysBMaY Naray, Michael. (2013). Introduction to vectors part 3; subtraction and forces. Retrieved from http://youtu.be/IceUOR6dAYQ NSW Board of Studies. (2002 – revised 2009). Physics Stage 6 Syllabus. Sydney, NSW: Author. NB: Quiz questions were written by the author and are CC: Free to Use.
Author view:
Audience:
Subjects:
Language:	English
LAMS Version:	2.4.1.
License:	Attribution-Noncommercial-ShareAlike
Support Files:	No files
Sharing with:	Everyone in Public
Status:	Active
Average Rating:	Not rated yet!
Number of downloads:	3 times
Number of previews:	37 times
Authored By:	mike naray
Date:	08 April 2013 07:32 PM
User Comments on Introduction to Vectors sequence Add comments to Introduction to Vectors sequence