Psychology 3443G-001 (Online for 2020-21)
Development of the 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.
1.0 CALENDAR DESCRIPTION
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.
3 lecture/seminar hours; 0.5 course.
2.0 COURSE INFORMATION
Instructor: Daniel Ansari
Office and Phone Number: WIRB 5180, 519-661-2111 Ext. 80548
Office Hours: Mondays 9.30-10.30am; 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: Jaimy Hannah
Office: WIRB
Office Hours: Tuesdays 1-2pm
Email: jhanna62@uwo.ca
Time and Location of Classes: asynchronous, virtual
Students who are in emotional/mental distress should refer to Mental Health@Western
http://www.uwo.ca/uwocom/mentalhealth/ 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 wish to contact Student Accessibility Services (formerly known as Services for Students with Disabilities) at 519-661-2147.
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
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 skills4.1 STUDENT LEARNING OUTCOMES
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Learning Outcome |
Learning Activity |
Assessment |
|
Depth and Breadth of Knowledge.
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Assigned readings Writing assignments Weekly Lectures |
Midterm Paper Final Paper Lay Summaries 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
Lay Summaries
|
|
Communication Skills.
|
Weekly Lectures Writing Assignments |
Lay Summaries Midterm Paper Final Paper |
|
Awareness of Limits of Knowledge.
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Weekly Lectures Writing Assignments |
Lay Summaries Midterm Paper Final Paper |
|
Autonomy and Professional Capacity.
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Writing Assignments |
Lay Summaries Midterm Paper Final Paper |
5.0 EVALUATION
Quizzes. (5%):
Every week, starting the week of January 18th, you will be asked to complete a short quiz that relates directly to the required readings, lecture and supporting material assigned for that week. You should be able to complete these quizzes by reviewing the required materials for the topics. The quizzes will always be made available on OWL together with the lecture of that topic and can be used as a self- assessment (i.e., did you grasp the important components of the topic). The deadline for all quizzes to be completed is Monday, April 12th, 11:59pm (official last day of classes), but you are strongly encouraged to complete each quiz after reviewing the materials and readings for individual topics. Please note: failure to complete the quizzes by the indicated deadline will result in a grade of 0.
Lay Summaries (15%) and Feedback (10%) on 4 lay summaries:
Being able to summarize research findings in a way that is understandable to the general public is an critical communication skill. You will be asked to write two (2), 250-word summaries of a research article related to the course content. To do so, you are asked to independently find two research papers (not review or opinion articles) using scholarly search engines such as PsychInfo, PubMed, Google Scholar etc. and provide a lay summary of the background, aims, results and implications of the research article you found.
In addition to being asked to write two lay summaries of articles you have independently found, you will be asked to grade 2 you will randomly be assigned two blog posts written by your peers to evaluate. You will be given a grading rubric and instruction on how to grade before the first deadline.
The deadline for submitting the first lay summary is: Monday, February 1st 2021, 11.59pm.
The deadline for submitting your reviews of 2 of your classmates lay summaries is: Friday, February 26th 2021, 11.59pm
The deadline for submitting the second lay summary is: Monday, March 15th 2021, 11.59pm
The deadline for submitting your reviews of 2 of your classmates lay summaries (2nd round) is: Friday, April 2nd 2021, 11.59pm
Please note: There will be a late submission penalty. Specifically, 5% from the grade will be deducted for every day that the submissions are late.
Midterm Paper (30%)
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 Wednesday, February 17th 2021. Please make sure that you save your midterm in Microsoft Word Format. Please title your paper in the following way: Your Name_Midterm_Paper_3443
Please note: 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 (40%)
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 2500 (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 12th 2021. Please make sure that you save your midterm in Microsoft Word Format. Please title your paper in the following way: Your Name_Final_Paper_3443
Please note: There will be a late submission penalty. Specifically, 5% from the grade will be deducted for every day that the submissions are late.
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.
Please note: Grades will not be rounded.
