Diff – f7cbfae2e3 – chromium/src – Git at Google.
Zoom is a great program for video conferences. That is, providing it works. If you need to join a scheduled meeting, the last thing you want is to encounter a problem or error code. That's why we're here to help you. We're going to list the most common Zoom errors and tell you how to fix them. The cara mengatasi zoom error 104 114 – none: common Zoom issue is being unable to connect to a meeting. Though the Zoom client itself may load fine, you will encounter the problem when clicking a join link or after entering your meeting ID and password.
This manifests itself with many /27689.txt codes:,,,,and The first step is to allow Zoom through your firewall. The exact steps for this will depend on what firewall you use. On Windows, cara mengatasi zoom error 104 114 – none: default firewall is provided by Windows Security. If this doesn't work, you should temporarily disable the firewall entirely. Just remember to reverse this after the Zoom call. A second solution is to temporarily disable your anti-virus.
Again, these steps will vary if you use a third-party program as protection. On Windows, the /21994.txt anti-virus is provided by Windows Security. Once done, try to access the Zoom meeting again. Windows should automatically turn your virus protection cara mengatasi zoom error 104 114 – none: on after a while, but it's best to double-check.
If you get an error that XmppDll. To resolve this, you should manually install the latest version of Zoom, which you cara mengatasi zoom error 104 114 – none: do via the Download Center. This is a package that installs some necessary components that Zoom, and many other applications, require.
To grab the necessary file, go to the Microsoft Download Center. Select your language, click Downloadopen the EXE file, and follow the instructions that display. The full message you will receive is "There is no disk in the drive. Please insert a disk into the drive.
Despite the error, you don't need to insert anything anywhere. This occurs because Zoom is looking for a file path that doesn't exist. Alternatively, you might see error code during installation. This means that Zoom can't overwrite an existing file due to a running process. Now, you just need to reinstall Zoom. You can get the latest version from the Zoom Download Center. First, check that you have enough disk space. Look at how much space you have left on the здесь where you are cara mengatasi zoom error 104 114 – none: Zoom.
If it's in the red, with only megabytes remaining, it's time for a tidy up. Here's how to clean Windows If that's not the problem, try updating Zoom via the Download Centerrather than the program itself.
If necessary, replace C with the drive you have Zoom installed on. Then click OK. In the folder that opens, you посетить страницу источник see a file called installer. Attach this to a ticket on the Zoom Support site for further assistance.
This error can happen during installation and is caused either by incorrect permissions or a driver conflict. First, you need to run the Zoom installer as an administrator.
If you're trying to update via the program itself, grab the installer from the Zoom Download Center instead. Right-click the Читать file and choose Run as administrator. Then follow the standard installation process. If you still get the error, it's a driver problem. You can use Windows Update to check for driver updates:.
If cara mengatasi zoom error 104 114 – none: updates are found, that doesn't necessarily mean your drivers are the most recent version. You should visit your manufacturer's website to grab the latest files.
If you need more help, see our guide on how to find and replace drivers. It you see this, it means that you have not been granted the correct license to join the webinar. Alternatively, the host's webinar license could be expired. The host needs to visit Zoom User Management as an account owner or admin.
Here they can grant you the correct permissions to join the webinar, or find out how to renew their webinar license if applicable. Hopefully you now have Zoom up and running. If not, visit the Zoom support site for more resources and contact information. Now it's time to discover all the fun potential of Zoom, like hosting a quiz night or watching Netflix with friends. Can't Connect to Zoom The most common Zoom issue is being unable to connect to a meeting. Configure Your Firewall The first step is to allow Zoom through your firewall.
Do a system search for Windows Security and open the app. Click Allow an app through the firewall. Click Change settings. Click OK. What Is Algorand?
– How to Fix 7 Common Zoom Problems and Error Codes
That is, providing it works. If you need to join a scheduled meeting, the last thing you want is to encounter a problem or error code. That's why we're here to help you. We're going to list the most common Zoom errors and tell you how to fix them. The most common Zoom issue is being unable to connect to a meeting. Though the Zoom client itself may load fine, you will encounter the problem when clicking a join link or after entering your meeting ID and password.
This manifests itself with many error codes: , , , , , , , , , , , , , , , , , and The first step is to allow Zoom through your firewall. The exact steps for this will depend on what firewall you use. On Windows, the default firewall is provided by Windows Security. If this doesn't work, you should temporarily disable the firewall entirely. Just remember to reverse this after the Zoom call.
A second solution is to temporarily disable your anti-virus. Again, these steps will vary if you use a third-party program as protection. On Windows, the default anti-virus is provided by Windows Security. Once done, try to access the Zoom meeting again. Windows should automatically turn your virus protection back on after a while, but it's best to double-check.
If you get an error that XmppDll. To resolve this, you should manually install the latest version of Zoom, which you can do via the Download Center. This is a package that installs some necessary components that Zoom, and many other applications, require. To grab the necessary file, go to the Microsoft Download Center. Select your language, click Download , open the EXE file, and follow the instructions that display.
The full message you will receive is "There is no disk in the drive. Please insert a disk into the drive. Despite the error, you don't need to insert anything anywhere. This occurs because Zoom is looking for a file path that doesn't exist. Alternatively, you might see error code during installation.
This means that Zoom can't overwrite an existing file due to a running process. Now, you just need to reinstall Zoom. You can get the latest version from the Zoom Download Center. First, check that you have enough disk space. Look at how much space you have left on the drive where you are installing Zoom. The object is to get students to go beyond appearance to investigate properties. In a dynamic environment the properties of an object are shown through its behaviour rather than through its static appearance at one instant in time.
In the first construction, on the left, students drag each of the four vertices, and only when they drag vertex D do they find that the construction does not truly determine a square.
