Posted: June 2nd, 2015

Topic: Learning log2-3 and professional plan

 

The first part of my assessment is shown as follow.

The following information is learning log question 6-10. Please answer these questions referring to week 6- week 10 power points lecture slides.

Please note, regarding to question 10, my second teaching area is Chinese.

In addition, I have done Week 6 question part A. You may rewrite it or change it if there is any mistake such as grammar mistakes.

• Week 6, Session 6A

In Week 5 and Week 6 we looked at the Australian Curriculum: Mathematics, in particular the content and proficiency strands. We also introduced the idea of needing to construct learning objectives to define the goals of our teaching (and we will spend more time over the coming weeks refining our ability to write learning objectives). The following questions require you to a) answer a mathematical question b) identify what content descriptors align to the question, c) consider what actions or thinking you undertook to answer the question (i.e., ways in which you demonstrated your proficiency) and d) write learning objectives that bring together the identified content and proficiency.

Q 6a) Consider the following text-book style question. Provide a fully worked solution, drawing upon your knowleege of not only formulating and rearranging equations but also the various proportional reasoning strategies and representations. Imagine that the worked solution is your ‘cheat sheet’ that you might prepare prior to giving the worked solution on the whiteboard – it should provide all of the information that you would want to write on the whiteboard so as to clearly explain (and model) your mathematical work.

A computer-internet connection has a download speed of 500 kilobytes per second. How long will it take to download a 24.6 megabyte file? (1Mb = 1024Kb)

NOTE: You may use the three-column ‘think-say-show’ format to present your solution if you wish, but it is not a requirement.

 

Q 6b) Compare your solution against the content descriptors of the Australian Curriculum:Mathematics and

1. i) Nominate which year level you think this internet question might be appropriate for.
2. ii) From your chosen year level, identify and briefly justify which of the content descriptors describe the knowledge needed to answer the internet question (quote the content descriptors in full). Annotate your sample solution to explicitly identify in which parts of the sample solution the identified knowledge is being used.

iii) Considering only the two proficiencies of Fluency and Reasoning, for each proficiency write one learning objective that could be demonstrated by a student when they successfully complete the internet question.
Relevant assessment criteria:

• Content – Mathematically accurate. Use of appropriate mathematical terminology.
• Pedagogy – Diagrams and other non-textual representations effectively used to explain the mathematical thinking applied to answer the question.
• Planning – The identified content descriptors are carefully aligned to the question and its solution and the justification provided is appropriate.
• Assessment – The Fluency and Reasoning learning objectives are constructed using the ‘qualifier+verb+content’ pattern, are clear and concise, and are aligned to the question and the sample solution provided.
• Professional communication – All diagrams are clear. Good choice of language to explain steps of solution and to justify the content descriptors.

Week 6, Session 6B

In this session we discussed several pedagogical frameworks. common to these was the idea of choosing suitable contexts in which to situate learning – these should be contexts of potential iinterest to students and of whcih they have some intutive, experience-based understanding. For your second assessment item, you need to think about some relevant context in which to develop your students’ understanding of your chosen content (from Year 7, Year 8 or Year 9).

 

Q 6c)

1. What is the topic that you plan to develop a unit of work for?
2. In one paragrpah, describe a context you think might be appropriate, and why.

NOTE: You may, if you choose, decide to change your choice of content at a later stage. This is just to get you thinking and for us to provide you with some feedback regarding your idea of a suitable context.

Relevant assessment criteria:

• Content – context is well aligned to the concept(s) of the chosen topic
• Numeracy – the context is likely to have life-related significance to the students
• Professional communication

Session 7A

In Sessions 6BA 76B and 7A you have spent time completing mathematical investigations and planning a lessons.In particular, you used the variation of the of 5E model presented in the Pearson series of textbooks, and based upon your experience of one of these investigations, attempted to create a lesson plan.

Across the semester, we have done several in-class activities, including:

1. The Bungie Barbie activity
2. The Swamp problem
3. The LEGO robotics activity

All three of these activities could be the basis for a 5E-style investigation.

