Psychology 3443G 001 FW23
Development of Mathematical Brain
If there is a discrepancy between the outline posted below and the outline posted on the OWL course website, the latter shall prevail.
WESTERN UNIVERSITY
LONDON CANADA
Department of Psychology
Fall/Winter 2023-2024
Psychology 3443G Section 001
Development of the mathematical brain
- CALENDAR DESCRIPTION
An examination of how children develop numerical abilities from infancy onwards, focusing on the roles of memory, spatial ability and language. The course will also examine well-publicized studies on the poor levels of performance in mathematics among North American students and compare this to student performance in other countries.
Antirequisite: Not Applicable
Prerequisite(s): Both Psychology 2801F/G and Psychology 2811A/B, or the former Psychology 2820E, or both the former Psychology 2800E and the former Psychology 2810, and one of Psychology 2040A/B, Psychology 2410A/B, Psychology 2220A/B, Psychology 2221A/B or Neuroscience 2000.
3 lecture/seminar hours, 0.5 course
Unless you have either the prerequisites for this course or written special permission from your Dean to enrol in it, you may be removed from this course and it will be deleted from your record. This decision may not be appealed. You will receive no adjustment to your fees in the event that you are dropped from a course for failing to have the necessary prerequisites.
2.0 COURSE INFORMATION
Instructor: Daniel Ansari
Office and Phone Number: WIRB 5180, 519-661-2111 Ext. 80548
Office Hours: Wednesdays 1-2pm & Fridays 3-4pm or by appointment. All office hours will be held on Zoom: https://westernuniversity.zoom.us/my/daniel.ansari
Email: daniel.ansari@uwo.ca
Teaching Assistant: Suesan MacRae
Teaching Assistnat Office: WIRB
Teaching Assistant Office Hours:
Teaching Assistant Email: smacra2@uwo.ca
Time and Location of Classes: See Student Centre for Timetable
Delivery Method: In-Person
Students who are in emotional/mental distress should refer to Health and Wellness @Western https://www.uwo.ca/health/ for a complete list of options about how to obtain help.
Please contact the course instructor if you require material in an alternate format or if you require any other arrangements to make this course more accessible to you. You may also contact Accessible Education at aew@uwo.ca or 519-661-2147.
2.1 Online Learning Notice: Please note: For courses delivered in an online format, include an online component, or are required to pivot online, students must have a reliable internet connection and computer that are compatible with online learning system requirements. Some courses may also require the use of a remote proctoring platform to ensure assessments are taken fairly in accordance with Western’s policy on Scholastic Discipline for Undergraduate Students and Scholastic Discipline for Graduate Students.
3.0 TEXTBOOK
The readings, with a few exceptions, will be recently published, peer-reviewed journal articles or book chapters. For this course to be productive, interesting, and successful it is imperative that you do all the readings. For your convenience I have posted the readings on the OWL website (https://owl.uwo.ca) for this course. If you have difficulties accessing the materials or if you find that materials are missing from the website, please contact the TA.
4.0 COURSE OBJECTIVES & LEARNING OUTCOMES
The first aim is to enable students to gain a detailed understanding of how children develop numerical abilities. The emphasis will be on the development of mathematical skills. We will review psychological, educational, evolutionary, and neuroscientific perspectives on number development. The course takes a journey from infant numerical abilities to children’s difficulties with fractions and cross-cultural differences in mathematical abilities. Against the background of research findings, we will be discussing the various developmental changes in children’s numerical understandings. The second aim is to encourage students to think about mathematical education and development from multiple perspectives and to see the relationships between education and basic research in this field. The final objective of the course is to develop reading, critical thinking, writing, and public communication skills
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Learning Outcome |
Learning Activity |
Assessment |
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Depth and Breadth of Knowledge.
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Assigned readings Writing assignments Weekly Lectures |
Midterm Paper Final Paper Quizzes |
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Knowledge of Methodologies.
