From e5f4454b8afe73120fd39f15ea60b18f744a81f1 Mon Sep 17 00:00:00 2001
From: "Dobbertin, Niclas" <niclas.dobbertin@mailbox.org>
Date: Mon, 14 Oct 2024 16:29:50 +0200
Subject: update

---
 paper2/thesis.tex | 32 +++++++++++++++++++-------------
 1 file changed, 19 insertions(+), 13 deletions(-)

(limited to 'paper2/thesis.tex')

diff --git a/paper2/thesis.tex b/paper2/thesis.tex
index 4fb4097..5d0d8d1 100644
--- a/paper2/thesis.tex
+++ b/paper2/thesis.tex
@@ -60,6 +60,7 @@ Living in a complex environment like the real world, a plethora of different tas
 much more efficient if knowledge from tasks can be reused in other tasks
 
 
+\citet{Frensch_1991} observed differences in learning speed depending on condition, i.e. the order in which procedures are presented.
 
 % \citep{anderson}
 % \citep{Taatgen_2013}
@@ -201,14 +202,14 @@ For example x\_2 means taking the second value of variable x.
 Other procedures require finding the maximum or minimum value of a variable or of previous solutions.
 An example of how the screen could look during a trial is shown in Figure~\ref{fig:frensch}.
 
-The experiment starts with 75 training trials, each representing a water sample, in which a random choice of 6 procedures has to be solved in the order they are presented.
+The experiment starts with 75 acquisition trials, each representing a water sample, in which a random choice of 6 procedures has to be solved in the order they are presented.
 The last procedure is always picked in the selection process, as it uses all previous results for a water sample to calculate the final solution.
-Afterwards 50 testing trials take place, in which the third procedure from the training phase is switched for the unpicked one.
-There are three conditions that determine the order in which procedures are presented in the training phase, however the procedure for the final result is always last.
+Afterwards 50 transfer trials take place, in which the third procedure from the acquisition phase is switched for the unpicked one.
+There are three conditions that determine the order in which procedures are presented in the acquisition phase, however the procedure for the final result is always last.
 In the fixed condition, the order is randomized once at the start and stays constant during all trials.
 In the random condition, procedure order is randomized between each trial.
 In the blocked condition, the first procedure has to be solved for all trials before moving on to the second procedure, etc.
-The testing phase always uses fixed order.
+The transfer phase always uses fixed order.
 
 
 How modeled:
@@ -232,7 +233,7 @@ Procedures \\
 
 \bigskip
 \small\textit{Note}. The seven translated procedures used in this experiment.
-Six of them are used in the training phase, in the testing phase one procedure is swapped with the unused one.
+Six of them are used in the acquisition phase, in the transfer phase one procedure is swapped with the unused one.
 The bottom procedure is always included as it calculates the total water quality.
 \end{table}
 
@@ -252,14 +253,19 @@ The bottom procedure is always included as it calculates the total water quality
 
 \section*{Model}
 
-Improvements in task performance are mainly dependent on production compilation, as the order and how efficiently the mathematical operations are performed are the main subject of the task.
-Utility learning matters mostly on production selection and ordering, however the task itself is mostly linear.
-It can still play a significant role if alternative or shortcut productions for mathematical operations exist.
-E.g.\ a production that swaps argument 1 and argument 2 in addition or multiplication may reduce time spend, dependent on how the algorithm functions.
+The goal of the model is an accurate representation of how a human would solve this task and improve over time.
+Optimally the models solving time would, in each condition, improve similarly to previous human results.
+Looking at the ways an ACT-R model can improve, production compilation seems to be the important function compared to utility or chunk learning.
+A lot of small subtasks have to be accomplished for a single trial, such as finding correct variable values, solving multiple mathematical operations and typing the answer.
+These steps however need to be repeated for each trial and while the numbers and with them the mathematical operations can change a bit, the overall order and structure of subtasks stays the same.
+Production compilation therefore promises strong improvements to solving times, as many steps can be combined into a single one, eliminating time deciding on the next step.
+Additionally numbers in this task are often small, allowing some common operation to be saved as productions in procedural memory, removing time calculating or trying to retrieve from declarative memory.
 
-The subsymbolic system of ACT-R also involves mechanisms to gauge retrieval chance and activation strength in the declarative memory.
-This is used to model learning and retrieval of new memory chunks.
-In this task however, the subject already has knowledge of mathematical facts and \todo{``not learn new facts really during exp''} \
+Utility learning is needed to evaluate the usefulness of compiled productions, but since the task and subtask order is very rigid, should have no important role in learning otherwise.
+Chunk learning doesn't seem impactful either, as there are too many permutations of variable values and too few trials to memorize helpful information.
+
+To complete the experiment in a manner a human adult would, the model is given a baseline of knowledge and skill to start with.
+This includes basic knowledge of possible numbers and mathematical operations it has to solve.
 
 \subsection{Implementation}
 \todo[inline]{chunktypes, pre-knowledge}
@@ -380,7 +386,7 @@ Details about these difficulties will be reviewed in the Discussion.
 
 \begin{figure}[H]
     \centering
-    \caption{Mean solution time in training and transfer phase}
+    \caption{Mean solution time in acquisition and transfer phase}
     \label{fig:RT}
         % \includegraphics[width=1.1\textwidth]{RT.png}
 
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