MatMatics/Literature

• It is not clear if there is a progressive changeover from limitations of competence to constraints imposed by working memory in children’s mental addition, nor when any such change takes place.
  • Theory: children's mental math ability is constrained more by competence of performing math calculations than by working memory span, while adults' ability is constrained more by working memory span.
• People suffer less from their working memory span limitations in performing mental addition if the problem is visible to them during the course of problem-solving.
  • The experiment show visual presentation of math problem benefit both younger and older children, and for older children the benefit is more significant.
  • Explanation: the written page acts as an external memory thereby reducing the load on working memory
• The integer addition speed and the working memory span are positively correlated.
  • Explanation 1: the speed of mental operations reflects the efficiency of processing and that more efficient operations require less working memory capacity, leaving more free for storage (Case et al., 1982).
  • Explanation 2: faster operations allow less time for information stored in working memory to be forgotten (Towse & Hitch, 1995).

• 3rd grade is the transitional age when children change their strategies of simple mental addition - from counting to memory retrieval. Some children start to use memory retrieval while solving addition problems
• 4th graders' memory retrieval strategies operate more efficiently, but are still easily disrupted when the math problem is confusing
• The transition of mental structure for addition lasts into 6th grade, where sixth graders and adults show very similar patterns in strategies, reaction time (RT), and correctness

• The authors questioned whether there is any relationship between the two facts below:
  • The small facts bias of simple addition and multiplication facts in elementary school textbooks for grade 1-6: large-number facts (numbers >5) occurred up to half as frequently as those with operands in the 2-5 range
  • For both adults and children, responses to larger basic facts are both slower and more error prone than their solutions to smaller facts
• The whole-number arithmetic facts are eventually stored in long-term memory in a network-like structure and are retrieved by the same processes as those responsible for the retrieval of verbal knowledge. The facts storage has a particular level of strength, whose values vary as a function of an individual's practice and experience.

and paradoxical effects of incentives on skillful performance. Journal of Personality & Social Psychology, 46, 610-620.

• Baumeister (1984) found that increased conscious attention directed to one’s own performance, induced, for example, by social pressure to perform well, disrupted the performance of a well-practiced video game.
• When customers at a video game arcade were asked to try to get the best score they could, there was a significant drop in performance (with an average of 25%), as compared with the previous trial, which had been observed by the experimenter without the participant’s awareness.

• Three groups of children are compared for their strategy choice of solving mental addition problems: math disabled (MD); normal; gifted
• The Strategy Model - strategies that children often use in addition (from basic to developed):

1. Counting fingers - children use their fingers to physically represent the problem integers and then count their fingers to reach a sum
   • Min: based on counting only the smaller value integer
   • Sum: based on counting both integers
2. Fingers - children use their fingers to represent the integers but do not visibly count them before giving an answer
3. Verbal counting - children count audibly or move their lips as if counting implicitly;
   • Min / Sum
   • The gifted group has faster verbal counting than non-gifted groups (normal + math disabled)
4. Retrieving from long-term memory
   • The main difference between strategies used between gifted and non-gifted groups
   • The gifted group used this strategy in both easy and difficult addition problems

• MD children are more likely to use basic strategies, while gifted children are more likely to use developed ones.
• Younger children's strategy choice patterns are similar to the MD group, while older children's are similar to the gifted group

This dissertation makes recommendations on how to design multimedia mathematics learning environments to address children's affective. cognitive. and pedagogical needs. Moreover, this research contributes to an increased understanding of how to design better game-based educational software. A few of the findings of this research are:

• 1. Interface design in educational software plays a crucial role in how learners interact with the educational content.. and consequently how they acquire knowledge and what knowledge they acquire. The results showed significant achievement differences among students who used different interface styles. Interface techniques such as ·scaffolding and gradual removal of visual feedback can promote reflective cognition and improve learning.
• 2. Direct manipulation graphical interfaces should be used with care in the context of interactive multimedia mathematics learning environments. The conventional interface design guideline calling for easier interaction and exertion of minimal cognitive load does not necessarily apply to educational environments.
• 3. By carefully taking into account children's cognitive and affective needs, the design can help children enjoy learning mathematics.
• 4. Inclusion of background music and visual aesthetics can make a learning activity more enjoyable.