Monday, April 20, 2009
ALTERNATIVE ASSESSMENT FOR ELEMENTARY SCHOOL MATHEMATICS
Theme: Sports commentary on school’s Annual Running Fiesta Special Event
Method of Assessment: Observation
Topics in Mathematics: Speed, Time and Distance
1.) To assess students’ interpretation of speed, distance and time in an alternative assessment method using observation.
- A video clip of the school’s running fiesta special event was recorded involving the best 2 runners in the school. Students doing the math assessment are given a graph on the running performance (distance vs time graph) of the two best runners in the school.
- Using the performance graph, students are required to interpret the performance of the individual runners and use the interpreted results to produce a simulated commentary on the race (assuming the role of a sports commentator). Students are also required to answer the key questions given below to generate interpreted results which further prompt them (as scaffolding to commentary activity) in producing the commentary and post-run performance summary.
- Equipped with the interpreted results, students do an individual audio recording while watching the video recording of the running event in the school’s computer lab, simulating how a sports commentator will comment on the running event..
- Students are graded according to their ability to:
answer the key questions correctly
use their interpreted results to produce a commentary
With the performance graph, students interpret the performance of the runners at different points of the event:
1. Who was the faster/slower runner after the first quarter of the distance (600metres)?
2. Who had the greatest acceleration/ deceleration in the race?
3. At which point of time/distance did the two runners ran neck-to-neck?
4. At what point of time/distance did the two runners run neck-to-to neck again? What happened?
5. What were their fastest speeds of the runners during the race?
6. What were the average speeds of the runners in the race? What are the differences between the fastest and the average speeds?
7. Did the fastest runner run with a more constant speed or with more variations in speed throughout the race than the other runners?
- Journal Writing: Students write a reflection on their learning journey to identify their key learning points. (e.g. can I use the same method to benchmark my own running performance?)
Reflection on how this alternative assessment will help students on the topic on speed:
This mode of assessment helps pupils to associate speed to daily life. Maths problems on the topic of speed usually include questions involving transportation, running or walking distance. Pupils might not be able to understand how fast or how slow the speed of a particular person or object is. They may not even know that everyday, their life involves speed. Through this mode of assessment, pupils will also understand why the formula for speed will be as such instead of just memorizing a formula. Furthermore, this mode of assessment is interesting as pupils take on the role of sports commentator. Instead of just calculating the speed of an object or a person, taking on the role of sports commentator allows them to predict whether someone will win a race from what they observe. They can also see how constant speed is being put to play. This mode of observation also caters to diverse needs of the class for example pupils who are more verbal.
Wednesday, February 4, 2009
Alternative assessment methods are more successful in learner-centered environments, where students are able to evaluate their own learning, and learn from the evaluation process. It can be conducted within or outside classrooms, and depending on the tasks the duration could range form days to weeks to even months or years.Some features that alternative assessment includes are: Assessment is based on authentic tasks that demonstrate students’ ability to attain goals, students get an opportunity to assess themselves and their peers, students are being assessed over a period of time.
Alternative assessment techniques for Maths include portfolios of childrens’ work from the time of introduction of a concept to the time of its ending, journals writings on Problem solving to evaluate students’ ability to communicate Mathematically, which also helps students to develop skills and strategies for solving new and difficult problem sums, Self-assessment where students use materials to model 3-D plane figures, Checklists to record leaning tools and strategies, reflections on students’ learning, using manipulatives like place value blocks and a place value mats, Maths trails, Interviews and many more. One disadvantage of this mode of assessment may be time factor, where there may be insufficient time to carry out assessment as planned, or there may be lack of resources to carry out the tasks.
Bearing the aim of alternative assessment and the time factor for assessment in mind, our group had decided to have the Maths Webquest as our alternative assessment. This will be used for the upper primary to teach graphs. The questions in the webquest will be designed and posted by the teacher every week, to test on the subtopics that they have learnt for that particular week. This will continue every week until the whole chapter has been taught.Students will have to do the online questions at the end of each week.
The questions designed by the teacher will be based on the current issues like the number of foreign talent in Singapore or the number of retrench cases in banks and so on. This taps on NE and also incporates English and Maths. Students' interest level will be maintained and they will be more aware on the current issues too. On top of that, teh webquest was chosen becasue students will be more engaged and interested due tothe use of IT. The assessment will be over a few weeks. Since there may be insufficient time to test students on the entire chapter,bearing in mind to touch on all objectives, this may be a better mode of assessment. Students will be assessed progressively over a few weeks, and each week at most 2 objectives will be tested. This will be easier for the teacher to assess and also keep track on students' understanding, before proceeding to the next level of teaching of the topic.