This motivates students to discuss the properties of quadrilateral ABCD as revealed by dragging the figure. Is ABCD a "real" square? Which polygons are real squares? By manipulating the figures and identifying similarities and differences, students pay more attention to the properties and come to a deeper understanding of how a square is different from other quadrilaterals. In the context of a Sketchpad activity, the act of summarizing requires students to decide which of the behaviours they have observed are important and which are not.
For instance, in an activity comparing the geometric transformations of translation sliding , rotation, and reflection, students summarize first by examining all three transformations applied to the same preimage object. In the process, they deepen their understanding of the transformations they have been studying. Although virtual manipulatives such as dynamic geometry constructions were not specifically part of the studies summarized by Marzano et al.
In the United States, there is an ongoing effort to reform the teaching of mathematics, exemplified in the publication Principles and Standards for School Mathematics National Council of Teachers of Mathematics, NCTM , p. These representations can help students form compelling mental images of the mathematics they are studying, enabling deeper understanding and better retention. Students begin with a point between 0 and 10 on the number line, and estimate its value. In this instance, they might say it appears to be halfway between 6 and 7.
Students then press a button to zoom the portion of the number line containing the point in order to see it more clearly. First the part of the number line containing the point drops down, as on the left, and then it expands to show more detail. Students again estimate the number. At the conclusion of the activity, they can ask to see the actual location of the point expressed numerically.
The representation entailed in zooming the number line relates to and reinforces the meaning of the representation as a string of digits. In another activity, students can explore the connection between the three-dimensional view of a cube and the two-dimensional representation of its net.
Their task in the diagram on the left is to draw segments on the cube to show the pattern that should appear on each face based on the patterns shown on the net. Once they finish, they can press a button to wrap the net around the cube, resulting in the partially-completed animation shown on the right. Many teachers prefer to have two or three students work together on an activity, finding that the small group promotes mathematical discourse and helps students learn from each other and develop a sense of self-reliance.
Two key conclusions from the research are these: 1. Organizing groups based on ability levels should be done sparingly. Cooperative groups should be kept rather small in size. Marzano et al. The value of mixed- ability groups quickly becomes apparent as all the students benefit from the process of teaching and learning from each other. The value of small groups is clear as students have more opportunity to interact directly with the software.
The first student then tries to match the slope measurements with the lines, as in the sketch shown below on the left.
In this instance the first student has matched three of the measurements correctly and gets three points. Then the students trade places to give the second student a chance to match the slope measurements with the lines.
Feedback should be timely. Feedback should be specific to a criterion [as opposed to norm-referenced]. Students can effectively provide some of their own feedback. Such immediate feedback is certainly timely, and also has the advantages of being criterion- referenced, of coming from a source other than the teacher, and of being non-judgmental. When students work in pairs or small groups, additional feedback comes from other group members—also a particularly effective kind of feedback.
The student receives immediate feedback as the rabbit goes beyond the target, with no need for the teacher to intervene, and the image makes the required corrective action easy for the student to determine: Because the rabbit actually hit the target but continued on, the number of jumps was too great. In another example, calculus students can begin to learn about antiderivatives by constructing a slope probe: a short segment whose slope is determined by a given function.
The figure on the left shows the trace left by a student dragging such a probe in the direction of its slope a slope which changes according to the value of the given function to trace out the approximate antiderivative of the given function.
The probe can be seen at the right end of the trace. During the dragging process, the slope of the probe gives the student constant feedback as to the direction of the antiderivative, and the thickness of the trace gives the student feedback as to the accuracy with which they are following the correct direction. From the research, here are some useful tips for teachers: 1. Hypothesis generation and testing can be approached in a more inductive or deductive manner.
Teachers should ask students to clearly explain their hypotheses and their conclusions. In inductive hypothesis generation, students manipulate the sketch to generate a large number of cases and use their direct observations to form a conjecture. In deductive generation, students consider what they already know about the mathematics embodied in a sketch and form a conjecture based on that knowledge. In either case students go on to test the conjecture in the same sketch or in a different sketch.
Properly used, the generation and testing of hypotheses leads students to see the importance of presenting logical arguments for their conclusions. Seeing the value of and feeling the need for proof is an important consequence of hypothesizing and testing.
A student has positioned the two red markers to add two secret numbers, with the sum shown below, also in code. The student drags the markers to different positions, observes the sum, and uses the observations to makes hypotheses. Additional dragging is required to test the hypotheses, and the student continues generating and testing hypotheses until she has broken the entire code.
By playing multiple games and improving their strategies, students improve their ability both to generate hypotheses and to test them. Crack the code. They construct the triangle and one exterior angle, measure the exterior angle and the remote interior angles, and form a conjecture about how they are related.
They test their conjecture by performing a calculation and the dragging the vertices to vary the angles. Finally, they do a rotation and a translation of the original triangle that suggest the path to a proof.
Various studies point to the kinds of cues and questions that are most effective: 1. Cues and questions should focus on what is important as opposed to what is unusual. Questions are effective learning tools even when asked before a learning experience. The questions presented in activity worksheets, and the questions teachers use both with individual students during the activity and with the entire class in a summary discussion, should tend toward an appropriately high level. Teachers often get impatient and either call on the first student to volunteer or answer a question themselves if no student volunteers quickly.
This is usually a mistake; students need time to think about a question and formulate their own answer. Providing this wait time will elicit better answers from a wider variety of students, and will make it possible for those students who are not called on to compare their own answer with the answers given by other students.
An effective related strategy is to call on several students to answer a question in turn, allowing each to express the answer in their own words. The activity Cartesian Graphs and Polar Graphs provides an excellent opportunity for teachers to use this strategy. First, make a wild guess about what it will look like, and write down your guess. There is growing sentiment that classroom teachers … are almost impervious to change….
