Tag: mathematical tasks

Posted in Humor

Christmas GeoGebra Applet

Posted on by

candlesHere’s wishing you the choicest blessings of the season. The applet was adapted from the work of Wengler published in GeoGebra Tube. Being an incurable math teacher and blogger I can’t help not to turn this unsuspecting christmas geogebra applet into a mathematical task.

Observe the candles.

1. When is the next candle lighted?

2. On the same coordinate axes, sketch the time vs height graph of each of the four candles?

3. What kind of function does each graph represents?  Write the equation of each function?

3. If the candles burns at the rate of 2 cm per second and all the candles are completely burned after 20 seconds, what is the height of each candle? (Note: These are fast burning candles 🙂 )

[iframe https://math4teaching.com/wp-content/uploads/2012/12/PEACE.html 650 700]

Posted in Assessment, High school mathematics

Conference on Assessing Learning

Posted on by

The conference is open to high school mathematics and science teachers, department heads and coordinators, supervisors, tertiary and graduate students and lecturers, researchers, and curriculum developers in science and mathematics.

http://www.upd.edu.ph/~ismed/icsme2010/index.html

Plenary  Topics and Speakers

1. The Relationship between Classroom Tasks, Students’ Engagement, and Assessing Learning by Dr. Peter Sullivan

2. Assessment for Learning: Practice, Pupils and Preservice Teachers by Dr. Beverly Cooper

3. The Heart of Mathematics Teaching and Learning: Assessment and Problem Solving by Dr. Allan White

4. Assessing the Unassessable: Students’ and Teachers’ Understanding of Nature of Science by Dr. Fouad Abd Khalic

5. Lesson Study in Japan: How it Develops Critical Thinking Skills by Prof Takuya Baba

6. Classroom Assessment Affective and Cognitive Domains by Dr. Masami Isoda

7. Assessment cum Curriculum Innovations by Dr. Ma. Victoria Carpio-Bernido

8. Strategies for teaching Mathematics to classes with Diverse Interests and Achievement – Having Problems with Problem Solving? by Dr. Peter Sullivan

9. Assessing Learners’ Understandings of Nature of Science – The New Zealand Science Hub by Dr. Beverly Cooper.

Aside from parallel paper presentations and workshops, there will also be parallel case presentations by science and mathematics teachers involve in Collaborative Lesson Research and Development (CLRD) Project of UP NISMED. CLRD is the Philippine version of Lesson Study.

Clickhere for conference and registration details.

Posted in Math investigations

Exercises, Problems, and Math Investigations

Posted on by

The quality of mathematics students learn depends on the mathematical tasks or activities we let our students engage in.

Mathematical activities/tasks can be categorized into three types: exercises, problem solving, and math investigations.

Standard exercises

These are activities with clearly defined procedure/strategy and goal. Standard exercises are used for mastery of a newly learned skill – computational, use of an instrument, and even new terms or vocabulary. These are important learning activities but must be used in moderation. If our teaching is dominated by these activities, students will begin to think mathematics is about learning facts and procedures only. This is very dangerous.

Problem solving activity

These are activities involving clearly defined goals but the solutions or strategies are not readily apparent. The student makes decision on the latter. If the students already know how to solve the problem then it is no longer a problem. It is an exercise. Click here for features of good problem solving tasks. It is said that problem solving is at the heart of mathematics. Can you imagine mathematics without problem solving?

Math investigations

These are activities that involve exploration of open-ended mathematical situation. The student is free to choose what aspects of the situation he or she would like to do and how to do it. The students pose their own problem to solve and extend it to a directions they want to pursue. In this activity, students experience how mathematicians work and how to conduct a mathematical research. I know there are some parents and teachers who don’t like math investigation. Here are some few reason why we need to let our students to go through it.

  1. Students develop questions, approaches, and results, that are, at least for them, original products
  2. Students use the same general methods used by research mathematicians. They work through cycles of data-gathering, visualization, abstraction, conjecturing and proof.
  3. It gives students the opportunity communicate mathematically: describing their thinking, writing definitions and conjectures, using symbols, justifying their conclusions, and writing and reading mathematics.
  4. When the research involves a class or group, it becomes a ‘community of mathematicians’ sharing and building on each other’s questions, conjectures and theorems.

Students need to be exposed to all these type of mathematical activities. It is unfortunate that  textbooks and  many mathematics classes are dominated by exercises rather than problem solving and investigations tasks, creating the misconception that mathematics is about mastering skills and following procedures and not a way of thinking and communicating.

Samples of these tasks are shown in the picture below:

Click here and here for a sample teaching using math investigation.