Planning and Reviewing a Unit of Work - Assignment Example

Planning and Reviewing a Unit of Work Contents Introduction setting About The Unit Where The Unit fits in Prior Learning Rational and Literature Review Assessment Handling Data by John Costello ICT in Mathematics Overview of the Lesson Grid Lesson 1, Handling data cycle and writing a hypothesis Lesson 2, Tally data and draw graphs Lesson 3, Out and about collecting data Lesson 4, Draw graphs using ICT Lesson 5, Mean, Mode, Median and Range Lesson 6, Evaluations Lesson 7, Correlation Evaluation and Review References Handling Data Introduction Class setting These lessons where designed for year 8 top set at Hove Park School. There are 13 classes in year 8. There are three top set classes with 30 pupils in each class. In the second set there are five classes, also with 30 students each, and in the third set there are two classes that have 20 students per class.The three bottom set classes have 10 (some might be less) students per class. Most of the students are working towards level 5. There are five students working at level 4 and eight working towards level 6. There is couple of girls in class that like to chat the entire time. One this girl is working at level 4. There are about six boys who behave in the same manner but one of these students is working towards level 6. For this task students were working in pairs and he was paired up with child who constantly requires help and in on SEN register. About The Unit In this unit I will be planning to cover the following (lesson objectives): Discuss a problem that can be addressed by statistical methods (hypothesis) Discuss how to collect data to answer a question (hypothesis) Identify possible sources of data Plan how to collect the data and sample size Collect data [primary (questionnaire) or secondary data (existing data)] Perform Mathematical reasoning (Mean, Mode and Median) Illustrate your finding using suitable diagrams or graphs Explain why you have used them Write a short conclusion on your finding Could you have done anything better? Are you happy with your findings? This unit is expected to take about 6 lessons. Prior Learning Students should know: How to find the mean, mode and the median of non-grouped data How to find the range of a set data How to draw bar charts for discrete data (possible other charts e.g. scatter graphs, pies charts…) Where The Unit fits in This unit is according to the “Key Stage 3 National strategy” and it is designed for students in year 8 (teaching was slightly modified to fit according to the class tutor wishes, the lessons plan were slightly reduce by using secondary data, however all methods were thoroughly discuss so that the students would meet the objectives now and in the future. Data Handling is first taught in primary school. In fact, my daughter who is in year 3 (1st year of junior school) has done a survey by counting different type of transport (cars, van, motorbike …etc) at a traffic lights and drawing a bar chart using the data. In the key objectives for the Year 3 the DfEE (1999) (Framework p3) states that, “Solve a given problem by organizing and interpreting numerical data in simple lists, tables and graphs”. In year 4 they are taught the vocabulary of data handling, such as survey, questionnaire, data, tally charts ..etc. They will also look at and create graphs like bar and pictogram - where the symbol represents several units - in details. This theme of work is then continued in year 5, 6 and onwards. Handling data The handling of data is an established part of the National Curriculum at all key stages. It makes up a significant part of the curriculum and also a regular feature in the exams. Handling data also appears in the other cross-curricular subjects such as ICT, History and Geography and many more. According to the National Curriculum, students should be taught all four phases of the data handling cycle. Key Stage 3 National Strategy (2001) describes the four phases using the diagram. (diagram below is copied from page 18 of the Key Stage 3 National Strategy, Guide for the Framework). Specify the problem and plan This topic should identify questions that students can address for their statistical report. Discuss how they would go about to proving it, survey and questionnaire and how they would go about collecting data. Collect data from a variety of sources For this area students should design their own questionnaire and decide where to collect their data from. They should also collect primary or secondary data Process and represent data This is stage where students should draw the graphs, in their exercise book and using ICT. Then they need to calculate mean, mode and median. This stage focuses on use of ICT for graphs. Interpret and discuss data Here students interpret their graphs and using the mean, mode and median draw their conclusion relating back to their hypothesis. In our Professional Studies at University and in my first placement school, in the Learning Style lecture we learned about the three most important learning styles, auditory, visual and kinaesthetic. Handling data cover all three learning styles and for this reason students should be enthusiastic to learn this topic. Rational and Literature Review Assessment Assessment can be done at various times throughout a year. There are various ways to assess students work. More importantly, assessment may be used for various purposes. Not only is assessment used to gauge the level of learning that a student gains, it can likewise be used to improve the way the student learns. When one considers this purpose, the term Assessment for Learning comes to play. According to the Qualifications and Curriculum Authority, a non-departmental public body sponsored by the DfES, Assessment for Learning, "Assessment for Learning is the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there" (Assessment Reform Group, 2002). Assessment