Learning Theory, Pedagogical Practice, and Appropriateness of Resources - Report Example

Learning theory, Pedagogical practice, & Appropriateness of Resources /Activity used in lesson Aim: As mentioned by Sullivan & Mousley, teaching is both an art and science but when it comes to teaching math as an art and as a science, it is much complicated. This explains why it is important to have a clear aim when designing a lesson plan. In other words, we should be apparent about what exactly will students’ be doing, and how these activities will be done? However, in this lesson plan there is not apparent aim about what the students will learn. The aim in the lesson points out that; the students will be involved in the identification of objects in terms of their masses but these objectives have not been indicated in the outcomes as well as in the indicators sections. In particular, the focal point of the lesson activities was to compare the masses of various objects. Therefore, the aim should have mentioned that the students will compare and describe the masses of objects as highlighted in the outcomes and indicators section. In addition, the lesson plan has not shown the kind of mathematical skills that the students will be using to achieve the outcomes of the lesson. In the aim section, the teacher approves that; having prior knowledge about mass. It is significant to use a certain type of arrangement when students are being taught about the concept of mass and measurements. According to Booker, Bond, Sparrow, & Swan (2010), a student is able to learn about measurements by understanding about physical features. Therefore, it is important to offer children the opportunity to manipulate objects that have the features that they can examine and view what can be measured. However, there is no clarity in the aim about the knowledge of students about measurements and more so, there is no sufficient information in the aim about the experiences of the children in the exploration of the mass attribute. At the same time, when language used by the children is taken into consideration, it is apparent that the right language has not been modeled because the children, even after they have had a few lesson, still describe that water bottle is heavy because it hurts. Booker et al (2010) point out that it is fundamental to develop the language of children and make it elaborate e.g it is the teacher’s responsibility to create the right language to be used. On the other hand, it is clear that the students have not experienced the differences in masses of the objects through the use of activities as suggested in the syllabus such as; trying to push, pull or lift objects, such activities will help them describe objects using everyday language and will lead them to ask questions about mass (NSW Board of Studies, 2002). Teaching and learning activities: Introduction: The teacher states that the time frame allocated for introduction is 10 minutes but the introduction showed that it would take more than ten minutes. When pedagogy is considered, this is not good quality pedagogy. Teaching has begun with the implementation of the lesson plan whereby the teacher asks the students a question after which the students learn from activities that require the students to directly experiment. This is because; the content articulates that the children will be directly comparing two masses by hefting. This is a rich method of education since the children interact with their environment when they are performing the experiments and using the objects they are familiar with. This section of the lesson plan is constant with Piaget theory (Southwell, 1992) for teaching about mathematics because students are actively involved in learning and interacting with their surroundings. When the lesson plan is compared to constructivist learning theory, the lesson plan somewhat succeed. First, in the introduction part, the teacher asks, ‘How can we tell when something is heavier, lighter or the same as another object?’ By using open ended questions, the students are expected to create their own knowledge according to constructivists. The constructivists also encourage collaboration among students hence, when the teacher instructs the students to work in pairs or groups, they exchange questions and answers (Booker et al, 2010). The teacher has been able to achieve this element when she encouraged the students to do activities in pairs and also work as a class. The students were given the chance to explain their answers through brainstorming and the peers challenge the responses in a polite way. At the same time, the introduction highlights some good ideologies that would be helpful to the students in the understanding of the concept of mass. As suggested by BOS (2007), hefting activity is the right types of activity that can be used for early stage one as pointed out in the syllabus. Conversely, no more than two objects can be used for the purposes of comparison. In the lesson plan, hefting is a good activity but the problem is that, it should not have been included at the introduction part and instead, it should have been included at the body section. The NSW Quality Teaching Framework is founded on three frameworks of pedagogy that have associated with the improvement of the outcomes of the students, one of which is focused on cognitive quality (DET, 2010). The hefting activity is in-line with this pedagogy because the students are actively involved in the thinking process and they are allowed to interact with and among each other. This type of environment used for learning exhibits constructivist framework; where knowledge is actively developed, and new traditions of knowing are built by focusing on physical and mental activities (Booker et al, .2010). Additionally, of significant importance is the fact that the teacher in the hefting activity concentrated on promoting the use of the appropriate language with the aim of developing the children’s language and makes the language precise. The correct use of language is important for students and it should be developed an early stage. The students should be given clear explanations so that they recognise the difference between everyday language and the language used in mathematics (BOS, 2007). Body: In the body of the lesson plan, the students are expected to work on their own; for a period of 20 minutes. The individual activities are based on what