We have discussed that the teacher will prepare a rubric for the assessment. The same rubric will be used each week to keep track on the performance. For example if 10 questions are posted,and if students obatin 1-2 marks, they will be classified under the "beginner's" stage, if they obtain 3-5 marks, they will be classified under the "deveoping" stage, and if they obtain 6-8 marks thay will be under the "accomplished" stage and finally if they score 9-10 marks they will be under the "exemplary" stage. This rubric helps the teacher to gauge students' performance easily, and enblaes the teacher to alter the next lesson acccording to students' level of understanding.
Monday, February 2, 2009
AA responds to the individual learning styles and intelligences of pupils. It sould enable teachers to measure how far students have mastered a topic or a process skill over a period of time. AA provides students with the challenges that would prepare them for the real world outside their clasrooms and textbook context. It focuses students' learning more towards the process, development and evaluation of a problem or task rather than targeting at the final solution. Multiple forms of intelligences are also applied in AA to meet the different learning needs of students.
An Example of a Lesson:
At the end of the lesson, pupils should be able to solve mathematical problem sums through visualisation.
- Pupils to recall formula for area of semi-circle and a rectangle.
- Teacher to tell pupils that they are ready to solve the given problem sum.
Doing so motivate as well as stimulate students to come out with a solution.
- Teacher to introduce problem sum
Development 1: Sieving prior knowledge
- This lesson provides opportunities for both group work and individual.
- In groups, pupils are required to discuss and write out their thoughts or draw out their solution.
- Questions crafted in worksheet incorporate Multiple Intelligence (Visual Spatial intelligence and Logical Intelligence).
Development 2: Use of concrete materials to develop ideas
- Pupils are given manipulative of the figure to manipulate with.
- Concrete materials allow students to relate better to the question and allowing students to act out their thoughts to find out if their solution is feasible.
Development 3: Developing solution to problem sum
- After the 30 minutes group discussion, teacher to go through solution with the class.
- Pupils are asked to come up to the white board, using their manipulative to present their solution.
The use of students’ own manipulative allows personal involvement in the problem sums thus encouraging them to work for a solution.
- Teacher assists the teaching of students by asking ‘Why” questions.
E.g. Why did John mention that we need to find the area of the small semi-circle, medium semi-circle and triangle in order to find the area of the whole figure instead of the small, medium and large semi-circles?
- The questioning processes enable teacher to access students’ understanding of the lesson through their replies to the “why” question. It also allows teacher to clarify doubts, sort students’ thoughts as well as identify misconception.
Consolidation and Conclusion
- After discussion, pupils are asked to attempt another question in the worksheet individually.
- Question is crafted in such a way that students could apply what was taught earlier.
- This emphasizes and evidences the learning process as an active demonstration of knowledge which is one of the characteristics of alternative assessment.
- Marks allocation provided on the worksheet allows students to focus more on the process rather than the answer.
- Through pupils’ submitted worksheet, teacher is then able to assess individual understanding. Pupils are assessed on the process steps they used to solve the problem sum instead of their answer.
- Teacher to provide manipulate for the question if students fail to grab the skill of visualization.
Rubrics for the Task
According to Hancock, alternative assessment is an ongoing process involving the student and teacher in making judgements about the students’ progress using non-conventional strategies. It differs from traditional assessment where conventional strategies like students selecting a response from a given list, such as multiple-choice, short answer or true/false questions. Instead it involves assessment in which students create a response to a question or task.
Examples of alternative assessments include:
· Essays or mathematics journal writing. (E.g.: Writing to explain to their peers how to derive at the answer or teach a concept)
· Oral presentations
· Practical Skills
Features of Alternative assessment:
The assessments are usually based on authentic tasks where students can relate to and demonstrate their ability to accomplish the learning goals.
Teachers and students focuses on the discussion that is taking place, not on right and wrong answers, hence giving students opportunity to participate actively in their learning process.
Students will take ownership of their learning and set criteria for successful completion tasks.
Students’ meta-cognition skills would be developed as they have opportunities to assess themselves as well as their peers.