in this light is viewed as process aimed at improving student acheivement in the classroom setting. This purpose veers away from the conventional practice of considering assessment as the end and not a means to an end. With Assessment for Learning, student assesment is considered as a means by which teachers can assist students in furthering their achievement in school. Students are not judged but rather, they are provided with feedback from which they can gain insight from so as to help them perform better in the classroom. Looking through my professional studies lecture notes, “Assessment for Learning”, also handout for on “Assessment for learning” given during our visit to St Paul’s Catholic School on February 8th 2006 and reading “Learning and Teaching in Secondary Schools” by Ellis (ed) 2004, they all talk about peer, self, teacher, formative and summative assessments. This are the more traditional views or types of student assessment. "Inside the Black Box: Raising Standards Through Classroom Assessment", Black and William, (2001) provides evidence that classroom assessment (formative), is a better for improving student learning. In todays times, the use of standardized testing has oftenly been used in order to determine student accountability as well as to gauge the level of achievement of the student. Such standardized tests are considered a form of summative assessment. Basically, summative assessment is the method which attempts to summarizr what the student has learned at a particular time. More often than not, summative tests are given at the end of a stage. Summative assessment is useful when one considers student assessment an an integral part of the learning process wherein feedback from the teacher may help the student improve his performance. However, summative assessment does have its use particularly when teachers try to improve the organization of their courses or when schools revise their curriculum. Teachers and the school administration make use of the general information that summative assessment offers in their effort to accomplish the said goals. Formative assessment occurs when teachers feeds information back to te students in ways that enable the students to learn better, or when students can engage in a similar, self- assessment process. Black and Wiliam showed that formative assessment is effective for students who have low attainment level in school, thus narrowing the gap between low and high achievers while raising overall standards. Formative assessment shares the same goals with that of Assessment for Learning in that both of them are meant to improve student learning and not judge it. The primary purpose of formative assessment is high-quality learning. However, despite its positive goals, Black and William have pointed out that teachers today have yet to fully utilize formative assessment. Instead of prioritizing genuine high-quality learning, teachers today still instruct students in way that will only lead to rote and superficial learning (Black and William, 2004). With todays instruction leaning heavily on standardized testing as a means of student assessment, we may just see more students learning less from school. As such, there is a great need to alter the teachers perception of assessment and change it towards formative assessment and Assessment for Learning. It is only through such means that student learning and achievement may be genuinely improved. Handling Data by John Costello Handling data has moved a long way since my school days. Costello (1995) states, The collection and representation of information is an established part of work in primary schools where block graphs, pictograms and mapping diagrams are commonly on display, during early 70s (1970 and 71) I was never taught graphs. In fact graphs are taught has early as year 3 in the primary school and is part of the DfEE (1999). According to my daughter she did graphs in Year 2. When mathematics was taught in old days, students had to create their own graphs. The computer has changed all this. Basically a computer can create a graph instantly. Because computers are now used to create graphs this means that the students have more time to analyse the statistics from the graph but not necessary understand where the graphs comes from. Then the question is do they know how the graphs were created in the first place? Costello states, that the information collected is a means to an end and not an end in itself. This means that we would by-pass construction of graphs this would then allow us to concentrate on the results of data which now become more important. In real lives, television and newspapers are always showing graphs regarding retail price index, the rate of inflation, the level of unemployment, the ‘average’ rise in wages, the Financial Times share index and a variety of other numbers, the end game is how we interpret the results which is more vital. Costello says there are two methods of teaching how to handle data. One is working out Mean, Mode, Median and range using large set of data. The other involves questions and giving problems for students to solve. Costello states that, the students find the concepts of statistics natural, because they need them in order to solve the problem, because without this they are confused and all of us by nature of our intelligence need to make sense of information that has been presented to us. We need to known how everything adds up and equates. A good example that Costello mentions is how Goodchild used box of matches to ask his students what does the average of 35 matches in box mean. ICT in Mathematics With todays booming technology, a continously increasing importance has been placed on the use of information and communication technology (ICT) in instruction. This fact is particualrly true when considering mathematics instruction. As pointed out by the National Curriculum in Action (NCAction), "The