they had read on the textbook. When constructivist theory is used, then the teacher has not applied the theory because; there is no collaboration depicted in the learning strategy (Booker et. al, 2010, p.407). The students did not even ask questions about the activity. According to Booker et al (2010), constructivist theory illustrates that learning is a process of socialisation and explanation. However, in the lesson plan, explanation is absent although reflection and analysis was given sufficient time. The students sat together and asked questions and/or exchanged their results. In line with the syllabus ( Board of Studies, 2002,p.7), “ Learning mathematics will help students demonstrate confidence in applying mathematical knowledge, skills and understanding to everyday situations and solution of everyday problems”. The workbook activity is not realising this purpose of the syllabus. It is important that the best math teaching practice is used and for the children should participate in the development of new ways of thinking hence; to help them develop new ways of thinking, everyday experiences, games, play and real objects should be included in the learning process (Booker et al., 2010). The text book activity does not depict meaningful experiences, because it does not connect the children to real life experiences such as play or games. According to Sparrow and Hurst (2010), text book activity is not a good activity to be used for teaching. This is because; the activity does not encourage the students to interact with each other and at the same time, it does not involve the students in the lesson and it does not incorporate any concrete materials. For that reason, text book activity involves repetition of practices that leave the students with negative perception of mathematics. Further, the activity does not allow for the use of concrete materials thus it would have been preferable that the students use materials, play and games that are familiar to them (Booker et al, 2010). Conclusion: During conclusion, the students reflect on what they have learned. Booker et al (2010), state that reflection is important in learning especially when learning mathematics. The use of materials is also helpful because it helps the students to better understand and to effectively reflect on the tasks and situations and in turn improving their mathematical skills. However, in this case, the reflection of the students was not based on experiencing materials. Piaget asserts that, practical use of materials is an essential element in developing mathematical thought (Southwell, 1992). This mathematical thinking was inadequate when the teacher applied the textbook activity, which also means that; the assessment of the learning of the students based on the text book activity did not reflect the actual learning. In addition, the plan is also criticised on the fact that the content outcome of the lesson was expected to be the direct comparison of masses through hefting but this was not given much attention in the lesson body activity. Another critique is that the content outcome of this lesson was to compare masses directly by hefting which was not the main focus of the lesson body activity. Conclusively, as much as the lesson concludes effectively with students participating in group discussion, there should have been more questions that concentrate on reflection and the relation of the lesson with real life experiences. Reflection helps in the construction of strong mathematical relations hence the teacher should set aside enough time that the students can use in the reflection of their learning. Assessment strategies: In the lesson plan the teacher has noted two assessment strategies: 1. Anecdotal evidence from student discussions will be collected. 2. Work samples from students’ workbooks will be marked and annotated. There are two assessment strategies employed by the teacher. The first strategy used for assessment is appropriate for the class and the activities that have been planned e.g. engaging in hefting and sharing experiences; however, the second strategy of assessment is not valuable because; it does not focus on mass outcome as indicated in the lesson plan. “MES1.4: Compares the mass of two objects and describes mass using everyday language”. The use of one strategy for assessment in undertaking the planned activities is an indication that the activities are commonly undertaken in the classroom. As pointed out by The Australian Association of Mathematics Teachers Incorporation (AAMT) (2008) learning assessments occur frequently in classroom hence the assessment strategies employed by a teacher should be effective. Regardless of the irrelevance of the second strategy of assessment, it forms a platform from which the students can learn various elements of mathematics. AAMT (2008) suggests that, the use of various assessment strategies improves the mathematical ability to examine various mathematical elements and it also helps the students improve their mathematical skills. Furthermore, assessment is vital to the development of the student’s confidence. Syllabus Content, Appropriateness of Resources/Activity used within the lesson Process outcomes 1 and it is indicators: WMES 1.2: Uses objects, actions, imagery, technology and or trial and error to explore mathematical problem. In the lesson plan, it is evident that the teacher has stated the applying strategies. Students lift various objects and then they compare and conclude which one is heavier. Although applying strategies in the process section has been done and has been done correctly, the indicators for reasoning has been used instead of indicator of applying strategies. That is, the applying strategies outcome needs to follow specific indicators. The specific indicators involve; Uses direct comparison to determine which of two objects is heavier. Compares the masses of two objects by hefting. (NSW Board of Studies, 2002) Process outcome 2 and it is indicators: WME1.4: Uses concrete materials and/or pictorial representations to support conclusions. The teacher has also considered the reasoning outcomes in the lesson plan. When the students develop this kind of ability to predict masses of objects, they should also be able to point out why the objects have different masses. The explanations should relate to concrete or pictorial representations (NSW Board of Studies, 2002). When focus is