Q7a) Choose one of the three above-mentioned activities and design a work sheet that students could complete, much the same as the worksheets that you yourself worked through in class in the last few sessions (i.e., the Pearson investigations). Your worksheet should include all phases of the 5E model (Engage, Explore, Explain, Elaborate, Evaluate) and may optionally include the ‘Big Question’ and ‘Extend’ phases as used by Pearson. Your work sheet should be no more than 2 pages long, preferably only 1.

Q7b) For your 5E-based investigation, identify the following:

1. i) Target Year level
2. ii) Assumed knowledge

iii) Focal content

1. iv) 2-3 learning objectives

This information should provide an overview of your investigation, and so provide guidance to a potential teacher if they were to be deciding whether this investgation is appropriate for their class of students.

Q7c) Write a brief discussion summarising how you believe your worksheet has acheived the intentions of each phase of the 5E model (no more than 1-2 sentence per phase).

Relevant assessment criteria:

• Content –   Focal content of the investigation is carefully and clearly defined. Worksheet content is mathematically accurate and is sequence in a way that would develop students connected schema (Bell’s principle 1) by providing intellectual challenge (Bell’s principle 5).
• Pedagogy – sequencing of activities in the investigation reflects the ideas of planning discussed in class, in particular the idea of building upon student prior knowledge in familiar contexts through to the scaffolded application of new ideas in unfamiliar contexts (Bell’s principle 2). Pedagogical principles and strategies that have been discussed during the semester (e.g., use of physical, iconic and symbolic representations; proportional reasoning strategies) are incorporated as appropriate.
• Planning – Aligned to learnign objetives. The worksheet is clearly organised with regards to the 5E’s model, and this organisation is reflected in the discussion (Q 7c)
• Resources and ICTs – the investigation makes meaningful use of resources, including ICTs as appropriate, to effectively scaffold students’ learning.
• Assessment –  Learning objectives are aligned to the identified focal content. Suitable formative assessment (i.e., in the form of carefully worded questions) is incorporated into the worksheet. Formative assessment is aligned to the learning objectives. Opportunities for students to receive feedback (Bell’s principle 3) and for them to reflect upon and review their learning (Bell’s principle 4) are explicitly incorporated into the investigation.
• Professional communication – the worksheet is error free and of a standard that would be appropriate for parents to receive.

Session 7B, 8A and 8B

There are no specific Learning Log questions related to the content of the Session 7B-8B, in particular questioning and the use of the RAMR cycle.

 

HOWEVER, I do expect that the ideas we discussed regarding the different types and purposes of questions (Session 7B) would be integrated into your 5Es-based investigation (the Session 7A questions) and of course within your Professional Plans (Assessment Item 2). Similarly, the RAMR cycle (Session 8A) is one way that you might consider organising the content of your unit and/or lessons, such that students were able to ground their learning in realistic contexts and be supported in their transfer of new knowledge to unfamiliar situations. Finally, the providing opportunities for students to develop their skills at transferring ideas from contexts that are simple familiar to those that are complex unfamiliar was discussed in Session 8B, and I hope that you include in your professional plans in-class opportunities to scaffold students’ abilities to do such transfer.

Q10c) ONLY TO BE ANSWERED BY STUDENTS WHO DID NOT TAKE FIELD EXPERENCE THIS SEMESTER

In Session 10B we discussed Numeracy. Based upon your knowledge of your other teaching area, answer the following questions.

1. i)Find a junior secondary (Years 7-10) learning activity or resource from your other teaching area, and include this in your submission.
2. ii)Compare the selected learning activity to the Numeracy Continua (https://www.qcaa.qld.edu.au/downloads/p_10/numeracy_indicators_yrs7-10.pdf), and identify which elements and at what levels the your chosen learning activity corresponds to.

iii) Choose one specific potential numeracy demand of the learning activity – summarise what you anticipate students may have difficulties with.

