EDMA 262 - Task 1 Part 2 Week 8
- 2. WEEKLY REFLECTION Throughout this week’s content I had grasped an increased and enhanced formal perspective upon the concept, skills and strategies of measurement. Prior to this experience, I had obtained a very vague concept upon measurement in contrast to the detailed perspective represented within the study of concepts within this unit. However, alike other concepts, I had vaguely learnt about the concept of measurement and it’s skills and various thinking strategies. Within the future I aim to educate my students in as much detail as possible upon the generalized concept of measurement, what can be measured, the different units of measurement that exist, different tools that can be used for the conduction of measurement as well as educating my students upon diverse thinking strategies and perspectives of conducting the measurement of the object and diverse ways to do so. In addition, I would continuously propose open ended questions, such as, ‘Do you think any object can be measured?’ continued with ‘how do you think you would measure that object?, what tool would you use?’, ‘Why do you think that is the correct answer?’ and “Can you please explain to me how you go your answer?’.
- 3. CONCEPTS, SKILLS AND STRATEGIES Concepts: Measurement - to measure anything we need to count units. This aspect can change depending on what it is that is being measured. (Understandings of this concept are gained through real life experiences) Skill: To identify that we need to measure and gain an understanding upon the concept of area as opposed to length or volume as difference from capacity is also a concept. Once an understanding of the concept is obtained, attributes can then be determined upon what units are to be used to measure the object. Furthermore, the units determined will be used to measure the object, from this, the actual counting of the units or using a mathematical formula/equation to determine the answer. Children should have a clear understanding of the attribute they are measuring Concept are to be established before the students learn about formulae for measurement. An image must be built within the child’s head of the concept and question proposed. Thinking Strategies: - There are two different types of units that are used to measure objects; Arbitrary; non-standard units of measurement such as the use of paddle pop sticks, body parts, pencils and straws. Standardised: Standard units of measurement that involve technology such as rulers, clocks and measuring tapes. As mentioned within the lecture and tutorial, children gain an understanding upon the difference between the two by making comparisons and having discussions to support them in gaining an understanding of the difference between them both. This video depicts a detailed description upon the concept of measurement and units, which may become useful for students when the topic is being formally introduced (convert to Australian metric system/explain, demonstrate or ask children what units of measurement we use) - https://www.youtube.com/watch?v=zsv7bYSrzMU
- 4. MEASUREMENT IN APPLICATION TO THE LANGUAGE MODEL VerbalConcrete Materials Symbolic Children’s Language Materials Language Mathematics Language Symbolic Language Longer, shorter, thicker, wider Hands, fingers, Lego, claps, stomps, jumps, feet, hand spands blocks, measure, estimate Length, width, area, volume, circumference, diameter, calculate, perimeter, volume, radius, capacity Mm, cm, m, km, seconds, minutes, hours Fingers, Hands, toys of the same length, leaves (natural materials of the same length), Lego blocks Ruler, pencil, rubber, books, blocks, containers, measuring cup, shoes, rhythms (clapping, stomping, jumping), matchsticks, paddle pop sticks, Ruler may be needed for measuring the object to obtain units which may be proceeded to be used for counting or calculating the result with the formulae This resource would be useful for students that are beginning to learn about the different units used for measurement. This resource enables students to practice select the appropriate units for measurement for mass, length and capacity for diverse objects and projects of the resource. - http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths /measures/index.htm This resource is designed and constructed for teachers. This resources is a digital resource book designed to help teachers plan and implement assessment of the teaching and learning of assessment strategies, specifically understanding units and making direct measurements. Furthermore, it also includes a diagnostic map with mathematical outcomes and achievement levels. - http://det.wa.edu.au/stepsresources/detcms/navigation/first-steps-mathematics/ Concept: Counting units to describe an attribute. Skill: To identify what needs to be measured. Thinking Strategy: Using prior knowledge of shapes (e.g. hand claps) to informally measure the length of an object. (as students are advancing, they progress to using rulers, then using formula to calculate the perimeter etc – not learnt by rote)
- 5. TEACHING STRATEGIES When introducing the topic to students it may be useful to have an additional visual/IT integrated resource implemented within the discussion. This resource contains an animation with audio commentary that defines the concept of measurement as well as introducing seven different types of units of measurement. (length, area, height, time, temperature, mass and volume) - http://skwirk.com.au/esa/WhatCanBe_Measured.html An additional teaching resource that may be of great use is a book called ‘Teaching Measurement’ compiled by the New South Wales Government with contributions from Dr Lynne Outhred from Maquarie University. This source contains useful resources for teachers to use in planning practical, meaningful and enriching learning experiences for students in relation to measurement. Furthermore, it contains, lesson ideas, lesson plans, advice about teaching the subject and various strategies that can be utilized for effective understanding. - http://www.schools.nsw.edu.au/learning/7- 12assessments/naplan/teachstrategies/yr2014/img/teaching_measurement_es1_s1.pdf An additional useful resource, is the general integration of ICT within the classroom. Programs such as excel, Geogebra and general graphing and constructing tables upon word. If teachers have difficulty in using various programs, utilizing the internet for demonstration videos may become useful as they would depict detailed steps in creating the graph, image etc (Teachers may also learn from this)
- 6. MISCONCEPTIONS Alike with every mathematical concept, there are common misconceptions. Within this article by the Queensland Studies Authority (2005) common misconceptions within the mathematical concept of measurement are addressed. Some of these misconceptions include - https://www.qcaa.qld.edu.au/downloads/p_10/kla_maths_info_measurement.pdf - Confusion with rules, units and conversions. - Students perceive volume as a solid measurement and capacity as a liquid measurement. - Believe that rulers can be a tool used to measure area. - Volume and Capacity are often conceived as to be the same. To resolve these misconceptions it is important to to initially ensure that children understand the mathematical concept of volume and capacity before continuing upon the problems for those concepts. Some methods to resolve these misconceptions may be to have, Class Discussions/Demonstrations – proposing open-ended questions upon student’s current knowledge and thoughts upon the concept and having a class discussion to correct those misconceptions with visual material and examples. (conducted as a class) Pairing students for activities (Students with higher levels with ones of lower levels) – This is a useful activity so that students are able to collaborate and contribute their thoughts and ideas with each other and clarify any sections of certain misconceptions they currently have.
