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