1. iv)For your selected numeracy demand, locate a suitable resource that could be used to overcome the demand. This could be a suitable video, worksheet etc., Include this resource in your submission, and provide a brief discussion on how you would plan to use the resource to help students overcome the numeracy demand.

 

 

 

 

 

2. Professional Plans
   To demonstrate your developing understanding of mathematics education, the second component of Maths CS1 assessment will require you to plan a sequence of lessons and develop a set of associated classroom materials.

   The due date for the Professional Plans is Monday the 1st of June (start of exam prep week).

   The Professional Plans will be submitted using the Blackboard Assignment Tool (with Safe Assign plagiarism checking).

   The Professional Plans assessment item is worth 40% of your Curriculum Studies 1 grade.

Both the Learning Log and the Professional Plans will be assessed against seven criteria: Content; Pedagogy; Planning; Resources and ICTs; Assessment; Literacy and Numeracy; and Professional Communication. These criteria are explained in greater detail in the section below titled ‘Assessment Criteria’.

 

Qustion 6

a)

Question:   A computer-internet connection has a download speed of 500 kilobytes per second. How long will it take to download a 24.6 megabyte file? (1Mb = 1024Kb)

What do we know:   Internet download speed: 500 kilobytes/second Size of the file: 24.6 megabytes The relation between megabyte and kilobytes: 1mb=1024kb

What do we want to know:   TIME it takes to download the file

Formula:   Time= distance/speed In this question, the size of the file (the amount of megabyte) represent the distance   Therefore, based on the original formula, we will now have a new formula   Time = amount of megabyte/ speed

Solution:   According to the new formula, time = amount of kilobytes/speed   Time= the total amount of kilobytes / speed (500kb/s)   How do we find the total amount of kilobytes?   We know: 1.       the size of the file is 24.6 megabytes 2.       1mb=1024kb   How do we find how many kilobytes is 24.6 megabytes equivalent to?   1mb①                x1024                1024kb②   X24.6                                                   x24.6   x1024 24.6mb③                                      25190.4kb④     Horizontal: 1mb is equivalent to 1024kb, from the left hand side① to the right hand side②, we need to multiply 1mb by 1024 to get 1mb in the unit of kilobyte which is 1024kb. And also, 24.6mb③ converts into the unit of kilobyte④, we need to use 24.6mb③ multiplied by 1024 as well.   Therefore, we can work out ④ by using 24.6mb x 1024 = 25190.4kb     Check answer by looking vertically: From 1mb① to 24.6mb③, we multiplied by 24.6. And also, from 1024kb② to ④, we need to multiply 24.6 too.   Therefore, we can work out ④ by using 1024kb x 24.6= 25190.4kb   These two answers of ④ are the same. Therefore, our solution of finding the total amount of kilobytes is correct.   NOW, we have all the information we need, and back to the formula   Time= the total amount of kilobytes / speed (500kb/s) Time= 25190.4kb/(500kb/s) =50.3808s ≈50s (we just around our answer to the nearest second)

Conclusion:   The time it takes to download a 24.6mb file is 50s.

 

 

Hi, again writer.

Here is the second part of my assessment. Information is very detailed.

Unit plan and lesson plan formats will be uploaded in a separated attachment.

In this second assessment item, you will plan a short four lesson unit for a junior secondary mathematics class (each lesson should be nominally 1 hour in duration). In planning this unit, you should assume that the class is composed of average and higher achieving students, that is, there are no particularly low-achieving students.

You will design your unit of work based upon one of the options provided below. You should consider both the content description and the corresponding elaboration(s) that have been taken from the Australian Curriculum:Mathematics. In an attempt to further assist you in narrowing your focus as you try to interpret the content descriptors and establish the scope of your unit, a short description of the what students might be able to typically do by the end of your unit is provided. Based upon the information provided for each option, you will be able to write specific learning objectives aligned to each of the proficiency strands of the Australian curriculum.

