Week+11+-+Mastering+measurement

__**Learning Activity 11.1:** //**Circumference/Diameter**//__

//Utilised group work. Had students explain what they worked on and justify their answer to rest of class.// //Allowed students to make physical movements to represent circumference and diameter. Engaged prior knowledge of circumference of pumpkin.//
 * 1) How did Ms. Scrivner have students develop ownership in mathematical tasks?
 * 1) What were the effective techniques used for teaching the relationship between circumference and diameter?

//Reinforce learnings, highlight mistakes made i.e inches Vs cm.// //Vicki 25/7/11//
 * 1) Why would it have been valuable to have students do a second measurement?

Achor 09/08/2011 As you watch the video, consider how you will answer these three questions that are raised in the Analysis component at the end of the video: The teacher asked the students to do demonstrations for the classroom on what they have learnt. The teacher also asked engaging questions as well as asking for their opinion and thoughts. The teacher utilized group work by dividing the students into teams. The teacher got the students to use kinaesthetic techniques to measure the circumference or diameter; this allowed the students to be physically and verbally productive. It is revision for the students making their newly learnt knowledge more concrete and it can the perfect time for teacher to assess their progress **Sarah Wright**
 * 1) How did Ms. Scrivener have students develop ownership in mathematical tasks?
 * 1) What were the effective techniques used for teaching the relationship between circumference and diameter?
 * 1) Why would it have been valuable to have students do a second measurement?
 * Learning Activity 11.1 **
 * 1) ** 1. **** Miss Scrivenor had students develop mathematical ownership in class by allowing them to ‘hunt’ for their own data. They then used this data which they had worked to find and record for the purpose of finding a relationship between circumference and diameter. Miss. Scrivenor then had the groups present their data to the rest of the class. **
 * 2) ** 2. **** Miss. Scrivenor used a variety of techniques to teach her students about the relationship between circumference and diameter. She had them use their bodies to explore the relationship by asking them to pretend they were hugging a pumpkin (circumference was there arms and body) then they used their arms to demonstrate the diameter. Students also practiced finding the circumference and diameter of different circle objects in the classroom and recording their data. They then analysed data as a group to see if they could notice the relationship between the numbers (this was hard as most of the data collected was not correct and there for the relationship was harder to recognise). **
 * 3) ** 3. **** I think for the purpose of this lesson (identifying the relationship between circumference and diameter) it would have been beneficial to practice their measurement skills first so they were able to get more correct measurements so there would have been more reliable data to work with. **

__**Learning Activity 11.2: Further examination of the process of measurement**__

Vicki 25/7/11
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * Every triangle is half a parallelogram.Two congruent trapezoids can be put together to make a parallelogram. || Decimetre = 10cm stripImportant to have children measure real objects.Children begin counting ta one, and often begin to measure at 1 instead of 0.Measurement should also include exposure to line segments.Making own instruments can help children understand how to read them better i.e thermometerBegin estimating area by measuring in squares.Last step in measurement requires students to tell both the number and the unit.Children have difficulty reversing – children who can measure cannot always create something using measurements.New units should be related to others.Children often confused by area and perimeter.Important to relate teaching to measurements from different cultures.Allow children to think and estimate before measure. ||
 * **Questions I have and related things I do not understand from my reading**(See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||

Achor 09/08/2011
 * ** Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching ** || ** Ideas and examples related to mathematics learning and teaching that are //new// to me ** ||
 * * Formulas for areas are usually introduced to the more cognitively developed students later in school
 * Estimation is ability to guess the approximate measurement without physically measuring it
 * Students should be encouraged to estimate first. || * The concept of tolerance of error is very new to me.
 * Students learn measurements by first perceiving the attribute. ||
 * ** Questions I have and related things I do not understand from my reading ** (See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||
 * Learning Activity 11.2 **
 * Ideas that are familiar to me: **
 * ** Apartuses need to be used in measurement studies e.g – ruler, compass **
 * ** Students need hands on experiences when learning about volume **
 * Ideas that are new to me: **
 * ** Estimation reinforces the size of units and the relationship among units **
 * ** There are 2 types of estimation **
 * ** Important to teach students about other forms of currency **
 * Questions: **
 * Do American students have to learn the metric system? Sarah Wright 11.8.11 **

__**Learning Activity 11.3:** //**How long is a minute?**//__

Allows them to choose tasks they enjoy and can do best. Ultimately it allows students to take ownership of their work., which helps them to take in information and apply it. Relating it to the student’s perspective – things that could be done in one minute. Modelling & role play what can be done, watching the clock tick over. //Children may understand time concepts but be confused by the circular dial on a clock. By using analog and digital clocks helps students to relate the time concept to the clock face.//
 * 1) **//What is the importance of having students generate and choose specific tasks?//**
 * 1) **//What teaching strategies help develop students’ concepts of a minute?//**
 * 1) **//What is the value of the use of both analog and digital time pieces in this lesson?//**

//Vicki 25/7/11//

As you watch the video, consider how you will answer these three questions that are raised in the Analysis component at the end of the video: Students are able to take ownership in their learning by making decisions. The teacher incorporated teamwork where students were to take turn writing down data. Their abilities to do certain things have allowed them start discussions amongst themselves on times. Their social interactions and physical interactions with the stop watch allowed for them to generate their own learning experience in the classroom. They act as a prop in their learning, it allows for them to measure time for themselves. Achor 09/08/2011
 * 1) What is the importance of having students generate and choose specific tasks?
 * 1) What teaching strategies help develop students’ concepts of a minute?
 * 1) What is the value of the use of both analog and digital time pieces in this lesson?