An alternative assessment our group will be sharing is on Portfolio Assessment. Portfolio Assessment provides avenue for creating environments for students to reason, communicate, and problem solve. Teacher would be able to observe and monitor how students are developing these mathematical skills in their lessons and how much they are actually learning. This can be done because a Mathematics Portfolio would include
Problems posed by students which are being discussed as a class including the solution the problem posed.
· Draft, revised, and final versions of student work on a complex mathematical problem.
· A photo or sketch made by student of student's work with manipulatives.
· Papers that show the student's correction of errors or misconceptions.
· A summary of the description by the teacher of a student activity that displayed understanding of a mathematical concept.
· Mathematical journals
· Diagram representations of certain concepts
Benefits of Portfolio Assessment
With the inclusion of the above in a students’ portfolio, learning Mathematics makes more sense as students would be able to make clear linkages between the activities and work they did and its relevance for future references.
The portfolio also creates more opportunities for learning to take place as there are concrete evidences to be used as a basis of a class discussion. Teacher would be able to model good examples and clear misconceptions through the compiled pieces in the portfolio.
The portfolio also includes journal entries which provide opportunity for students to check for misconceptions and make use of the visual diagrams drawn to further understand a concept. It also explicitly defines the objective of a lesson which enables students to check whether they have learnt and understood the concept.
In conclusion, Portfolio Assessment provides a platform for students to recognize their strengths and weaknesses and thus, providing more opportunities for them to learn from their mistakes and misconceptions. It is also helpful for the Mathematics teacher in monitoring the students’ progress and understanding of the mathematical concepts taught. Teacher would be able to provide more focused and direct assistance in the areas where students are weak in. these are certain things which the traditional assessment is lacking in and thus, portfolio assessment plays a significant role in mathematics teaching and learning.
What is alternative assessment?
With the founding of Multiple Intelligences by Dr. Howard Gardner, professor of education at Harvard University in 1983, the traditional “pen-and-paper” examinations are known to focus mainly on the linguistic and logical-mathematical intelligences. Schools often neglect students who are gifted in the other 6 intelligences, namely :
- Spatial intelligence ("picture smart")
- Bodily-Kinesthetic intelligence ("body smart")
- Musical intelligence ("music smart")
- Interpersonal intelligence ("people smart")
- Intrapersonal intelligence ("self smart")
- Naturalist intelligence ("nature smart")
Therefore, alternative assessment is a more viable method of assessment for students to excel in the other intelligences. Alternative assessment includes :
In fact, any type of authentic assessments that move away from the traditional “end-of-year” examinations can be considered as alternative assessments.
Example of Alternative Assessment
Our group has decided to explore more on the usage of checklists in alternative assessment. In fact, we found out that checklists are easier to track students' progress relating to group activities compared to using rubrics.
To show how checklist is used in the classroom, we have created a visualisation activity for the students.
In short, visualisation is the ability to manipulate shapes and objects, either in 2-dimensional or 3-dimensional, in their mind. This ability is useful in topics such as Geometry, Tesselations and 3-dimensional objects.
In order to have an idea of how well your visualisation skill is, try this simple activity.
" The three figures below show a sequence by which a piece of paper has been folded. The last figure shows how this folded paper has been cut.
Which pattern (1-4) most closely resembles the unfolded form of figure C? "
- adapted from Paper Folding and Cutting Puzzles
We know that checklists are often used for observing performance or behaviour in order to keep track of a student's progress or work over a period of time. They are also used to determine whether students have met established criteria of a certain task or activity.Checklists can be useful for classroom activity assessment because they are easy to construct and use. We are also able to align closely with task objective.
In order to construct a checklist for our activity, we had to identify the different parts of a specific communication task and any other requirements associated with it.
Our group has identified four main objectives of the classroom activity:
As this is a group activity, the component of teamwork is essential to learn if students are able to work well in groups, communicate ideas and learn from one another.
The main objective of our activity is to Find Area and Perimeter of Figure Using Spatial Visualisation Skill. As such, we have come up with our checklist to assess if students are able to grasp this concept.
Objective: Find the area and perimeter of the given figure using Spatial Visualisation skill.
Arrangements: Students in groups of 4.
Task: Students are given a figure (as per below) that is made up of a semicircle and a rectangle. They are to find the area of the shaded part given only the length of the figure. Answers are to be given to 2 decimal places.
On the visualiser, the teacher will display the task.
The aim of this activity is to assess students' competency in visualisation. In this case, we are assessing whether students are able to solve the problem by first identifying the different basic shapes that made up the figure and using this to help them solve the problem with or without using the manipulative. As students start working on their task in finding out the area and perimeter of the shaded parts in the composite figure, teacher will walk around the class and assess each student using the checklist provided above.