nature of mathematics has changed considerably because of the availability of ICT. The processes of modelling, estimating, validating, hypothesising and finding information are becoming increasingly important." One way by which ICT has played a factor in teaching mathematics is through its facilitation of graphing. Graphs are now part of our everyday life. More importantly, our understanding of math is often related to graphical representations of information that aide us in understnading the complexities of todays world. We are bombarded with graphs regarding (Costello 1995) retail price index, the rate of inflation, the level of unemployment, the ‘average’ rise in wages, the Financial Times share index and a variety of other numbers which are produced using computers. How we interpreter these graphs is form of art it self. Bloomfield and Harries (ed 1995), It is rare to be able to interpret a graph without making some guesses and some assumptions. Graphs interpretation is not a mechanical process: the good interpreter of graphs is a scientist, a detective and storyteller rolled into one. We know that computers can help draw graphs intently so the matter remains how? The National Curriculum in Action (NCAction), states that: Pupils should be given opportunities to apply and develop their ICT capability through the use of ICT tools to support their learning. NCAction recommend that using the ICT pupils should produce graphs such as bar charts and pie charts. This can be done using software packages such as spreadsheets and databases. This is but one of the many wayds by which mathematical instruction may be improved through the use of tools that ICT provides us with. Lesson Grid Lesson Objective National curriculum Lesson 1 ·1 To make a hypothesis and say why Lesson 2 ·1 Decides which data to use verify the hypothesis, create a tally table of graph and draw graph in their exercise book. ICT Lesson 3 ·2 Draw graphs using ICT Lesson 4 ·3 How to perform Mathematical reasoning (mean, mode and median) Lesson 5 ·4 Write conclusion using the Mathematical reasoning Lesson 6 ·5 Talk and write conclusion on the out come and decide if they are happy with the outcome, could they done anything better Lesson 1 Group: Year 8 Venue: Room 18 Teacher responsible: Ms M Hayward Content: Data Handling Subject: Teaching Objectives: Learning Outcomes All will know the procedure of writing a Learn how to write a hypothesis and state why statistical report Most will know how write a hypothesis Without help Some will know how give good reason for their hypothesis Opportunities to develop Literacy Numeracy Citizenship Plenary to check the hypothesis written by students Use of ICT Differentiated activities Assessment opportunities 1. Learn the procedure of writing a statistical report Class monitoring. 2. Write a hypothesis for a given situation Plenary 3. 4. Lesson outline (including timing) 10 minutes: To introduce the topic Ask students: What do we mean by statistical report Tell students this is what the plan is for next six lessons 10 minutes: To talk about different problems that can be addressed by statistical methods Question: Who watches more television, boys or grils and why? Question: When mum and dad were young, who watched more television? Question: Now a day who watches more television, mums or dad? Question: Grand parents, who watches more television? Question: How would find out who watches more television? How do we find out (how collect the data)? (to be discussed in next lesson) 20 minutes: Get students to create a hypothesis and give a reason. Question: Who is better at Maths, boys or Girls and why? 10 minutes: Plenary, students to read their hypothesis to the class Students to ready out their hypothesis to the class. Lesson 2 Group: Year 8 Venue: Room 18 Teacher responsible: Mrs M Hayward Content: Data Handling (writing a statistical report) Subject: maths Teaching Objectives: Learning Outcomes All will create a very simple questionnaire Learn how to create a questionnaire .with some help Most will create a questionnaire (This is continued from previous lesson) Some will create an multipart questionnaire Opportunities to develop Literacy Numeracy Citizenship Plenary to use vocabulary matching Yes Use of ICT calculators Differentiated activities Assessment opportunities 1. Learn how create a questionnaire Class monitoring. 2. Create a tally chart and draw the graph in their exercise book Exercise book 3. 4. Lesson outline (including timing) 5 minutes: Refresh by going through what they did in the last lesson. 10 minutes: Explain the activity. What is questionnaire, how to record data, identify possible source of data, Question to ask: What is a survey? (A survey is investigation to find a information) What is questionnaire? ( A list of questions used to gather information in a survey) To find out who watches more TV boys or girls, mums or dad what sort of questions would you ask, (Discuss how to create a questionnaire) What sort of people would you target with the questionnaire? Mums and dad, primary school students, secondary school students. What would be wrong if only boys from primary school are used in a survey and only girls from the secondary school? What is primary data and what is secondary data? Where would you fid secondary data? A quick survey of the class on who watch more TV, boys or girls? Hours of TV watched Boys Girls 0 1 - less than 5 5 - less 10 10 - less 15 15 - less 20 More than 20 Question: how many degrees in a circle? If there are 30 students in a class, how degrees (angle) would it take to represent one student? 