We believe that this is an overly pessimistic view not only of staff development, but of the profession of teaching in general. We agree, however, that substantive change is difficult. Busy teachers who have been doing things the same way for a fair amount of time will have many valid reasons for not trying a new strategy. What is clearly required to alter the status quo is a sincere desire to change and a firm commitment to weather the inevitable storms as change occurs.
The adoption of GSP and GSP activities into the Malaysian mathematics curriculum presents a unique opportunity for teachers to consider using new instructional strategies to accompany the introduction of new instructional technology.
When teachers are trained to use GSP activities, they can also be trained in how to use the most effective instructional strategies with this new instructional tool. In conclusion, Sketchpad activities provide us with a unique opportunity both to change the way students learn mathematics promoting deeper learning, better retention, and a sense of the excitement and beauty of mathematics , and also to change the way teachers present mathematics to their students taking advantage of similarities and differences, summarizing, nonlinguistic representations, cooperative learning, effective feedback, generation and testing of hypotheses, and high-level cues and questions.
Pickering, D. J, and Pollock, J. Soon after I began my teaching career, personal computers also made their introduction to the classroom. It is interesting to look back over that time and, in particular, to ponder what we have learned from both classroom research and the wisdom of practice concerning the use of technology as an aid to learning.
From my perspective, as classroom teacher, researcher and academic, it is possible to make some fairly well-supported and sensible statements at this point in time concerning good teaching and learning, the teaching and learning of mathematics, and of algebra in particular. It is then possible to relate these to the appropriate and effective use of technology for the learning of algebra in a meaningful way. Students learn best when they are actively engaged in constructing meaning about content that is relevant, worthwhile, integrated and connected to their world.
Students learn mathematics best when a. They are active participants in their learning, not passive spectators; b. They learn mathematics as integrated and meaningful, not disjoint and arbitrary; c. They learn mathematics within the context of challenging and interesting applications.
Students learn algebra best when o It is not presented as meaningless symbols following arbitrary rules; o The understanding of algebra is based upon concrete foundations, with opportunities for manipulation and visualisation; o Algebra is presented as a vital tool for modeling real-world applications.
And the role of technology in the process? Good technology supports students in building skills and concepts by offering multiple pathways for viewing and for approaching worthwhile tasks, and scaffolds them appropriately throughout the learning process. They may also be used to introduce the symbolic notation of algebra in a practical and meaningful way.
Two major limitations may be identified with the use of such concrete materials in this context: there is no direct link between the concrete model and the symbolic form, other than that drawn by the teacher — students working with cardboard squares and rectangles must be reminded regularly what these represent.
Of even greater concern, these concrete models promote a static rather than dynamic understanding of the variable concept. Both these limitations may be countered by the use of appropriate technology to scaffold and support the tactile forms of these models. After even a brief exposure, students will never again confuse 2x with x2 since they are clearly different shapes.
The introduction of the graphical representation is too often rushed and much is assumed on the part of the students. Like the rest of algebra, the origins of graphs should lie firmly in number.
The use of scatter plots of number patterns and numerical data should precede the more usual continuous line graphs, which we use to represent functions. We now have tools which make it easy for students to manipulate scatter plots and so further build understanding of the relationship between table of values and graphical representation.
Once we have built firm numerical foundations for symbol and graph, our students are ready to begin to use algebra — perhaps a novel idea in current classrooms! The real power of algebra lies in its use as a tool for modeling the real world and, in fact, all possible worlds! Teaching algebra from a modeling perspective most clearly exemplifies that approach, and serves to bring together the symbols, numbers and graphs that they have begun to use.
The simple paper folding activity shown – in which the top left corner of a sheet of A4 paper is folded down to meet the opposite side, forming a triangle in the bottom left corner — is a great example of a task which begins with measurement, involves some data collection and leads to the building of an algebraic model. Students measure the base and height of their triangles, use these to calculate the area of the triangle, and then put their data into lists, which can then be plotted. They may then begin to build their algebraic model, but using appropriate technology, may use real language to scaffold this process and develop a meaningful algebraic structure, as shown.
Returning to the graphical representation, students may now plot the graph of their function, area x , and see how it passes through each of their measured data points — convincing proof that their model is correct — and usually a dramatic classroom moment!
This is powerful, meaningful use of algebraic symbolism. The building of purposeful algebraic structures using real language supports students in making sense of what they are doing, and validates the algebraic expressions which they can then go on to produce. Able students should still be expected to compute the algebraic forms required and perhaps validate them using a variety of means.
This use of real language for the definition of functions and variables has previously only existed on CAS computer algebra software and even there only rarely been used. The new TI-Nspire is a numeric platform non-CAS and so allowable in all exams supporting graphic calculators, but it supports this use of real language. Using CAS we can actually display the function in its symbolic form, and then compute derivative and exact solution, arriving at the theoretical solution to this problem.
The best fold occurs when the height of the fold is 7 cm, exactly one third of the width of the page. Using non- CAS tools, this same result may be found using the numerical function maximum command, or by using numeric derivative and numeric solve commands. Scaffolding is an important aspect of meaningful algebra learning, and computer algebra offers some powerful opportunities for such support. The real challenge in using CAS for teaching and learning, however, lies in finding ways to NOT let the tool do all the work!
Certainly these tools may readily provide automated solutions to extended algebraic processes, but there seems to me to be greater value in having the students do some or all of the work, and having the tool check and verify this work.
Such applications of these powerful tools remain yet to be explored. Conclusion Why do I like to use technology in my Mathematics teaching? Because, like life, mathematics was never meant to be a spectator sport. Outcome-based education is a system of education that focuses on the product rather than the process.
Hence, for two classes of students learning Calculus, they are given the task of working in groups of five to solve a set of application problems that are assigned to them at the onset of the semester.