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Weekly Lectures Assigned Readings |
Midterm Paper Final Paper Quizzes |
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Application of Knowledge.
|
Assigned Readings Weekly Lectures |
Midterm Paper Final Paper
|
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Communication Skills.
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Weekly Lectures Writing Assignments |
Midterm Paper Final Paper |
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Awareness of Limits of Knowledge.
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Weekly Lectures Writing Assignments |
Midterm Paper Final Paper |
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Autonomy and Professional Capacity.
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Writing Assignments |
Midterm Paper Final Paper |
5.0 EVALUATION
The evaluation and testing formats for this course were created to assess the learning objectives as listed in section 4.0 and are considered necessary for meeting these learning objectives.
Attendance and Participation (5%)
This course depends on your active participation in the class discussions. It is therefore crucial that you make every effort to attend every class and come prepared to participate. Often the instructor will ask for definitions of terms from a previous class and thereby conduct a mini-review of the preceding class at the beginning of each class. Your active participation is required for this part of each class.
Quizzes. (10%)
Every week, starting the week of January 18th, you will be asked to complete a short quiz at the beginning of class that relates directly to the required readings, lecture and supporting material assigned for that week.
Midterm Paper (35%)
The purpose of this assignment is to give you the opportunity to write a short paper on one of the topics of the first 5 weeks and thereby consolidate your knowledge on this topic. You are required to write a paper of no more than 1500 words (1.5 spaced, 12 pt. font). Longer papers will be penalized. During the second week the instructor will circulate a list of 5 possible essay topics/questions. You are required to pick one of these topics for your midterm paper. In your paper you should not merely rely on the class readings, but go beyond them and do your own independent literature searches. The Midterm paper is due by 11.59pm via OWL on Friday, February 9th 2024 at 11.59pm EST. Please make sure that you save your midterm in Microsoft Word Format. Please name the file that contains your paper in the following way:
Your First_Name_Last_Name_Final_Paper_3443_2024
Final Paper (50%)
To give you the opportunity to review literature in depth and to provide a cohesive summary of conceptual and empirical advances in the study of the Mathematical Brain, you are required to write a final paper of no more than 3000 (1.5 spaced,12pt font). You should choose the topic for your final paper from the topics within the syllabus and generate a question. You are strongly encouraged to discuss the topic of your final paper with the instructor or teaching assistant. You may also give the instructor a short plan of your final paper for review at least 3 weeks before the deadline. Your paper should be a critical review of the literature. Your paper should also contain a section on ‘Future Directions’ in which you discuss outstanding questions and ideas for future studies. The Final paper is due at 11.59pm via OWL on Monday, April 8th, 2024. Please make sure that you save your midterm in Microsoft Word Format. Please name the file that contains your paper in the following way:
Your First_Name_Last_Name_Final_Paper_3443_2024
5.1 POLICY ON MISSING COURSEWORK
Attendance and Participation (5%): Failure to attend class without following the procedures outlined in 11.0 below will result in a 0 grade for class participation for that class.
Quizzes (10%): Failure to complete the quizzes by the indicated deadline will result in a grade of 0.
Midterm Paper (35%): There will be a late submission penalty. Specifically, 5% from the grade will be deducted for every day that the submissions are late.
Final Paper (50%): There will be a late submission penalty. Specifically, 5% from the grade will be deducted for every day that the submissions are late.
PLEASE NOTE: Because this is an essay course, as per Senate Regulations, you must pass the essay component to pass the course. That is, the average mark for your written assignments must be at least 50%.
This course is exempt from the Senate requirement that students receive assessment of their work accounting for at least 15% of their final grade at least three full days before the date of the deadline for withdrawal from a course without academic penalty.
