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English, L. & Sriraman, B. (2010). Problem solving for the 21th
century. In B. Sriraman & L. English (Eds.), Theories of
Mathematics Education: Seeking new frontier. Berlin: Springer,
263-290 .
Mousoulides, M. Sriraman, B., Pittalis, M., & Christou, C.
(2007). Tracing students' modeling processes in elementary and
secondary school. Paper presented at 5th Congress of the
European Society for Research in Mathematics Education
(CERME – 5), Cyprus.
בעייה מתמטיקה
בעייה מתמטיקה
The best way to teach mathematical ideas is to start with interesting problems whose solution requires the use of ideas.
Use problem solving as a powerful means to develop substantive mathematical concept.
Real word problem
Integration within all topic
areas
Outside the class
a. complex systems.b. plan, monitor and assess progressc. adapt quickly to technologies.
בעייה מתמטיקה
Modeling
Mathematical models = "systems of Mathematical models = "systems of elements, operations, relationships and rules elements, operations, relationships and rules that can be used to describe, explain, or that can be used to describe, explain, or predict the behavior of some other familiar predict the behavior of some other familiar system”system”
Modeling problems are realistically complex situations where the problem solver engages in mathematical thinking beyond the usual school experience and where the products to be generated often include complex artefacts or conceptual tools that are needed for some purpose, or to accomplish some goal.
Modeling
Mathematical models = "systems of Mathematical models = "systems of elements, operations, relationships and rules elements, operations, relationships and rules that can be used to describe, explain, or that can be used to describe, explain, or predict the behavior of some other familiar predict the behavior of some other familiar system”system”
Elicit my own mathematics
meaningfulMake sense
identifying
selecting
Interpreting making representation Cyclic process
sorting
organizing
selecting
quantifying
Transforming large data
University’s CafeteriaConstruct models for selecting the best among a number of employees
Elicit my own mathematics
identifying
selecting
Interpreting making representation Cyclic process
sorting
organizing
selecting
quantifying
Transforming large data
Real world
Outside the class
בעייהמתמטיקהסטטיסטיקה
Reformulating the problem
Not just one right answer
Complex system
Hours, money, seasons
Leikin, R. (2004). Towards high quality geometrical tasks:
reformulation of a proof problem. In M. J. Hoines & A. B.
Fuglestad (Eds.) Proceedings of the 28th International
Conference for the Psychology of Mathematics Education, Vol.
3, 209-216 .
בעייה
The person has to be motivated to find a solution
No readily available procedures
The person has to make an attempt and persists to reach a solution
Several solving approaches
קריטריונים לקביעת איכות 4:הבעייה
בעיית חקר
The person has to be motivated to find a solution
No readily available procedures
The person has to make an attempt and persists to reach a solution
Several solving approaches
קריטריונים לקביעת איכות 4:הבעייה
challenging Cognitively demanding
High motivated
עד כמה לפתוח את ?הבעייה
גובה הטרפז שווה לקטע האמצעיםהוכח ש .1
הגובה לקטע האמצעיםהשווה בין .2 .
?מה תוכל לומר על טרפז זה .6
. שימוש בתוכנת גיאומטריה דינמית2מסעיף
.מצא יחסים אפשריים בין הקטעים היוצאים מאמצעי הצלעות הנגדיות .3
.אותה שאלה ללא הנחייה לבניית עזר. )לא רבלנטי לבעייה לעיל( .4
.מצא גדלים שווים בטרפז זה .5
מה ?ההבדל
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