Towards the end of fourteen weeks of study, these students are expected to display their work in a learning portfolio and do a short presentation, describing how the problems are solved.
The main purpose of providing the questions at the beginning of their learning process is for them to know clearly the learning outcomes expected of them at the end of the semester. The objective of this research is for the author to share her experience of implementing such measuring instruments in the teaching and learning of Calculus which may well be adapted by teachers or lecturers teaching mathematics in secondary schools or institutions of higher learning.
This technique may also be recommended as an alternative to the traditional pencil and paper method of assessment in the teaching of mathematics. The learning reflections described by the students involved in the study not only show the enjoyment that they value but also contribute to motivate their peers as well as the facilitators in their learning process.
Keywords: Learning outcomes, Calculus, Problem-based learning, Measuring instruments. Most mathematics textbooks recommended for schools state the learning outcomes for each chapter. The institutions of higher learning are concurrently emphasizing a similar approach.
This outcome is linked to the UTP Engineering Foundation program outcomes, one of which is to be able to apply knowledge of science and mathematics in problem solving, apply analytical skills to interpret and solve problems, communicate effectively in English and practice behavior that reflects good values in the learning process.
In writing reflections, students express their experience in learning Calculus throughout the semester. Research into metacognition indicates that the probable value of equipping students is for them to reflect on and even take control of their learning .
However, this type of assessment is yet to be a common practice in UTP. A committee of colleges, led by Benjamin Bloom, identified three domains of educational activities; Cognitive: mental skills or knowledge, Affective: growth in feelings or emotional areas or attitude, and Psychomotor: manual or physical skills .
On day one of the semester, each student is provided with hardcopies of the Engineering Mathematics II EMF Calculus learning outcomes, course syllabus, schedule for tests, quizzes and assignment due date.
A separate handout on the expected assignment is also issued to provide clear guidelines of the requirements, and scoring criteria for the assignment.
For this paper, the author focuses on the assignment that comprises of the problem solving which will be included in the development of the learning portfolio. Six learning outcomes of the UTP Calculus course are documented and amongst them are that at the end of the semester, the students should be able to apply the techniques of differentiation and integration in solving word problems.
There forth, a set of nine word questions are prepared for which students select five. The problems are given to the students at the onset of the semester whilst the students have yet to learn and be equipped with the knowledge and skills before being able to solve the problems. This is with the intention of exposing the objectives of learning the course to students so that they are made aware of the reason for doing the course.
The assignment is a group work, so the one hundred and forty four students must be designated to their respective groups. The designation is to be at random and not biased. Students will be expected to work with their course mates within the same program, some of whom they may have never known before. Each group is thus numbered and elects a team leader.
With the detail instructions dispensed to each individual student, the groups work on five word problems previously selected. The team leader manages and encourages the team members to working together and contributing to the group. A criterion-based scoring rubric developed by RubiStar , is made transparent to the students, so that they know exactly how they will be graded.
At the end of fourteen weeks of study, each group submits their work in a learning portfolio and prepares for a short presentation observed and assessed by the lecturer or facilitator, witnessed by their team members.
For this paper, discussion will focus on the reflections of the problem-based learning. The problems assigned to the students cover the topics that are done towards the end of the first half of the semester and those in the second half of the semester. Rates of change, optimization and solids of revolution are the main areas covered in the problems to be solved.
Having gone through the brain-storming sessions, research, and finally solving the problems as a team, the students are then expected to express their experiential learning in writing. For this piece of work the groups have a choice of individual write-up or a collective one. Students are given two weeks to choose a suitable time for them to do a short presentation. In the presentation, each student is given five minutes to explain what they need to do to solve a particular application problem.
Each student presents his or her solution independently without being assisted by the other team members. The score obtained during this presentation is rewarded to the respective student.
The marks obtained in the evaluation of the portfolios are awarded to the respective groups. The evaluation of the CLP and individual presentation is based on the neatness and organization, explanation, mathematical terminology and notation, mathematical concepts, and mathematical reasoning. The total score obtained in doing the presentation is awarded to each deserving student according to their respective performance.
Each student is provided with a copy of peer evaluation form that was to be filled during a class session and handed directly to the lecturer or facilitator. Students are thus randomly selected to team up with their colleagues whom may or may not be familiar. They respond well with this method of team formation. It is also interesting to note the population breakdown according to gender.
The number of female students in both programs is less than the male students. Table 1 shows the breakdown of student combination in terms of gender. The PE group which has 70 students comprises of a much smaller percentage of only Each team successfully solves five problems which have been selected from a pool of nine also by ballot draw.
The individual presentations are done in the presence of the lecturer as the examiner and the team members. Table 2 displays the average scores obtained by students in doing the CLP and the presentations. Table 2. For the EE group, the average score for the portfolio development is 4. Table 3 Quotations. Reflections by Students.
Thus teamwork is applied to EE complete this assignment. In addition, students become closer among each other…every 5 females student is given full commitment to complete tasks given..
For example, an engineer must know how to calculate the amount of material males needed to yield maximum results. He can calculate this by using optimization method he has learnt in Calculus. Working in EE groups is a good way to provide us with the opportunity. We also EE discover about how useful and essential mathematics in our daily life.
By learning this area of mathematics, we can relate the problems of our 4 males 1 daily world with calculus, and use it to solve problems. These skills can be vitally useful female for us in the future when we do our job as engineers. Besides that the knowledge that we gain now from Calculus can be used in 1 our future career as Differentiation and Integration plays a very important part in a life of PE a Petroleum Engineer.
We can improve our learning experience by helping our friends 4 males 1 understand the topic that they have difficulties understanding. Usually if we do any of female the exercises, we will always use the same method to solve those problems without looking for other methods. We also learn to cooperate PE with our course mate in order to complete our assignment and to excel in this subject.