shifted to the lesson activities, particularly in the hefting activity, the students are involved in the discussion of their findings. However, they do not exhibit reasoning in elaborating why one object is heavier than the other one. The teacher is expected to have encompassed reflection of lesson to improve the students’ reasoning ability. This is because; the correct use of reasoning is obvious in the lesson outcomes. Conversely, the teacher should have followed the lesson plan by including reflecting as the lesson plan indicates. For that reason, the outcomes should entail; WMES1.5 Links: ideas of mathematics and makes fixations with, and overview about the current knowledge and comprehension in relation to Early Stage 1 content. Having the capacity to predict the objects that are lighter than, heaver than or similar in terms of mass in relation to the other object. (NSW Board of Studies, 2002) Content outcome MES1.4: Compares the masses of two objects and describes mass using everyday language. Since the lesson plan is on a series of measurements in mathematics, content outcomes as well as content indicators have been included in the sub-strand mass by the teacher. In particular, the indicators included in the content part of the lesson plan are; 1. comparison of two masses by directly hefting 2. description of objects in respect to their mass In order for learning activity to be in-line with the content of the lesson, changes on the wording of the second indicator should be done because; the learning activity has not addressed the terms; ‘hard to push’ and ‘hard to pull’ in the second indicator. On the other hand, every aspect of the first indicator have been addressed by the teacher when the teacher set aside sufficient time and allowed the students to directly heft the objects and compare their masses. According to Lindsay & Scott (2005) primary school students are normally aware of the concept of mass as dealing with the issue of ‘heaviness’. Furthermore, the authors pointed out that, studies on masses of objects should support the concept of mass by letting the students compare the masses of objects through hefting. This is would have depicted what has been highlighted in the content of lesson plan and would emphasized what is in K – 6 Mathematics Syllabus Early Stage One Mass content (Document 3). Hefting Activity and Resources: In the hefting activity; there are several objects with different masses but similar sizes hence contributes to a better understanding of the mass concept. Southwell (1992) pointed out that the right materials to use in hefting activity are those that have the same size but different masses because; such objects will enhance how students grasp the concept of mass. According to Deine’s multiple embodiment principle; a concept is better understood when a wide range of representations are used (Southwell, 1992). In addition, as mentioned in the standards of AAMT (2006), a teacher’s lesson plan should be consistent with learning experiences because the experiences will help students acquire mathematical skills that would make them more knowledgeable. Task Two Three Alternative Activities Activity 1: Problem Solving One of my first suggestions as an alternate activity, to the textbook activity included in the lesson plan, would be for every student to pick different objects to be compared to an object in their hands. The objects that are picked should fall into the following categories in relation to the object that they have in their hand; larger and lighter larger and heavier smaller and lighter smaller and heavier same size and lighter same size and heavier same size and same mass In order to classify the objects they collect, the students will push, pull, lift, and use equal arm balance and others. In the process of undertaking these activities, the students will interact and record the information in their workbooks. For early stage 1 students, the teacher will have to facilitate the recording of the information in the workbooks. However, the students will have the right to decide on the method to be used in recording. In concluding the activity, students will work together and exchange information about their results with peers. This will involve finding out the different masses of objects collected i.e. the heaviest and smallest, heaviest and largest, lightest and smallest, lightest and largest according to the results. The findings will be used in voting for the objects to determine the winning object which will be the object with the heaviest mass. Follow up will be done to confirm the results about the objects as voted. A chart or a graph will be drawn by the whole class using the votes. Justification: This activity allows the students to interact and thus the students are able to create their individual knowledge (Southwell, 1992). Excellent instructors of mathematics are those who actively involve students in learning mathematical skills through communication with each other and among each other (AAMT, 2006). Problem solving is another major focus of prior activity. In problem solving, students personally undertake mathematical activities. Problem solving has been defined as the activity whereby the students personally explore mathematical task and t he students understand that it is their work. The activities involve; taking risks, testing, investigating, inquiring, and focusing (Sullivan & Mousley, 1994). Problem solving heartens the confidence of students to support their answers. Additionally, complex language is used leading to the development of the students’ mathematical understanding (Gervasoni, 2000) In addition to helping students solve problems. The activity is justified by the fact that it encourages interaction. Interaction is important because, according to Southwell (1992), it encourages individual construction of knowledge. AAMT (2006) also insinuate that excellent mathematics teachers actively involve students in learning and in the initiation of purposeful mathematical communications among peers and with peers. Activity 2: Mystery Boxes This is an activity that has been mentioned by the NSW Board of Studies Mathematics K-6 Sample Units of Work. In this activity, the students will be expected to identify the boxes that are heavy and those that are light. The main activities would include; lifting, pulling and pushing the boxes. Specific activities would include putting objects of