• Option 1: Year 7 Money and Financial mathematics

 

Focal content descriptor:	·         Investigate and calculate ‘best buys’, with and without digital technologies
Elaborations:	·         Applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g.
Student work:	·         By the end of this unit, students will be able to interpret the specification of prices when reading catalogs etc. They will be able to compare the value of goods (different brands or different suppliers) using the unitary method, when the prices is of goods is specified in a range of forms (e.g., price per piece vs. pieces per price). They will be able to justify purchase decisions and provide a reasoned explanation. They will be able to apply their knowledge and understanding of best buys to make life-related decisions regarding the purchase of goods and services.

• Option 2: Year 7 Real numbers

Focal content descriptor:	Express one quantity as a fraction of another, with and without the use of digital technologies
Elaborations:	Using authentic examples for the quantities to be expressed and understanding the reasons for the calculations
Student work:	By the end of this unit, students will be able to compare the relative sizes of measured quantities using multiplicative operations with decimals and common fractions. They will be able to describe verbally, graphically and with symbols these comparisons of size. They will be able to calculate the size of a quantity when given a known size and comparative fraction of another quantity. They will be able to apply their knowledge of multiplicative relationships between quantities to a range of real-life situations, such as cooking and distances between cities.

• Option 3: Year 8 linear and non-linear relationships

Focal content descriptor:	Plot linear relationships on the Cartesian plane with and without the use of digital technologies
Elaborations:	Completing a table of values, plotting the resulting points and determining whether the relationship is linear. Finding the rule for a linear relationship.
Student work:	By the end of this unit, students will be able to represent linearly related data in tables and straight lines on the Cartesian plane. They will be able to describe the relationship between the independent and dependent quantities in the relationship using informal sequential and positional rules. They will be able to use their mathematical models of life-related data to explain or justify interpolations or extrapolations. Students are able to recognise and apply their understanding of linear relationships in a range of life-related situations, including but not limited to situations in which time is the independent variable.

 

• Option 4: Year 8 Real Numbers

Focal content descriptor:	Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies
Elaborations:	Using percentages to solve problems, including those involving mark-ups, discounts, profit and loss and GST.
Student work:	By the end of this unit, students will be able to use percentage to describe the multiplicative relationship between two quantities. They will be able to calculate the size of one quantity given the size of another and a percentege-based relative comparison. They will be able to use percentage to describe the change amount, or difference in size, between two quantities. They will be able to describe a range of life-related situations, including those based on money, using perentages and make associated calculations.

 

• Option 5: Year 9 Geometric Reasoning

Focal content descriptor:	Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar.
Elaborations:	Establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence. Using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement (for example, scale diagrams). Using the enlargement transformation to establish similarity understanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof
Student work:	By the end of this unit, students will be able to use a range of strategies to enlarge or reduce two-dimensional figures, including simple maps and plans. They will be able to describe the properties of the enlarged or reduced figures in terms of quantities that have changed and quantities that have stayed the same. They will be able to recall, apply and explain tests for triangle similarity. They will be able to use their knowledge of similarity to identify corresponding sides in similar figures and, using scale factor, detemine an unknown dimension. They will be able to explain their geometric reasoning.

• Option 6: Year 9 Real numbers

Focal content descriptor:	·         Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems.
Elaborations:	·         Identifying direct proportion in real-life contexts.
Student work:	·                     By the end of this unit, students will be able to represent a set of proportionally related data in a table. They will be able to apply a range of strategies to determine an unknown value in a proportion or ratio relationship. They will be able to represent directly proportional relationships as straight line graphs. They will be able recognise the correspondence of the sequential rule, the slope of the graph, and the algebraic relationship y=mx. They will be able to model a range of life-related situations using their knowledge of direct proportion and its representation, including interpolating and extrapolating from a given data set.

 

Additionally, your unit may address other content descriptors that are relevant (either across strands or within the same strand).

Across the 4 lessons of your unit you are encouraged to plan to include a varied range of activities and resources. In your plans, you are required to include at least one instance of each of the following kinds of activites:

• a substantial investigation or mathematical modelling activity that provides students with a significant intellectual challenge and which should be conducted in small groups.
• a short independent learning activity (i.e., done individually, not as a group). Example activities include a short quiz, a worksheet etc. In a classroom, this activity could serve a formative assessment purpose – a way for you to collect evidence of student’s understanding during the unit.