This course also teach us how to manage our time wisely as this course is a heavy course and requires a lot of time to master it. A sample of such work is taken from four teams of the EE students and another sample of four teams picked from the PE students.
The students are able to value the course as a necessary tool in their daily lives apart from doing it for the sake of obtaining grades and gather credit hours for the course. The difficulties that they encounter while trying to find solutions to the problems have to be dealt with on their own. Students need to really know what they do in solving the problems before being able to do a good presentation and be able to respond well to questions posed by the examiner.
From the students reflections, they have amongst others, indicated that with this problem- based learning, a lot has been learnt: teamwork, commitment, ability in applying theory to practical life, opportunity to explaining to others, self discipline, improve learning, relevance and importance of mathematics, what it means to be hardworking and creative and time management.
To ensure that this type of assessment works and obtain full cooperation from students, careful planning must be done early, preferably before the start of the semester where the instructions for the CLP are clearly provided to students.
Above all, the problems selected for the purpose must serve to measure the learning outcomes. Thus the learning outcomes are to be the main focus for both lecturer and students in the teaching and learning of the course. The criterion-based scoring rubric is made available at the beginning of the semester so that students are mentally prepared of what is expected of them.
At the end of the grading period, the PE and EE students in this study have managed to obtain all the solutions to the word problems correctly by applying their knowledge on differentiation and integration techniques.
In conclusion, the learning outcomes have been achieved. Accessed 1 Januari The University of Kansas. Heterogeneous classroom defined in this paper is classroom in which students have a wide range of previous academic achievement, varying levels of tool proficiency and diverse learning styles. Quantitative data from a sequence of research studies conducted over a period from until on calculator mediated learning in mathematics were gathered and briefly reported. Having the knowledge of such diversity, it is hoped that more effective technology-integrated mathematics curriculum can eventually be developed to help more students to learn about pattern recognition and apply appropriate quantification using mathematics with fervour.
Stacey affirms that the judicious use of GC is crucial in harnessing the benefit of the technology. Hong and Thomas claim that proper use of the tool can lead to a more powerful and flexible understanding of the mathematical concept in Calculus. Penglase and Arnold contended that while GC can encourage the development of mathematical conceptual images, it may at times leave the students with incomplete understanding of the concepts.
They attested that the effectiveness of GC depends on the freedom and support available to its users. Martin and Pirie acknowledge that the values of computer or calculator as a teaching tool are dependent on how it complements the total learning environment. They sustain that in order to maximize the power of the technology teachers must know how to discern when the students are ready for personal teaching and in return provide them with appropriate teaching interventions.
Inevitably, the advent of GC technology has prompted the GC manufacturers and some mathematics educators to advocate the educational utility of GC in exploring mathematics and enhancing the teaching and learning of the mathematics content. Similarly, it is also commendable to study on how do GC technology benefit students from different achievement levels and of diverse learning styles.
In addition, this paper also reports the findings on the relationship between brain hemisphericity and tool proficiency. What is more challenging is to ensure that all students in a heterogeneous classroom have equal access to the tool and actively participate in the interactive learning activities. Heterogeneous classroom in this paper is defined as classroom in which students have a wide range of previous academic achievement, varying levels of tool proficiency and diverse learning styles.
Effective implementation of GC-integrated teaching in a heterogeneous classroom is presumed to be heavily dependable on the learning attitudes and perceptions from this wide range of students. Duffy and Cunningham articulate that tools mediate learning and the participants in the culture appropriate the tools to meet their goals. In this pretext, research studies undertaken in this paper concur that when we engage the GC technology, our focus should not solely concentrate only on what the tool can do, but also on how and what the students do with the tool and their perceived importance of the tool.
In the aspect of brain hemisphericity and learning styles, the research studies reported in this paper acquiesce with the cognitive neuroscientists that right-brain and left-brain dominant people exhibit different preference of learning or learning styles. According to Felder and Spurlin , learning styles can be classified according to different strengths and preferences in the ways students take in and process information. Therefore, the subject of interest in this study also includes the issue pertaining why students who receive the same instruction, knowledge, and skills on the use of GC performed differently in the learning task.
Below are the research questions: 1. Is there a difference between male and female students in their confidence in using GC to learn mathematics MatGC? The population of this study consisted of respondents who were taking mathematics course taught with GC in the three local institutions of higher learning. A random sample of respondents aged ranging from 19 to 26 years old was chosen. The respondents consisted of 64 males and females.
All of them had no previous experience in using GC. The instrument used in this study was a item survey questionnaire. All items were 5-point Likert scale ranging from 1 strongly disagree through 3 neutral to 5 strongly agree.
The 45 items measuring confidence in using GC to learn mathematics MatGC were adapted from an instrument called the Attitudes to Technology in Mathematics Learning Questionnaire Mtech which was developed and validated by Fogarty et al. The Cronbach alpha for MatGC was. Therefore, male and female students in the study sample did not show any statistical difference in their confidence towards using GC to learn mathematics. Table 2a. Respondents with grade A showed the highest mean score of In other words, it can be concluded that students with better grades in the Additional Mathematics are more confident in using GC to learn mathematics.
Table 3. These items were adapted from an instrument called the Attitudes to Technology in Mathematics Learning Questionnaire Mtech developed and validated by Fogarty et al. All items are 5-point Likert scale ranging from -2 strongly disagree through 0 neutral to 2 strongly agree.
A mean score of more than 0. The reliability coefficient alpha was 0. Besides confidence in using GC to learn the mathematics course, students were also asked to evaluate their preferred learning style and choice in using GC in the learning process.
Deviation MatGC 1. This is to say that these students believed that GC can enhance mathematics teaching and the use of GC can enhance their learning of mathematics.