The expectation for course grades within the Psychology Department is that they will be distributed around the following averages:
70% 1000-level to 2099-level courses
72% 2100-2999-level courses
75% 3000-level courses
80% 4000-level courses
The Psychology Department follows Western’s grading guidelines, which are as follows (see: https://www.uwo.ca/univsec/pdf/academic_policies/general/grades_undergrad.pdf
A+ 90-100 One could scarcely expect better from a student at this level
A 80-89 Superior work that is clearly above average
B 70-79 Good work, meeting all requirements, and eminently satisfactory
C 60-69 Competent work, meeting requirements
D 50-59 Fair work, minimally acceptable
F below 50 Fail
Note that in the event that course grades are significantly higher or lower than these averages, instructors may be required to make adjustments to course grades. Such adjustment might include the normalization of one or more course components and/or the re-weighting of various course components.
Policy on Grade Rounding: Please note that although course grades within the Psychology Department are rounded to the nearest whole number, no further grade rounding will be done. No additional assignments will be offered to enhance a final grade; nor will requests to change a grade because it is needed for a future program be considered. To maximize your grade, do your best on each and every assessment within the course.
6.0 ASSESSMENT/EVALUATION SCHEDULE
Every Tuesday at the beginning of class starting Tuesday, January 16th – Deadline for weekly Quiz.
Friday , February 9th 2024 – 11.59pm – Deadline for Midterm Paper
Monday, April 8th 2024 11:59pm – Deadline for Final Paper
7.0 CLASS SCHEDULE
Tuesday, January 9th: Introduction to the Course: Review of Topics and Assignments
No readings assigned for this week
Tuesday, January 16th: Origins of number representation: evidence from infants & animals
(Cantlon, 2012)
(Libertus & Brannon, 2009)
Tuesday, January 23rd: Basic number processing and its role in higher-level math learning
(Goffin & Ansari, 2019)
(Odic & Starr, 2018)
Tuesday, January 30th: Children’s development of verbal number skills
(Sella et al., 2021)
(Sarnecka, 2015)
Tuesday, February 6th: Mental Arithmetic & The role of Executive Functions
(Siegler, 2000)
(Clements, Sarama & Germeroth, 2016)
Tuesday, February 13th: Developmental Dyscalculia
(Bugden & Ansari, 2014)
(Fias, Menon, & Szucs, 2013)
Tuesday, February 20th: Reading Week – NO CLASS
Tuesday, February 27th: Mathematics Anxiety
(Sokolowski & Ansari, 2017)
(Maloney & Beilock, 2012)
https://thelearningexchange.ca/math-anxiety/
Tuesday, March 5th: The mathematical brain: neuropsychology & adult studies
(Matejko & Ansari, 2018)
(Vogel & De Smedt, 2021)
Tuesday, March 12th: The mathematical brain: evidence from children
(Peters & De Smedt, 2018)
Tuesday, March 19th: The effect of genetics on learning and the mathematical brain
(Kovas & Plomin, 2007)
(Sokolowski & Ansari, 2018)
Tuesday, March 26th : Gender Differences
(Kersey, Braham, Csumitta, Libertus, & Cantlon, 2018)
(Spelke, 2005)
Tuesday, April 2nd: Cross-cultural studies and international comparison studies
(Siegler & Mu, 2008)
(Rodic et al., 2015)
8.0 LAND ACKNOWLEDGEMENT
We acknowledge that Western University is located on the traditional lands of the Anishinaabek, Haudenosaunee, Lūnaapéewak and Attawandaron peoples, on lands connected with the London Township and Sombra Treaties of 1796 and the Dish with One Spoon Covenant Wampum.
With this, we respect the longstanding relationships that Indigenous Nations have to this land, as they are the original caretakers. We acknowledge historical and ongoing injustices that Indigenous Peoples (e.g. First Nations, Métis and Inuit) endure in Canada, and we accept responsibility as a public institution to contribute toward revealing and correcting miseducation, as well as renewing respectful relationships with Indigenous communities through our teaching, research and community service.