360/30 = 12 20 minutes : Distribute data for students to create a tally table and draws graphs in the exercise book 5 minutes: Talk about what they did in the lesson what they have learned. Lesson 3 Group: Year 8 Venue: Room 18 Teacher responsible: Mrs M Hayward Content: Data Handling (ICT) Subject: maths Teaching Objectives: Learning Outcomes All will how to use Excel and create a graphs Learn ho to construct graphs using Excel. Most will know how to use Excel without help and draw Bar charts. Some will draw pies charts and or than one graphs Opportunities to develop Literacy Numeracy Citizenship Plenary to use vocabulary matching the lesson. Yes ICT Use of ICT calculators Differentiated activities Assessment opportunities 1. Calculate statistical reasoning (Mean, Mode and Median Class monitoring. 2. Lesson outline (including timing) 5 minutes: First couple of minutes will used to get the class settle into ICT room. 5 minutes: Class discussion on use of Excel to produce graphs. (First question is to find out how many students know how to use Excel. Drawn graphs using Excel). Show some example of pie charts. 30 minutes: To enter data on Excel sheet and draw graphs using the data. Progress is assessed by checking the graphs that students have produced. Students to self assess their work against teachers. See how their graphs differs form the teachers. Provide help and assistance as required 10 minutes: packing, printing and saving the work in their folder Lesson 5 Group: Year 8 Venue: Room 18 Teacher responsible: Mrs M Hayward Content: Data Handling Subject: maths Teaching Objectives: Learning Outcomes All will calculate three averages Learn why we need to calculate three averages. Most will Some will know how to pich the correct averages for evaluation Opportunities to develop Literacy Numeracy Citizenship Plenary to use vocabulary matching the lesson. Yes Use of ICT calculators Differentiated activities Assessment opportunities 1. Calculate statistical reasoning (Mean, Mode and Median Class monitoring. 2. Lesson outline (including timing) 15 minutes: Starter: Class discussion of mean, mode, median and range. Write the definition on the board for students to copy in their exercise book. Write a question of the board for students to calculate mean, mode, median and the range. (see Exercise 1) 15 minutes: Question: why do we need to to work out three averages (MMM)? Get students to do the question to answer this, Exercise 2 20 minutes : Get students to work out the MMM for the report and decides which one they are going to sue for the evaluation and why Evaluation After talking to the ICT teacher, I discovered that year 8 students had done graph such as line, bar and pie charts. There topic was to calculate the price of a holiday which they had to present that information to their target audience. From the hindsight it would have been a perfect opportunity for cross curriculum work with the ICT department. Assessment If I was to do the unit of work again I would involve pupils in peer and self assessment. This would encourage student to listen to each other during plenary session and get them self motivated. Peer comments can help students build self esteem. (see “Assessment for learning” hand out given at St Paul’s school on February 8th and see Professional Lecture note on “Assessment for Learning” and “Inside a black box” ). In future I would ask students to do peer assessment, and the first thing that I would suggest is that for every negative/improvement that they can suggest/point out they must try and find two positive things that the student has done. This would help boost up the self esteem of students being assessed. With a clear goal setting students can be as effective at marking/judging as a teacher. Peer and self assessment Self-assessment is a process by which pupils learn more about themselves. Moreover, self-assessment is a useful tool for teachers. It aids the teacher in helping the student improve their learning just as it helps the student realize what he must do on his own to improve his learning abilities. Basically, as students learn how to identify the areas of improvment in their respective learning processes, they develop their own methods of improving these as well. By doing so, self-assesment improves learning which is beneficial for both teacher and student. With self-assessment, students need not rely heavily on the input of their instructors. Student assessment of other students work has many benefits both for the leaner and the assessor. This is known as peer assessment. In my opinion self and peer-assessment go hand in hand. They have many advantages. Peer assessment can help self-assessment. By judging the work of others, students gain insight into their own work. For peer assessment teacher needs to get students to read out loud their work to the class or by getting students to exchange work for comments or marking. In order for this to work teacher must have clear guidelines for students to follow when judging/assessing peer’s work. In both self and peer assessment, the teacher takes up a new role in the assessment process. In the traditional concept of assessment, the teacher primarily serves as the assessor. However, in self-assessment as well as peer-assessment, the teacher takes up the secondary role. He serves as the facilitator who guides the students in their attempt to evaluate their own performance as well as that of their peers. Getting students to list the strengths and weakness of their peers work at the same time being careful not encourage any negative comments. Guidelines should also be made clear about what they should look for in a given task and for this to work, the teacher must be aware of weaker student’s self esteem/confidence. This in general will teach students how to judge/assess their own work and build their on self esteem. The teacher must take up the vital role in this process. He must lay out the guidelines usually in the form of guide questions that students may refer to when they undergo both self-assessment and peer-assessment. Moreover, the teacher must guide the students so as to ensure that their feedback for their peers would be constructive. This is the only way by which peer-assessment will be