In other words, these students understood well that the tool is meant to help to amplify their routine calculation. Detailed discussion of the research finding can be found in Rosihan and Kor Study 3: Impact of the use of GC in the learning of Statistics In , a sample of 76 second year diploma in business students participated in this study. These respondents were non-mathematics majors but were required to pass Statistics paper in order to graduate.
All of them had no experience in using GC. Each student was given a GC during the lesson. The course contents include the one and two variables descriptive statistics, some principles of data collection methods and sampling techniques. The author conducted the whole course in twelve lessons. One lesson was two hours long and there were all together twelve lessons taught with the use of GC.
All items are 5-point Likert scale ranging from 1 strongly disagree through 3 neutral to 5 strongly agree. Cognitive Competence has six questions measuring attitudes about intellectual knowledge and skills when applied to statistics.
Affect has six questions measuring the positive and negative feeling concerning statistics. Values has nine questions measuring attitudes about the use, relevance and worth of statistics in personal and professional life. Table 5 below displays the total sum of scores for the six aspects before and after GC intervention. Table 5. N Mean score Asymp. Figure 1 shows the comparison of the scores before and after the intervention.
Comparison of mean scores before and after GC engagement It was found that after the GC intervention students in the study sample were generally more positive towards statistics SATS. They appreciate more about the knowledge and skills they learn in statistics cognitive competence , feel better about statistics affect and also regard highly the importance of statistics to their future values.
Their attitudes towards using GC to learn statistics STech had improved as well indicating that they favour the use of the tool in learning statistics. For the aspect of easiness, the higher the total score indicates statistics is perceived easier as a subject. In the study sample, the total score for Easiness was lower after the GC intervention indicating that students in the study sample found that statistics taught with GC is more difficult than before.
As for the different ability in the technological skills groups, Kruskal-Wallis test was used to test if the low, medium and high group in STech has any influence on the post-test and final score for Statistics. The result is shown in Table 6. Table 6. Sig Post-test Low 13 However, the low skills group scored the lowest in both test. Respondents who were confident in using GC to learn statistics were not necessarily the high achievers in the assessment for the study sample of 76 respondents.
Details of the results can be found in Kor A study was conducted in to examine the differences in brain hemispheric processing modes and learning styles among 44 undergraduates who undertake the specialized mathematics course using the GC. The purpose of the study was to explore the connection between brain hemisphericity, learning styles as well as confidence in using the GC.
Brain-Dominance Questionnaire and Index of Learning Style Inventory were administered to the respondents at the commencement of the course. The GC Confidence questionnaire was administered at the end of the course after students had mastered most of the GC skills. Thus a positive mean score indicates a favourable response.
Table 7 below describe the characteristics of learning styles outlined by Felder and Solomon Table 7. Types of learners and learning styles Types of learner Learning styles Active Retains and understands information best by discussing in group, applying it or explaining it to others.
Reflective Prefers to think about and work out something alone. Sensing Likes to learn facts, solve problems by well-established methods. Good at memorizing facts and doing hands-on laboratory work. Dislikes complications as well as surprises. Resents being tested on material that has not been explicitly covered in class. Doesn't like courses that have no apparent connection to the real world.
Intuitive Prefers discovering possibilities and relationships. Likes innovation and dislikes repetition. Good at grasping new concepts and is more comfortable with abstractions and mathematical formulations. Doesn't like courses that involve a lot of memorization and routine calculations. Visual Remembers best what is seen in pictures, diagrams, flow charts, time lines, films, and demonstrations. Verbal Get more out of words from written and spoken explanations. Sequential Tends to gain understanding in linear steps, with each step following logically from the previous one in a logical stepwise paths in finding solutions.
Deviation t 2-tail Left-brain However, t-tests indicated that there were no significant differences in GC confidence across brain hemisphericity as well as learning styles Table 8.
However, there was no statistical significant association between brain hemisphericity with active-reflective as well as visual-verbal learners. Furthermore, no statistical significant association between brain hemisphericity with gender, race, and program of study was reported. Table 9. Chi square test on brain dominance and learning style. Left-brain Right-brain Total Intuitive-sensing category Intuitive 2 4. Study 6: Brains hemisphericity, learning styles and confidence in learning mathematics with MAPLE In year , a survey was conducted on 28 students in a Calculus class enhanced with Maple software.
The Maple software was chosen instead of GC in this study as these students are required to learn Maple in their Calculus I as stated in the syllabus. The frequency distribution of the respondents classified under the eight learning styles across three brain groups is shown in Table Table In the contrary not all left brain learners agreed to this statement. Table 13 depicts the results of the breakdown to Question 8.
Percentage responses to Maple technology efficacy in relation to learning styles Question 8: I am not able to follow the Maple lab lessons. Hence, the result shows that students who are reflective, sensing, verbal and global find it more difficult to follow the Maple lab lessons. Also, students who are reflective, sensing, verbal and global find it more difficult to follow the Maple lab lessons. The result of this preliminary small scale survey from a small number of students however shows that left brain learners and also learners who are active and visual are more tool competent than learners from other categories listed as above.
As students engage in the rigorous learning tasks with GC technology they will subsequently develop ownership of their learning as well. Student learning styles are diverse in a classroom. Therefore, it is important that every technology-integrated mathematics lesson needs to be designed to address the needs of a variety of students to ensure an effective instruction.
It is also noted that students who were confident in using GC to learn mathematics were not necessarily the high achievers in the assessment. However, the results obtained pertaining brain hemisphericty and confidence in utilizing the GC is still inconclusive.