9.0 STATEMENT ON ACADEMIC OFFENCES
Students are responsible for understanding the nature and avoiding the occurrence of plagiarism and other scholastic offences. Plagiarism and cheating are considered very serious offences because they undermine the integrity of research and education. Actions constituting a scholastic offence are described at the following link: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf
As of Sept. 1, 2009, the Department of Psychology will take the following steps to detect scholastic offences. All multiple-choice tests and exams will be checked for similarities in the pattern of responses using reliable software, and records will be made of student seating locations in all tests and exams. All written assignments will be submitted to TurnItIn, a service designed to detect and deter plagiarism by comparing written material to over 5 billion pages of content located on the Internet or in TurnItIn’s databases. All papers submitted for such checking will be included as source documents in the reference database for the purpose of detecting plagiarism of papers subsequently submitted to the system. Use of the service is subject to the licensing agreement, currently between Western and Turnitin.com (http://www.turnitin.com).
Computer-marked multiple-choice tests and/or exams will be subject to submission for similarity review by software that will check for unusual coincidences in answer patterns that may indicate cheating.
In classes that involve the use of a personal response system (PRS), data collected using the PRS will only be used in a manner consistent to that described in this outline. It is the instructor’s responsibility to make every effort to ensure that data remain confidential. However, students should be aware that as with all forms of electronic communication, privacy is not guaranteed. Your PRS login credentials are for your sole use only. Students attempting to use another student’s credentials to submit data through the PRS may be subject to academic misconduct proceedings.
Possible penalties for a scholastic offence include failure of the assignment/exam, failure of the course, suspension from the University, and expulsion from the University.
10.0 POLICY ON THE USE OF EXAM PROCTORING SOFTWARE
Tests and examinations for online courses will be conducted using a remote proctoring service. By taking this course, you are consenting to the use of this software and acknowledge that you will be required to provide personal information (including some biometric data) and the session will be recorded. Completion of this course will require you to have a reliable internet connection and a device that meets the technical requirements for this service. More information about this remote proctoring service, including technical requirements, is available on Western’s Remote Proctoring website at: https://remoteproctoring.uwo.ca.
In the event that in-person exams are unexpectedly canceled, you may only be given notice of the use of a proctoring service a short time in advance.
11.0 POLICY ON ACCOMMODATION FOR ILLNESS OR OTHER ABSENCES
Western’s policy on Accommodation for Medical Illness can be found at:
https://www.westerncalendar.uwo.ca/PolicyPages.cfm?PolicyCategoryID=1&Command=showCategory&SelectedCalendar=Live&ArchiveID=#Page_12
If you experience an extenuating circumstance (e.g., illness, injury) sufficiently significant to temporarily make you unable to meet academic requirements, you may request accommodation through the following routes:
- For medical absences, submitting a Student Medical Certificate (SMC) signed by a licensed medical or mental health practitioner in order to be eligible for Academic Consideration;
- For non-medical absences, submitting appropriate documentation (e.g., obituary, police report, accident report, court order, etc.) to Academic Counselling in their Faculty of registration in order to be eligible for academic consideration. Students are encouraged to contact their Academic Counselling unit to clarify what documentation is appropriate.
Students must see the Academic Counsellor and submit all required documentation in order to be approved for certain accommodation.
https://www.registrar.uwo.ca/faculty_academic_counselling.html
Students seeking academic consideration:
- are advised to consider carefully the implications of postponing tests or midterm exams or delaying handing in work;
- must communicate with their instructors no later than 24 hours after the end of the period covered SMC, or immediately upon their return following a documented absence
Students seeking accommodation for religious purposes are advised to contact Academic Counselling at least three weeks prior to the religious event and as soon as possible after the start of the term.
12.0 CONTINGENCY PLAN FOR RETURN TO LOCKDOWN: IN-PERSON & BLENDED CLASSES
In the event of a COVID-19 resurgence or any other event that necessitates the course delivery moving away from face-to-face interaction, all remaining course content will be delivered entirely online, either synchronously (i.e., at the times indicated in the timetable) or asynchronously (e.g., posted on OWL for students to view at their convenience). The grading scheme will not change. Any remaining assessments will also be conducted online, as determined by the course instructor.