- 7. ACARA LINKS Earliest mention of Measurement – Foundation year (ACMMG006) Year 1 – ACMMG019
- 8. ACARA LINKS Year 2 – ACMMG037 Year 2 – ACMMG038
- 9. ACARA LINKS Year 2 – ACMMG039 Year 2 – ACMMG040
- 10. ACARA LINKS Year 3 – ACMMG061 Year 3 – ACMMG062
- 11. ACARA LINKS Year 4 – ACMMG290 Year 4 – ACMMG085
- 12. ACARA LINKS Year 4- ACMMG086 Year 5 – ACMMG106
- 13. ACARA LINKS Year 5 – ACMMG109 Year 5 – ACMMG110
- 14. ADDITIONAL TEACHING STRATEGIES This video clip depicts some strategies and techniques for teaching students the concept of measurement - https://www.youtube.com/watch?v=YQj3h7isWcc Within this resource, students are enabled to extend and revise their knowledge as well as make conversions between units, have access to text- based material and are enabled to practice the questions repeatedly. - http://www.bbc.co.uk/bitesize/ks3/maths/measures/use_of_measure/activity/ This resource may be useful as an additional demonstration for students to view as it depicts a circumstance in which an object is being informally measured - http://splash.abc.net.au/home#!/media/29655/ Getting students physically involved within mathematical tasks can also encourage participation as they must partake in the activity to obtain the results (Can be done in groups, individually or as a class, this video depicts an example) - https://www.youtube.com/watch?v=qK2zP-L_3S8
- 15. CHAPTER SUMMARY What students learn within each year level in relation to measurement.
- 16. CHAPTER SUMMARY CH: 17 Process of measuring, 1. Identify the attribute being measured (using a third object to compare) compare objects and events - perceptually - directly - Indirectly 2. Measure with informal units 3. Measure with standard units and include the concept of repeated units 4. Apply measurement to real-life contexts (length – ‘ belt is the same length even when it is curled up’/length of a pool etc) Children will learn these concepts as they progress throughout their mathematical education, 1. A unit must remain constant 2. A measurement must include both a number and the unit 3. Estimation is an important process to encourage children to use whenever they are measuring. 4. Two measurement may be easily compared if the same unit is being used. 5. One unit may be more appropriate than another to measure an object. 6. There is an inverse relationship between a certain number of units and the size of the particular unit. 7. Standard units are needed to communicate effectively for calculations. 8. A smaller unit gives a more exact measurement 9. Units may be combined or subdivided to make other units. 10. Units must match the attribute that is being measured. Measuring with informal units – compare two objects, specifying with an attribute instead of comparing two objects you compare an object with a unit and investigate how many units would be equal to that object.
- 17. CHAPTER SUMMARY CH: 17 E.g. in measuring a region of a square you can investigate how many square units can cover the region specified. Additional Informal units, - Capacity: Spoonfuls, cups, scoops, jugs, jars, bottles, jelly, mould, buckets and bags - Volume: Cubes, matchboxes, wooden blocks, lunch boxes and cereal boxes - Mass: Rocks, shells, buttons, fruit, metal washers, coins, play dough, marbles, golf balls. - Time: Years, days, months, minutes - Length: Digits, inches, hands, hand spans and cubits - Area: Handprints, Stamps, envelopes, tiles, bread tags, playing cards - From measuring with informal units, children will then progress to standards units of measurement, - Various types of concepts of measurement used (with descriptions) Units for the concepts used within measurement.
- 18. REFERENCES Australian Curriculum Assessment and Reporting Authority. (2016). Curriculum. Retrieved from,http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1 ABC. (2012). BBC Bitesize: Measure. Retrieved from, http://splash.abc.net.au/home#!/media/29655/ Best Practices Weekly. (2011). Teaching Measurement Concepts. Retrieved from, https://www.youtube.com/watch?v=YQj3h7isWcc Birmingham. (2012). Measures. Retrieved from, http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/measures/index.htm Department of Education. (2003). First – Step Mathematics. Retrieved from, http://det.wa.edu.au/stepsresources/detcms/navigation/first-steps-mathematics/ Kids – Euc – kids Educational Games. (2015). Math for kids: Measurement “how you Measure up” Fun learning games for children. Retrieved from, https://www.youtube.com/watch?v=zsv7bYSrzMU MotherTeresaPrimary. (2011). Investigating Length. Retrieved from, https://www.youtube.com/watch?v=qK2zP-L_3S8 New South Wales Department of Education and Training. (2002). Teaching measurement: Early Stage 1 and Stage 1. Retrieved from, http://www.schools.nsw.edu.au/learning/7-12assessments/naplan/teachstrategies/yr2014/img/ teaching_measurement_es1_s1.pdf Queensland Studies Authority. (2005). About Measurement. Retrieved from, https://www.qcaa.qld.edu.au/downloads/p_10/ kla_maths_info_measurement.pdf