From the checklist, we can gather if students are:
1) Able to break the shapes to simpler shapes : Under Presentation, to see if students are able to make Mathematically relevant observations and/or connections and be able to use a strategy that leads to a solution of the problem.
2) Able to work the problem out eventually without the aid of manipulatives : Under Accuracy, if appropriate concepts are used and the correct procedure are applied.
3) Able to communicate their method effectively : Under Communication and Presentation as a whole.
4) Able to work collaboratively : Under Teamwork as a whole.
Being able to break up the figure into basic shapes is the first step towards solving the problem. Once students are able to do so, they can then proceed to find the area and perimeter of the shaded parts. There are more than one ways or method to solve the above problem. Students are free to choose how they want to solve the problem. They will then share their methods with the whole class during the presentation.
Sunday, February 1, 2009
Alternative assessment techniques consist of observing students working in class, asking questions, and listening to their answers. They involve student presentations, extended projects and performance tasks. The creation of portfolios and written journals that show and describe students' work are very useful techniques. Other less frequently used but viable techniques are the use of interviews, conferences and student constructed tests.
One of the techniques which our group wish to explore and share will be Questioning.
1) How can this technique be used effectively?
It can be used to assess problem-solving competence by asking students questions related to the four-step problem-solving plan:
Such kind of questioning should uncover what the student is experiencing difficulty in, as well as demonstrate the kinds of questions he should ask himself. Listening to the students' descriptions of their thinking and observing their written work provides a more accurate assessment of problem-solving skills than simply grading answers on tests.
In addition, questioning and observing students in a problem-solving context can give a teacher an in-depth understanding of a student's ability to think, communicate ideas and make connections.
The teacher may lead with a moderately easy question such as the following:-
"How would you find the unit price of meat, if 3kg cost $15.85?"
A correct response may be followed by more probing and demanding questions such as,
"How would you find the unit price of meat if 1.6kg cost $8.45?
An incorrect response may be followed by probing but less difficult questions such as
"What is the price for 1 kg of meat if 2kg costs $10?
"How did you get your answer?"
A student's ability to make connections can be assessed similarly. The above sequence of questioning can be followed by questions such as,
"If a student makes $6.50 for 3.5hours work, how would you find her hourly rate?"
These kinds of questioning allow the teacher to follow a student's thinking, or the teacher can change directions and pursue other ideas or thoughts the students may express. Thus the teacher and student can attain a fuller and deeper understanding of the process being evaluated.
Types of Questions
- Questions to Guide Instruction
- Questions for Error Analysis
- Open-Ended Questions
-If I change the problem to this, how would then you solve the problem? (for Problem Solving)
-Explain your solution (for communication)
-Explain why the solution to the equation is incorrect (for Reasoning)
-Do you see any relations between this idea to that, that we have discussed? (for Connections)
Alternative assessment focuses other assessment modes other than the traditional pen and paper tests. Alternative assessment also focuses more on how students learn rather than the learning results.
In this example, we will explore mathematics skills of spatial visualisation. Pupils will be asked to use manipulatives and visualise how to solve the problem. Rubrics on how the pupils will be assessed on their learning are also shown below.
The concepts covered include:
• use of formulae to calculate the area and circumference of a
• finding the area and perimeter of
∗ semicircle (half circle)
∗ quarter circle
• solving word problems involving area and perimeter.
Rubrics for Assessment of Pupils
Manipulatives To Be Used
Pupils are presented with two manipulative, a pink and a green manipulative resembling the image in the question.
Pupils will place the green manipulative onto the pink manipulative to recognise that the length of both is the same (based on the dotted lines) however the circumference of both the semicircles are different.
Pupils will then apply their thinking skills to visualise that both the semicircles can be cut off from the pink manipulative to form a circle, leaving behind a rectangle.
Pupils will see that Runner X has run the length of the rectangle and the circumference of the circle.
Step 4: (Image 4)
Pupils will apply the same step from above to visualise that both the semicircles can be cut off from the green manipulative to form a circle, leaving behind a rectangle.
Pupils will see that Runner Y has run the length of the rectangle and the circumference of the circle.
By obtaining the lengths of the rectangles and the circumference of the circles, pupils will obtain the perimeter of both the pink and green manipulative respectively, thereby obtaining the answer to the question.