 * Learning Activity 11.3 **
 * 1. **** Allowing students to choose and generate specific tasks allows them to develop ownership for the task, this increases motivation. **
 * 2. **
 * Students had practiced using a clock timer **
 * Students discussed things they could do in a minute **
 * Students practiced timing things they could do in 15 seconds **
 * Students talked about there is 60 seconds in a minute **
 * Students then timed specific tasks and observed how the timers ticked over from seconds to minutes at the minute point **
 * 3. **** Being able to understand that though they look different (digital & analog) they are the same units of measurement. **
 * Sarah Wright **

__**Learning Activity 11.4:** //**Maths Munchies**// **– Connecting/disconnecting attributes**__ Sarah Wright 11.8.11
 * 11.4 **
 * Length= 72 **
 * Width= 2 **
 * Height= 2 **
 * The lollies would be in a rectangular shape (like starburst or zappo’s), they would be wrapped in a paper material that could be recycled. **

Using your group discussion from activity 11.4. Write what your group see the value of open ended investigations in supporting children’s mathematic learning.

Hey this is all I have had a chance to do so far, so much reading and final assignments! But will try help look over final draft etc. Sarah Wright
 * Open ended investigations are essential for students to develop their own sense of ownership of learning’s and to make discoveries of new concepts for themselves. They do this by comparing, constructing and estimating their answers, they are forced to think about the task and use their knowledge to find the solution. Open ended investigations present opportunity for practical experiences which provide rich opportunities for developing good attributes to mathematics (Booker, et al., 2010, p. 515). **


 * No right or wrong answers, allowing investigation leading to discoveries in other areas (Booker, Bond, Sparrow & Swan, 2010)
 * Multiple concepts attended to
 * Development of a positive attitude towards mathematics
 * Constructing of own knowledge, as per Piaget and Vygotsky's constructivist theories through the use of open ended questioning

Suzanne


 * Children are able to use their problem sovling skills to find solutions to the problem.
 * Children can brainstorm their ideas with other sudents knowing that there is no right or wrong answer.
 * Leads to greater understanding in mathematics when children develope the concepts themselves.
 * Children can develop relationships between mathematical concepts they already know to help them solve the problem.

Kerrie Wyer - 13/8/11.

Using open ended investigations in mathematics can offer great value to students’ learning. In the instance of activity 11.4 (Maths Muchies – Connecting/disconnecting attributes) there is no right or wrong answer as to how the product should be packaged. For a student then this allows investigation into ways that they might prepare something. This investigation can then lead to discoveries of other areas, perhaps such as a formula (Booker, Bond, Sparrow and Swan, 2010).

In presenting an activity like 11.4 to students, where there is no right or wrong answer, students are attending to various concepts of mathematics, whether knowingly or not. As a student thinks about how they would like to package sweets, they are estimating at first what they think might work. Similarly volume is considered, as a student thinks about how in the packaging sweets should sit, whether there should be space between them or one against the other. Measurement is considered also. Multiple concepts are being attended to.

With the use of ‘hands on’ activities, particularly those with no fixed answer, students can further a positive attitude towards mathematics. Using manipulatives in a practical way can help students develop an appreciation towards mathematical concepts and mathematics in general (Booker et al, 2010).

Furthermore, in presenting this sort of activity to students, it sets a challenge. Students will discover ways to present the sweets – that is, they are constructing their own knowledge in this area. This follows with Piaget’s and Vygotsky’s theories of constructivism. Open ended questions encourage discussion.

Open ended questions have great value in mathematical learning. Students can investigate without fear of being right or wrong. Open ended questions allow for the possibility of further mathematical discoveries, and the use of multiple mathematical concepts. Constructivism is naturally used through the investigating the possibilities of an open ended question. The use of appropriate manipulatives can also help foster a positive attitude towards mathematics.

Reference:

Booker, G., Bond, D., Sparrow, L. & Swan, P. (2010). //Teaching Primary Mathematics,// (4th Ed.). Frenchs Forest, New South Wales : Pearson Australia

It's 130pm, and no one had written anything, so I have thrown this together. I will leave it up until 5ish, if no one has made any comment, suggestions etc, I will then post to the mathsmates contributions on the DB. Cheers, Suzanne

Kristy - seems there was some confusion this week. I had put this up on the DB and then saw your contribution to the DB was added a few hours later. I took the above down from the DB, leaving yours as you were the assigned person this week. Good to see the contribution, it was well written. :)