different masses in the boxes. The students will not be allowed to see the objects hence the students will make predictions about the masses of the boxes without seeing what inside. Students will push or pull the boxes and then say whether the box is lighter or heavier. As a group, they will note down the objects that are extremely heavy to lift and need pushing or pulling. Afterwards, the students will compare the boxes with items around them. In order for the students to present the views about the masses of the boxes, the students will be instructed to use terms such as easy to push, hard to lift, hard to pull etc. The results will be put into writing. Justification: I suggested ‘Mystery Boxes’ as an alternate activity because it considers all the outcomes and the indicators of the syllabus as highlighted in the lesson plan. The students will have the chance to make use of objects, activities, images, technology and even trial and error in the prediction of heaviness or lightness of objects when compared to (NSW Board of study, 2007). According to Sullivan & Mousley (1994), mystery boxes activities help students develop their communication skills because they talk, they listen to each other, and they share and report. Additionally, this activity helps the students to have the curiosity of wanting to learn more and as a result, they are encouraged to learn. This activity has been referred to as multiple embodiment principle whereby, boxes having similar sizes but different weight are used. It is noted to be an effective approach for teaching the concept of mass (Southwell, 1992). As pointed out in NSW BOS (2007, p.108), mystery Boxes is an activity that enables students “compare the masses of two objects and describe mass using everyday language”. The activity is best for teaching as it allows the students work together and create a list of objects. Working together is supported by the constructivist theory (Woolfolk & Margetts, 2010). Students are also actively involved in learning especially when the students pull and push boxes. The activity in in-line with Piaget theory which supports the point of view that students should be actively involved in learning and that they should not only interact with each other, but with their environment as well (Southwell, 1992). Activity 3: Everyone can balance The activity is from NSW Board of Studies Mathematics K-6 Sample Units of Work (2007). The activity will be a step by step procedure where students learn the basis of balancing and use the knowledge to compare masses. Students will stand and stretch out the arms in a way of simulating balance. As a demonstration, the teacher will place an object in two hands and the students will be asked to predicate the effect of the object on balancing The students will then be offered objects that they will use to state their activities and verify their forecast. Students will brainstorm about their predictions i.e. why they though item B was heavier than item C but lighter than item A. The students will record their findings using drawings and then they will label what they have drawn. Justification: By using various items in the classroom, the students are granted the chance of using a wide range of items and this is a concept that has been encouraged by NSW BOS (2007); in such that; students need to be given the opportunity to use activities, items, technology, trial and error and or imagery in the prediction of masses of objects. Since the activity involves the active participation of the students, it encourages the students to enjoy the mathematical tasks and to be creative. Sparrow and Hurst (2010) are of the opinion that when students are exposed to positive experiences during math lessons, their attitude towards mathematics becomes positive. Therefore, the students will not only learn, but they will also enjoy math lessons. The activity makes it possible for the students to use pictures to verify their predictions (NSW BOS, 2007). This is the best display of teaching practice because it considers the elements that have been considered in the second alternate activity e.g. learning together. Using equal arm balance to learn as a class and allowing the students to learn through predictions, letting students to record information from their experience displays the best teaching practice. The activity enables the students construct their individual knowledge. The students should know theory responsibility in the construction of their knowledge as suggested by constructivist theory Woolfolk and Margetts (2010). Evident from the activity, the students are expected to make predictions and point out the impact of placing objects in their arms. The students are expected in the activity to record the findings using drawings and labels. As noted by Woolfolk and Margetts (2010), the assumptions made by students in their predictions and experiences (drawing and labeling) help the students gain a better understanding about their surrounding. References: AAMT. (2008). The practice of assessing mathematics learning. Retrieved April 28, 2011, from the Australian Association of Mathematics Teacher’s (AAMT) website: www.aamt.edu.au Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). teaching primary mathemtics. Australia: pearson. Lindsay, M., & Scott, A. (2005). Estimating Eggs. APMC, 10(4), p. 4 – 8. Adelaide: AAMT. NSW Board of Studies. (2002). mathematics years K–6 syllabus. Sydney: Author, Quality teaching in NSW public schools coding scale overview (2010). Retrieved September 24, 2011, from the NSW Department of Education and Training (DET) Website: HYPERLINK "http://www.curriculumsupport.education.nsw.gov.au" Oxford, R. L. (1992). Cooperative learning, collaborative learning, and interaction: Three communicative strands in the language classroom. The Modern Language Journal, 81(4), 443-456. Southwell, B. (1992). How children learn. Nepean: University of Westen Sydney. Standards for excellence in teaching mathematics in Australian schools (2006). Retrieved September 24, 2011, from the Australian Association of Mathematics Teacher’s (AAMT) website: HYPERLINK "http://www.aamt.edu.au" Sparrow, L., & Hurst, C. (2010). Effecting affect: Developing a positive attitude to primary mathematics learning. APMC, 15(1). Sullivan, P., & Mousley, J. (1994). What Quality Mathematics Teaching Looks Like. Reflections, 19(1), p. 2 – 5. Unknown Publication and Place. Read More