In , it was found that that there was no significant difference in GC confidence across brain hemisphericity. But the pilot survey in with Maple indicated that left brain learners have a higher Maple technology efficacy than right brain learners. This finding concurs with the survey on the Maple technology efficacy that students who are reflective, sensing, verbal and global find it more difficult to follow the Maple lab lessons. Having knowledge of the diversity, this paper concludes that the true challenge hereafter is to devise a technology-integrated mathematics curriculum that can eventually help the students to learn about pattern recognition and apply appropriate quantification using mathematics with much fervour.
Constructivism: Implications for the design and delivery of instruction. Jonassen Ed. Felder, R. Index of learning styles questionnaire. North Carolina State University. International Journal of Engineering Education, 21 1 , Forgaty, G. Validation of a questionnaire to measure mathematics confidence, computer confidence, and attitudes towards the use of technology for learning mathematics.
Mathematics Education Research Journal, 13 2 , — Gal, I. Monitoring attitudes and beliefs in statisticcs education. Garfield Eds. IOS Press. Hong, Y. Using computer to improve conceptual thinking in integration. Pehkonen Ed.
Lahti, Finland: Program Committee. Koh, T. Integration of Information technology in Singapore school mathematics curriculum. Yang, S. Chu, T. Ang Eds. NIE, Singapore. Kor, L. The Impact of the use of graphics calculator on the culture of statistics learning. Unpublished PhD thesis. Mariani, L. Brain-Dominance Questionnaire.
Making images and noticing properties: The role of graphing software in mathematical generalisation. Mathematics Education Research Journal, 15 2 , McCarthy, B. Mesa, V. The use of graphing calculaotrs in solving problems on functions. Penglase, M. The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal, 8 1 , Rosihan, M. Undergraduate mathematics enhanced with graphing technology.
Sadler-Smith, E. Cognitive style, learning and innovation. Technology Analysis and Strategic Management, 10, Stacey, K. Helping students learn to do mathematics well with technology. Ismail, Koh, H. Penerbit USM. Representation as conceptual tools: Process and structural perspectives. Utrecht, The Netherlands. Wu, D. CAS and teaching of Calculus. The use of technologies in education has become vitally important and necessary in the learning process today.
Students could learn better especially the more difficult subjects with the help of technologies. One such technology which is portable and relatively affordable is graphing calculators. The use of graphing calculator in mathematics education has become synchronous in daily classroom teaching and as an examination tool. A graphing calculator is a technological tool that can process the mechanical steps of procedure in solving mathematical problems but it does not provide the interpretation or explanation for the answer obtained.
Numerous researches have been conducted in the use of graphing calculator in the area of learning mathematics. However, very few researches have been done in the area of question designing by incorporating the use of graphing calculator. The purpose of this paper is to explore the area of examination questions designing by incorporating graphing calculators. The focus of this paper will be to share the ideas and experiences on how to design examination questions that incorporate the use of graphing calculators.
Students could learn better, especially the more difficult subjects with the help of technology. One such technology, which is portable and relatively affordable, is the graphing calculators.
Even though Graphing Calculators have been used in mathematics education since , its use in Malaysian mathematics education is still at the initial state. Only some programs at the higher institutes of education, both public and private, are already using graphing calculator.
The use of graphing calculator in teaching mathematics Mathematical Studies and Specialist Mathematics was introduced in with the old syllabus and in the following year, a new syllabus incorporating the graphing calculator was introduced. The Mathematical Studies syllabus consist of three major topics namely calculus, statistics and matrix. Whenever new technology is introduced in the education system, the teachers face numerous challenges.
Therefore, in order to successfully implement it, the first step is to provide sufficient product trainings especially on how to use the graphing calculator. These staff development trainings will equip teachers with the confidence to deliver in classroom teaching.
Experts in the field such as Professor Peter Jones will provide training. Since this kind of staff developmental trainings are mainly focused on the classroom delivery with the use of technology, teachers have trouble in setting the examination questions that incorporate the use of graphing calculator.
Most of the time the questions are based on the old curriculum where by students use graphing calculator just to do the long tedious step by step work.
Very few researches had been done in the area of question design and assessment that incorporate the use of graphing calculator.
In the constructivist method of learning, students actively build their own conceptual understanding instead of being passive learners and having teachers to transmit all the knowledge to them. The constructivist perspective of learning mathematics has two major goals for students; first, to help students to construct complex conceptual structures that would help them to deal with different problem solving situations, and second to develop them into self-motivated and autonomous mathematical thinkers Cobb, Learning is extremely appealing in the constructivist perspective as the students construct their own understanding and is very conducive to build strong problem solving skills.
However, the advancements in technology is directly influencing the concepts delivery in classrooms. The literature shows that educators are taking initial steps towards using technology as this would produce visual images, organize and analyze data and calculate mechanical computations faster. Technology today, is a device that can be used to help students to go beyond obtaining an answer and also to provide the opportunities for deeper understanding and thinking skills in learning mathematics.
The use of these technologies in mathematics education is demanding more from students and their teachers as they need to approach problems in different ways that now requires thinking and understanding rather then just number crunching Cates, ; A.
Since technology has taken the burden away from students, having to spend much of their time on algorithmic procedures to arrive at an answer, they now can channel the time and energy on interpreting the answer.
The incorporating of the technology in mathematics enables students to engage in higher order thinking and understanding about the result or answer and concepts relating to those numbers.
Now, students have to provide explanation, interpretation, draw conclusion, evaluate or communicate their answers. Students still need guidance from teachers on how to interpret and analyze the answer obtained from graphing calculator for them to gain meaningful understanding of concepts that they are learning. They are required to show complete step by step working where the emphasis is on getting steps correct.
When these kinds of questions are administered to the students with graphing calculator knowledge, they would do well and probably score full mark. This does not serve the purpose of the assessment and teachers cannot be proud of it. Therefore, the examination questions should be designed in such a way that they would be able to assess the ability of students to use graphing calculator effectively to arrive at the answer and able to evaluate the answer.