13.0 STATEMENTS CONCERNING ONLINE ETIQUETTE
In courses involving online interactions, the Psychology Department expects students to honour the following rules of etiquette:
- please “arrive” to class on time
- please use your computer and/or laptop if possible (as opposed to a cell phone or tablet)
- please ensure that you are in a private location to protect the confidentiality of discussions in the event that a class discussion deals with sensitive or personal material
- to minimize background noise, kindly mute your microphone for the entire class until you are invited to speak, unless directed otherwise
- In classes larger than 30 participants please turn off your video camera for the entire class unless you are invited to speak
- In classes of 30 students or fewer, where video chat procedures are being used, please be prepared to turn your video camera off at the instructor’s request if the internet connection becomes unstable
- Unless invited by your instructor, do not share your screen in the meeting
The course instructor will act as moderator for the class and will deal with any questions from participants. To participate please consider the following:
- If you wish to speak, use the “raise hand” function and wait for the instructor to acknowledge you before beginning your comment or question.
- Please remember to unmute your microphone and turn on your video camera before speaking.
- Self-identify when speaking.
- Please remember to mute your mic and turn off your video camera after speaking (unless directed otherwise).
General considerations of “netiquette”:
- Keep in mind the different cultural and linguistic backgrounds of the students in the course.
- Be courteous toward the instructor, your colleagues, and authors whose work you are discussing.
- Be respectful of the diversity of viewpoints that you will encounter in the class and in your readings. The exchange of diverse ideas and opinions is part of the scholarly environment. “Flaming” is never appropriate.
- Be professional and scholarly in all online postings. Use proper grammar and spelling. Cite the ideas of others appropriately.
Note that disruptive behaviour of any type during online classes, including inappropriate use of the chat function, is unacceptable. Students found guilty of Zoom-bombing a class or of other serious online offenses may be subject to disciplinary measures under the Code of Student Conduct.
14.0 OTHER INFORMATION
Office of the Registrar: https://registrar.uwo.ca
Student Development Services: www.sdc.uwo.ca
Psychology Undergraduate Program: https://www.psychology.uwo.ca/undergraduate/index.html
If you wish to appeal a grade, please read the policy documentation at: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/appealsundergrad.pdf
Please first contact the course instructor. If your issue is not resolved, you may make your appeal to the Undergraduate Chair in Psychology (psyugrd@uwo.ca).
Copyright Statement: Lectures and course materials, including power point presentations, outlines, videos and similar materials, are protected by copyright. You may take notes and make copies of course materials for your own educational use. You may not record lectures, reproduce (or allow others to reproduce), post or distribute any course materials publicly and/or for commercial purposes without the instructor’s written consent.
Policy on the Recording of Synchronous Sessions: Some or all of the remote learning sessions for this course (if scheduled) may be recorded. The data captured during these recordings may include your image, voice recordings, chat logs and personal identifiers (name displayed on the screen). The recordings will be used for educational purposes related to this course, including evaluations. The recordings may be disclosed to other individuals participating in the course for their private or group study purposes. Please contact the instructor if you have any concerns related to session recordings. Participants in this course are not permitted to privately record the sessions, except where recording is an approved accommodation, or the student has the prior written permission of the instructor.
References:
Bugden, S., & Ansari, D. (2014). When Your Brain Cannot Do 2 + 2: A Case of Developmental Dyscalculia. Frontiers for Young Minds. https://doi.org/10.3389/frym.2014.00008
Cantlon, J. F. (2012). Math, monkeys, and the developing brain. Proceedings of the National Academy of Sciences of the United States of America, 109 Suppl, 10725–10732. https://doi.org/10.1073/pnas.1201893109
Clements, D.H., Sarama, J.,Germeroth, C. (2016) Learning executive function and early mathematics: directions of causal relations. Early Childhood Research Quarterly, 36, 79-90.
Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 43–47.
Goffin, C., & Ansari, D. (2019). How Are Symbols and Nonsymbolic Numerical Magnitudes Related? Exploring Bidirectional Relationships in Early Numeracy. Mind, Brain, and Education, 13(3). https://doi.org/10.1111/mbe.12206
Kersey, A. J., Braham, E. J., Csumitta, K. D., Libertus, M. E., & Cantlon, J. F. (2018). No intrinsic gender differences in children’s earliest numerical abilities. Npj Science of Learning, 3(1), 12. https://doi.org/10.1038/s41539-018-0028-7
Kovas, Y., & Plomin, R. (2007). Learning Abilities and Disabilities: Generalist Genes, Specialist Environments. Current Directions in Psychological Science, 16(5), 284–288. https://doi.org/10.1111/j.1467-8721.2007.00521.x
Libertus, M. E., & Brannon, E. M. (2009). Behavioral and Neural Basis of Number Sense in Infancy. Current Directions in Psychological Science, 18(6), 346–351. https://doi.org/10.1111/j.1467-8721.2009.01665.x
Maloney, E. A., & Beilock, S. L. (2012). Math anxiety: who has it, why it develops, and how to guard against it. Trends in Cognitive Sciences, 16(8), 404–406. https://doi.org/10.1016/j.tics.2012.06.008
Matejko, A. A., & Ansari, D. (2018). Contributions of functional Magnetic Resonance Imaging (fMRI) to the study of numerical cognition. Journal of Numerical Cognition. https://doi.org/10.5964/jnc.v4i3.136
Odic, D., & Starr, A. (2018). An Introduction to the Approximate Number System. Child Development Perspectives. https://doi.org/10.1111/cdep.12288
Peters, L., & De Smedt, B. (2018). Arithmetic in the developing brain: A review of brain imaging studies. Developmental Cognitive Neuroscience, 30, 265–279. https://doi.org/10.1016/j.dcn.2017.05.002
Rodic, M., Zhou, X., Tikhomirova, T., Wei, W., Malykh, S., Ismatulina, V., … Kovas, Y. (2015). Cross-cultural investigation into cognitive underpinnings of individual differences in early arithmetic. Developmental Science, 18(1), 165–174. https://doi.org/10.1111/desc.12204
Sella, F., Slusser, E., Odic, D., & Krajcsi, A. (2021). The emergence of children’s natural number concepts: Current theoretical challenges. Child Development Perspectives, 15(4), 265-273.
Sarnecka, B. (2015) Learning to represent exact numbers. Synthese, 198, 1001-1018
Siegler, R S. (2000). The rebirth of children’s learning. Child Development, 71(1), 26–35.
Siegler, Robert S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences. https://doi.org/10.1016/j.tics.2012.11.004
Siegler, Robert S., & Mu, Y. (2008). Chinese Children Excel on Novel Mathematics Problems Even Before Elementary School. Psychological Science, 19(8), 759–763. https://doi.org/10.1111/j.1467-9280.2008.02153.x
Sokolowski, H. M., & Ansari, D. (2017). Who Is Afraid of Math? What Is Math Anxiety? And What Can You Do about It? Frontiers for Young Minds. https://doi.org/10.3389/frym.2017.00057
Sokolowski, H.M., & Ansari, D. (2018) Understanding the effects of education through the lens of biology. NPJ Science of Learning,17
Spelke, E. S. (2005). Sex differences in intrinsic aptitude for mathematics and science?: a critical review. The American Psychologist, 60(9), 950–958. https://doi.org/10.1037/0003-066X.60.9.950
Vogel, S. E., & De Smedt, B. (2021). Developmental brain dynamics of numerical and arithmetic abilities. Npj Science of Learning, 6(1), 22. https://doi.org/10.1038/s41539-021-00099-3