In your submission, you will describe in detail one of each of the previous kinds of activites (see below for futher details).

For this Curriculum Studies 1 assessment item you are NOT expected to create a corresponding summative assessment task. In your planning, all four lessons should be devoted to classroom teaching and learning; do NOT allow time for students to complete an end-of-unit test etc.
Your submission for this assessment task should include the following five elements:

1. Discussion

You will discuss the rationale of your unit’s design, that is, how your unit’s design has been influenced by Bell’s five principles for the teaching and learning of mathematics.

HINT: Whilst it is likely that the discussion will only be finished after the other elements of your plans are complete, it is strongly recommended that you consider your implementation of Bell’s five principles EARLY in your planning and design of the unit.

The discussion should be 500 words in length (+/-10%, not counting reference list) and should be written in third person with appropriate APA styled references, if required.

2. Unit Plan

Using the template that will be provided during the semester, your unit plan will highlight:

• The content descriptors addressed by the unit (i.e., the selected content description option from the above list plus any additional content descriptions that you identify as relevant).
• The set of unit-level learning objectives (i.e., aligned to the description of the student work provided for each option)
• Identification of any prerequisite knowledge that is necessary for students to understand before beginning the lesson sequence.
• A clear description of the sequence of mathematical content (facts, skills, concepts and their corresponding physical, iconic and symbolic representations) to be developed within each lesson of the unit.
• Definition of learning objectives for each lesson.
• The identification and brief description of the main mathematical activities to be used in each lesson that are aligned to the sequence of mathematical content and which lead to the attainment of each lessons’ learning objectives.

As a part of preparing the unit plan, you will need to consider how your unit of work contributes to your students’ development of the general capabilities, most likely literacy, numeracy and/or ICT competency.

3. Lesson plan

You will provide a detailed plan for the first lesson (only) in the sequence.

Using the template provided during the semester, your lesson plan will clearly identify the conceptual sequence of the lesson and for each activity or section of the the lesson clearly describe what you (the teacher) will do, what the students will do and what formative assessment strategies will be used.

NOTE: Avoid making your first lesson purely revision of prior knowledge – this first lesson should make substantial contributions to the students’ knowledge and understanding of your selected content descriptor(s) and the associated unit-level learning objective(s).

To support the first lesson plan, you should provide copies of all materials referred to in the first lesson plan (e.g., copies of relevant textbook pages, website links, printed or electronic resources etc.). That is, if someone was to teach this lesson based upon your submission they would have all the materials needed, ready to go.

4. Investigation or mathematical modelling activity

You will describe the investigation or math-modellig actvity that small groups of students will complete during the lesson sequence.

Your investigation or math modelling activity could be used early in your unit (in which case it would probably be aimed at helping students to construct new ideas) or later in the unit (in which case it would probably be aimed at providing students with an opportunity to transfer or apply their new ideas).

This element of your submission should include:

1. a) A set of teacher notes that explain to a teacher how to use the investigation or math modelling activity (i.e., how you have planned to use it, in enough detail such that another teacher could conduct the activity without further explanation).
2. b) All stimulus, including worksheet(s), that would be given to the students. If stimulus includes Powerpoint slides, include these as an appendix to your submission.
3. Independent learning activity

You will describe an independent learning activity that students will complete during the lesson sequence.

This element of the submission should include a copy of any materials (worksheet etc.) that would be given to the student.

As you are putting your plans together, consider the target audience to be a supervising teacher on Field Experience. Do your plans provide a clear and accurate description of the content and approach you would like to take in class? Have you provided enough detail such that you and your supervising teacher could have a robust discussion about what you plan to do, such that the teacher could offer good quality feedback before you take charge of their students? Would your plans instil confidence in your supervising teacher – would you appear to be well prepared?