A Typical Investigation s Lesson
Adapted from Beyond Arith metic
By Jan Mo kr os, Susan Jo Russell, Karen Econom opo ulous, p . 14
Mathem atics is a way of approach ing a problem by using one�s own
logic and powers of observation. It is not a recipe for problem solving,
but rather a collection of ways of using reasoning, m odels, evidence,
exam ples, and counter exam ples to discover m eaningful patterns in
num b ers, in 2-D and 3-D space, and in data. Like science, m a them atics
has standard proof: An argum ent m u st be supported by evidence, and
conclusions must be logically derived.
An InvestigInvestig
ations session lasts for about one hour . A typical lesson usually has a
warm up, main lesson or choice tim e and a debriefing tim e at the end of the session.
Introduction
(warm up)
This par t of the le sson will p r obably take 5-15
m i nutes. The teach er sh ould be careful not to
�give away� any of the m a them atics, leaving
plenty for the students to discover.
During the f i rst p a r t
of the mathematics class,
the teacher gathers the class together and �
� poses a problem,
� reads a story, or
� m odels a new ga m e .
� The teacher moves among the groups
of childre n . S(he) may�
� m odif y an activ ity to m a ke it m o re
access i ble o r challengin g,
� record observations,
� inte ract with stude nts where appropriate.
� ask probing questions to gain insight into
how the students thinking and
m a the m atical understanding. (see T e acher
Checkpoints and Observing the Students
for exam ple questions.)
Exploration
(lesson / cho i ce tim e stations)
The bulk of the class time is spen t here. Teachers
m a y organize the ses s ion as �Choice Tim e� so
students can move freely among a va riety of
activities.
During the Exploration time:
� Children a r e actively engaged :
� solving problem s, discussing their
strategies with peers followed by m a king
a record of their solution in num bers,
words, and/or pictures.
� playing m a the m atical gam e s, building
geom etric models, or collecting data.
Summary
(Debrief/Sh a ring)
The teacher pulls th e class togeth er to reflect on
the m a thematic s lea r ned during th e Exploration
tim e.
� Children m a y�
� share their thinking or approaches
� discuss gam e strategies
� relate today�s lessons to previously taught
m a them atics concepts.
� ask each other ques
tions.
� restate another student�s thinking.
The teacher encourages st udent sh aring by asking
thoughtful open-ended questions.
20 0 3 - 2 00 4\ M a t h \ T y p i cal I nve st i g at i ons Less on .d oc