242 Sinikka Kaartinen and Timo Latomaa
Table 2 (Continued)
14 Liisa yes, should we draw extending procedural;
symbolic
pictorialsignifier as a sign
of signified15 Karra x plus one continuing semiotic;
mathematizing;
symbolic
algebraicsignifier aspect of
sign16 Maritta multiplies three x plus three continuing signifier aspect of
sign
17 Annikki I fell off the cart evaluating identity;
evaluation of
one‘s
understandingno elements of signEpisode 3: Clarification through hands on activities
18 Maritta may I still advise, we had this x
squared four x and three as
giventutoring procedural;
starting
information of
the problemsignifier aspect of
sign19 Annikki yes okay but this handicraft
carried the important meaningquestioning procedural;
clarifying the
meaning of
actionsignifier connected
to signified20 Maritta The handicraft was to collect
these pieces into a connected
region in a way that there are no
holestutoring semiotic; the
meaning of the
actionsign21 Annikki this was one, two, three, four x thinking
aloudsemiotic; the
meaning of
cultural toolssign23 Maritta and now edge multiplied by
edgetutoring semiotic; the
mathematical
meaning of the
actionsign24 Annikki okay, clear agreeing identity;
understanding
the meaning of
the actionsocial sign4.1.3. Episode 3
This Episode 3 starts with Maritta‘s (turn 18) reaction to Annikki‘s comment by tutoring
“may I still advise, we had this x squared for x and three as given”. In doing so Maritta refers
back to the starting information of the problem situation. In her turn (turn 19) Annikki
expresses that she could not connect the bridge between the mathematical meaning of the
situation and the hands-on-activities with algebra tiles. Maritta‘s tutoring turns (turns 20 and
23) connected with Annikki‘s agreeing and thinking aloud turns nicely highlights the
interaction pattern where concrete activity was connected with the abstract nature of
mathematical reasoning. A Social sign and shared understanding were constructed.