A new look at old numbers, and what it reveals about numeration

In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. Similarities between the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics.

Physiological and subjective comfort evaluation under different airflow directions in a cooling environment

Indoor comfort is influenced by airflow direction, but subjective evaluations can differ. This study evaluates the airflow comfort with subjective assessments and physiological measurements, including skin temperature, electroencephalograms, and electrocardiograms. Nineteen participants entered a test room at 20°C after staying in a room at 32°C for acclimation. They were exposed to indirect and direct airflow conditions to their faces and performed four tasks under each condition: resting, counting to 10 s following time alerts, counting to 10 s in mind, and mental calculation. Subjective assessments showed relatively higher thermal sensation and pleasantness under indirect airflow. The psychological time calculated from counting behaviors was longer under indirect airflow, indicating suppression of negative emotions. The face temperatures significantly declined during experiments under direct airflow. The beta and gamma bands of electroencephalograms were inhibited under the indirect condition, and these amplitudes were negatively correlated with pleasant feelings. Electrocardiogram parameters indicated that sympathetic nervous activity was predominant during counting, following alerts and mental calculation in indirect airflow. This study supports the comfort of indirect airflow based on reliable evidence.

Training basic numerical skills in children with Down syndrome using the computerized game “The Number Race”

Individuals with Down syndrome (DS) present reduced basic numerical skills, which have a negative impact on everyday numeracy and mathematical learning. Here, we evaluated the efficacy of the adaptive (non-commercial) computerized game “The Number Race” in improving basic numerical skills in children with DS. The experimental group (EG; N = 30, Mage-in-months 118, range 70–149) completed a training playing with “The Number Race”, whereas children in the control group (CG; N = 31, Mage-in-months 138, range 76–207) worked with software aiming at improving their reading skills. The training lasted 10 weeks with two weekly sessions of 20–30 min each. We assessed both groups’ numerical and reading skills before and immediately after the end of the training, as well as at a 3-months follow-up. We found weak evidence for post-training groups differences in terms of overall numeracy score. However, the EG displayed substantial improvements in specific numerical skills and in mental calculation, which were maintained over time, and no improvement in reading. Conversely, the CG showed improvements in their reading skills as well as in number skills but to a lesser extent compared to the EG. Overall, “The Number Race” appears as a suitable tool to improve some aspects of numeracy in DS.

A game proposal for teaching math operations to 6th / 9th grade students

The purpose of this work is to serve as an aid tool for the teacher, for the students and for the development of the classes, however, we hope that the game is developed in an appropriate way so that it does not harm their performance. The objective of this work is to analyze the possibilities of teaching / learning of mathematical operations from the application of the game "the awakening of mathematics" for 6th and 9th grade students. The work methodology was developed for the students in order to solve such difficulties that some students were presenting during the math classes, developed from cardboard paper, A4 paper in 9x9 square format (9 squares in height and width), containing a total of 81 cells on the board, where the mental calculation of the four mathematical operations is proposed. It was realized that the use of the game should not be applied only as a means of interaction between students, therefore, if the teacher proposes the game as a teaching strategy, he should treat it as a vehicle for building knowledge, creating and experimenting.

Effect of Mental Calculation and Number Comparison on a Manual-Pointing Movement

The present study aimed at examining the effect of mental calculation and number comparison on motor performance measured as the movement time of a fast manual-pointing movement. Three experiments, involving a total number of 65 undergraduate subjects, examined the effect of mental subtraction (complex) and, respectively, of (a) mental addition (simple or complex), (b) mental multiplication (simple or complex), and (c) the comparison of dot sets and number comparison. Each number was written in Arabic. The movement times were analyzed by using a multilevel linear mixed-effect model. The results showed significant improvement of manual-pointing movement performance only after the complex calculations and after number comparison. Possible implication of attentional mechanisms specific to this arithmetical activity is further discussed.

Building Opportunities for Learning Multiplication

This chapter seeks to illustrate a comprehension-based learning approach focused on multiplication. We use episodes to show the potential of a teaching design of multiplication focused on the development of mental calculation based on tasks with appropriate contexts and calculations anchored in the use of benchmark numbers and operation properties, with examples to explain the ideas that are introduced. They are based on a collaborative work experience between a third-grade primary teacher and a researcher (the first author of this chapter). Using these specific examples, we discuss mathematical ideas and didactic options that can guide the actions of teachers when teaching multiplication. Finally, we discuss some points of convergence between the approach introduced here and the lesson study approach.

Can We Explain Students’ Failure in Learning Multiplication?

Teaching multiplication is a compulsory topic in elementary education mathematics programs. Much time is dedicated to teaching multiplication tables and algorithms, obtaining mediocre results. Recent investigations in neuroscience suggest that our way of teaching is not congruent with how the brain works and, as such, important changes should be made in teaching of numerical facts and algorithms. Additionally, other kinds of calculation, like mental calculation and calculations with a calculator, have not yet reached the level of importance of their use in education that citizens require in a contemporary society.

Numeracy Skills, Cognitive Reserve, and Psychological Well-Being: What Relationship in Late Adult Lifespan?

Background: The capacity of understanding and manipulating numerical stimuli (i.e., numeracy) can impact decision making. This investigation was conducted to examine whether number comprehension and mental calculation predict hedonic (i.e., Scale of Positive and Negative Experience, SPANE) and eudaimonic (i.e., Flourishing Scale) well-being in late adulthood, and whether cognitive reserve (i.e., education, time spent for gardening, and time spent for leisure activities) and non-verbal reasoning predict numeracy skills of old adults. Additionally, the effect of age on numeracy was examined, controlling for the effect of education and cognitive efficiency. Methods: One hundred and fifty-eight (i.e., 65–94 years old) community-dwellers completed a battery of tools assessing numeracy, cognitive and metacognitive efficiency, and psychological well-being. Results: Number comprehension, metacognition, time spent for leisure, and perceived physical health accounted for 23% of the variance in the SPANE condition, whereas metacognition, perceived physical health, time for leisure, and education explained 15% of the variance in the Flourishing condition. Moreover, cognitive reserve assessed in terms of vocabulary and education predicted mental calculation. Finally, aging significantly impacted the mental calculation performance of older participants. Conclusions: These findings suggest that numeracy skills can selectively impact the mental health and daily life of older adults.