The examination questions should be focused on the higher order thinking skills. The questions should go beyond getting the answer. It should be able to test the general ability of the students to draw conclusions. Teachers should be creative in setting such questions. The other area that would produce good examination questions is by simulating real life problems. In such questions, students have to provide the meaning to the numbers they had obtained and interpret it according to real world.
The graphing calculators allow students to represent, analyze and explore functions, statistics, geometry, calculus and matrices. Students would build deeper understanding of a mathematical concept since less time is spent in performing the manual calculations. By reducing the time spent on learning and performing tedious paper-and-pencil arithmetic and algebraic arithmetic, the use of calculator allows students and teachers to spend more time in developing mathematical understanding, reasoning, number sense and applications Pomerantz, Therefore, examination questions should be set in such away to stimulate these values.
Type one is known as graphic calculator active where use of technology is necessary to obtain the answers. In graphing calculator neutral type questions, students have a choice of using graphing calculator or to use traditional the method. A similar kind of classification was suggested by Kemp, Kissane and Bradley based on the expectation on the usage of graphing calculator; where graphic calculators are expected to be used by some students and not others and not expected to be used.
However, Beckmann, Senk and Thompson suggest that in a graphing calculator environment, classroom assessment should contain well balanced questions from three categories. The teacher or group of teachers will set the questions, and try it out. A complete paper will then be passed on to the vetting committee. The committee would check for errors, and make corrections and suggestions to the setting committee.
Once the corrections and adjustments are made, it will be given to the subject coordinator for final checking and sent for printing. After each examination, all lecturers in the department would meet to discuss the marking scheme prepared by setter. The whole process would take a few weeks. There are three major topics in the South Australian Matriculation, calculus, statistic and matrix. The examination questions test all these three topics and students can use graphing calculators.
Therefore, the questions are designed in such a way that they incorporate the use of graphing calculator. However, in this paper, only the designing of matrices examination questions will be discussed. According to Hiebert and LeFevre , procedural skill and conceptual understanding are the levels of mathematical understanding. Procedural skill include the familiarity with symbol manipulation, formulas, rules, algorithms and procedures, where else the conceptual understanding is a connected network of knowledge that students are able to apply and link mathematical relationship to various problem situations.
Since students can use graphing calculator to do the procedural skills, the examination should test more on the conceptual knowledge Shore, The exam question could require students to make conjectures out of their answers. The students would be doing few of procedural work with graphing calculator to obtain the answer and finally they need to generalize to mathematical concepts.
At South Australian Matriculation, the examination questions are designed in such a way that they will mainly assess the conceptual understanding and a small fraction would be assessing the procedural skills. The assessing of procedural skills and conceptual understanding normally will be in the same question but on different sub-questions. Most of the time students can use their graphing calculator to arrive at their answers.
Students could use paper-pencil approach if prefer. However, if the questions require the students to solve by using paper-pencil approach, NO mark will awarded if they obtain correct answer using graphing calculator.
No specific instruction will be given in the question as to which approach the students should use to solve the problems. However, there will be enough hints or indication given in the question itself and students have to identify them. If the question requires students to solve 4 by 4 or higher order, then the students should use graphing calculator. Sometimes the examination question is designed such that students have the option between paper — pencil and graphing calculator approach. In this case, students have the choice to choose which approach.
However, using graphing calculator would be ideal. If the teachers want to test on the procedural skills and at same time allow students to use graphing calculator, a known matrix will be given see example 1 a i. To solve this question, students could use graphing calculator or do it manually and full marks will be awarded regardless of what approach they had used to arrive at the correct answer. Since this question can be solved using graphing calculator, only ONE mark will be awarded to the final correct answer.
If students do it manually, the traditional method of paper-pencil, they will be losing time as they also will be awarded only one mark. Question on the conceptual understanding require a lot of time to solve and it would be difficult to do with traditional paper-pencil methods as the student will be spending their time to show the step-by-step working. Hence, the use of graphing calculator would be ideal to address the problem as students could save on time.
Since less time is used in doing paper-pencil works, the question will normally test the higher order thinking skill. The question will lead the students from a very specific and simple concept to more general concepts. The examination questions would be very structured or guided so that student can identify a pattern by analyzing and evaluating their answer.
Hence, the students are able to demonstrate their ability to generalize. Sometimes, the sub-questions can be repetition of the same skill, but the results of these sub-questions will later require the students to generalize see example 1. Incorporation of graphing calculator into examination questions allow the teacher to assess the higher order thinking skills.
As discussed above, it saves time. Besides that graphing calculator allow teachers to ask exploratory and discovery type of questions see example 1. School Science and Mathematics, 99 8 , Cates, J. Understanding algebra through graphing calculators. Graham, A. Statistical nuggets with graphing calculator. Teaching Statistics, 21 3 , Greenes, C. The use of calculators on college board standardized tests.
Fey Ed. A Romberg Ed. Heid, K. Calculators on tests — one giant step for mathematics education. Mathematics Teacher, 81 9 , Hiebert, J. Conceptual and procedural knowledge in mathematics: An introductory analysis.
Hiebert Ed. Iossif, G. The graphing calculator as a teaching aid in statistic. Teaching Statistics, 21 2 , Kemp, M. Graphing claculators use in examinations: Accident or design? Australian Senior Mathematics Journal, 10, Pomerantz, H.
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CAS and teaching of Calculus. Jonassen Ed. This is a package that installs some necessary components that Zoom, and many other applications, require. Above we have mentioned some possible reasons behind the Zoom Error Code Figure 5. The Malaysian students do not pay a fee and are bonded by an agreement compared to their Australian counterparts who pay a fee.