effective in improving student learning and achievement. Teacher assessment The key question that teacher needs to ask them self is how will I assess my students so it is meaningful to them? There are two major ways of assessing students work by a teacher. One is collecting, reading and marking their exercise books. The other way as stated by Ellis (2004), by observing, reading, questioning and interpreting students’ comments and actions. Both of the above process will help teachers plan/adapt/change his/her lesson according. This is an ongoing process. There are number of reasons why a teacher needs to assess a student. One could be to get a sense of their attainment level. The purpose behind this would be how to move the student from one level to other. Also, how to create targets needed for students to meet their full potential. The assessment should be included into the teacher’s lesson plan. Teacher assessment must not only be based on scores in examinations. Instead, teachers must focus more on the students participation in class. This may be a more effective means of assessing student learning when the teacher asks questions that will test the depth of knowledge of the student. For example, a question of "Is 5 a prime number?" must be followed up by a question such as "Why is 5 is a prime number?" It is through such questions that the teacher will get to determine whether the student genuinely gained knowledge or not. Formal Tests The other methods that are discussed by Ellis are internal and external (known as Summative assessment) formal test. At some stage all students are going to be marked by external examiner, it is import to stay focus on the national curriculum. At the same time their will be internal test and homework to check their learning process. This boils down to two things, subjective side of teaching, self motivating and the other side working towards the national curriculum and they need to be balance. Formal tests will also help compare the peformance of one student against others of his stage or grade level in the country. This information may then be used in developing revisions to the schools curriculum in order to keep it at par with that of the national curriculum. Assessment procedure for unit of work For this unit of work student’s progress in meeting the data handling required learning outcomes will be assessed in the following manner Discussing their work as part of the plenary session Monitoring and checking students work in the class. Collecting their exercise books to check their progress. The work performed in the classroom should be checked and verbal encouragement given. Lesson 1: Explaining the topic did not take long time. However discussing the procedure for writing the statistical report took more than ten minutes. There were lots of questions and answers by students. For some reason students were keen on doing this topic. Motivation was probable due to freedom to work in pairs and because it was topic they understood. However, they were not very keen on putting pen to paper and most had to be reminded that they had to give reason for their hypothesis. Here are some of the hypotheses written by the students: “Boys are clever then girls because we have more famous people like Einstein”. “Boys are clever then girls because we have more famous man”. “Boys are cleaver because we have Lewis”. Lewis is the intelligent boy in the class “Girls are cleverer then boys because boys cannot concentrate for long”. “Boys are clever because they are ore boys”. We also discuss if any one had taken part in any survey. Couple of students states they took part in food survey in ASDA (Holingbury). They had to test the food and tick the box to indicate which they like best. Lesson 2: Since the students were working in pair they get through work much quicker. Looking from the hindsight it might have been good idea to get the students to prepare their on questionnaire of their own even if they did not use it. On the other hand it would have been ideal homework question. Getting student to create a questionnaire would have deep-rooted topic in their mind. Lesson 3: ICT to draw graphs did not take long. It was shame that they did not have printer in school that worked for students to print their graphs. After the graphs were created, students were given example of the graphs created by the teacher (me) to compare their results against. If the students has done this then they were given freedom to play Maths games (on the following web pages: coolmaths, mymath) or search the internet to find any articles regarding who is clever (smarter) man or woman. Please find copy of article that one student found. In future ICT lesson it would ideal to ask students to find graphs that they print can explain to class or set this as home work question (find graphs in new paper, magazine, internal etc.. to explain to the class). References Bloomfield, A and Harries, T (ed 1995), Teaching, Learning and Mathematics – With IT, Association of Teachers of Mathematics, Handling Data page 5. Black, P & William, D (2004) Inside the black box: Raising standards through classroom assessment, Kings College London: London. Costello, J (1995) Teaching and Learning Mathematics 11 -16, Routledge, chapter 6 DfEE (2001), Key Stage 3 National Strategy, DfEE Available from: www.standards.dfes.gov.uk DfEE (1999), The National Numeracy Strategy, DfEE Ellis, V (ed 2004), Learning and Teaching in Secondary School, chapter 4. Haggarty, L (2002) Teaching Mathematics in secondary schools: A reader, Routledge: London. The National Curriculum for England, Mathematics (1999), The Stationary Office Available from: www.nc.uk.net National Curriculum in Action Available from: http://www.ncaction.org.uk/subjects/maths/levels.htm Qualifications and Curriculum Authority (2002) Assessment for Learning, DfES, [online] 19 March 2006, available at: http://www.qca.org.uk/7659.html. Read More