Although the Psychology Department does not require instructors to adjust their course grades to conform to specific targets, the expectation is that course marks will be distributed around the following averages:
70% 1000-level and 2000-level courses
72% 2190-2990 level courses
75% 3000-level courses
80% 4000-level courses
The Psychology Department follows Western's grading guidelines, which are as follows (see http://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
6.0 ASSESSMENT/EVALUATION SCHEDULE
Monday, February 1st 2021, 11.59pm – Deadline for 1st Lay Summary
Wednesday, February 17th 2021 – 11.59pm – Deadline for Midterm Paper
Friday, February 26th 2021, 11.59pm – Deadline to provide feedback on 1st round of Lay Summaries
Monday, March 22nd 2021, 11.59pm – Deadline for 2nd Lay Summary
Friday, April 9th 2021, 11.59pm – Deadline to provide feedback on 2nd round of Lay Summaries
Monday, April 12th 2021, 11:59pm – Deadline for Final Paper
Monday, April 12th 2021, 11:59pm – Final deadline to complete all the weekly quizzes (you are strongly encouraged to do this each with after reading the assigned papers and watching the lecture)
7.0 CLASS SCHEDULE
Week of January 11th: Introduction to the Course: Review of Topics and Assignments
No readings assigned for this week
Week. of January 18th: Origins of number representation: evidence from infants & animals
(Cantlon, 2012)
(Libertus & Brannon, 2009)
Week of January 25th: Basic number processing and its role in higher-level math learning
(Goffin & Ansari, 2019)
(Odic & Starr, 2018)
Week of February 1st: Children’s development of verbal number skills
(Sarnecka, Goldman & Slusser, 2015)
Week of February 8th: Mental Arithmetic & Fractions
(Siegler, 2000)
(Siegler, Fazio, Bailey, & Zhou, 2013)
Week of February 15th: Reading Week
Week of February 22nd: Developmental Dyscalculia
(Bugden & Ansari, 2014)
(Fias, Menon, & Szucs, 2013)
Week of March 1st: Mathematics Anxiety
(Sokolowski & Ansari, 2017)
(Maloney & Beilock, 2012)
https://thelearningexchange.ca/math-anxiety/
Week of March 8th: The mathematical brain: neuropsychology & adult studies
(Ansari, 2008)
(Matejko & Ansari, 2018)
Week of March 15th: The mathematical brain: evidence from children
(Peters & De Smedt, 2018)
Week of March 22nd: Gender Differences
(Kersey, Braham, Csumitta, Libertus, & Cantlon, 2018)
(Spelke, 2005)
Week of March 29th: The effect of genetics on learning and the mathematical brain
(Kovas & Plomin, 2007)
Week of April 5th: Cross-cultural studies and international comparison studies
(Siegler & Mu, 2008)
(Rodic et al., 2015)
8.0 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: http://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.
9.0 POLICY ON ACCOMMODATION FOR ILLNESS OR OTHER ABSENCES
Western’s policy on Accommodation for Medical Illness can be found at:
http://www.westerncalendar.uwo.ca/PolicyPages.cfm?PolicyCategoryID=1&Command=showCategory&SelectedCalendar=Live&ArchiveID=#Page_12
The full policy for consideration for absences can be accessed at: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/Academic_Consideration_for_absences.pdf
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:
- Submitting a Self-Reported Absence form (for circumstances that are expected to resolve within 48 hours);
- 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. The self-reported absence form must be submitted before the exam/coursework deadline in order to be valid. It may NOT be used for absences longer than 48 hours; coursework/tests/exams/etc., worth more than 30% of the final grade; or exams scheduled in the December or April final-exam periods: http://counselling.ssc.uwo.ca/procedures/medical_accommodation.html
Students seeking academic consideration:
- are advised to consider carefully the implications of postponing tests or midterm exams or delaying handing in work;
- are encouraged to make appropriate decisions based on their specific circumstances, recognizing that minor ailments (upset stomach) or upsets (argument with a friend) are not normally an appropriate basis for a self-reported absence;
- must communicate with their instructors no later than 24 hoursafter the end of the period covered by either the self-reported absence or SMC, or immediately upon their return following a documented absence
10.0 Contingency Plan for Return to Lockdown
In the event of a COVID-19 resurgence during the course 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.
11.0 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.
12.0 OTHER INFORMATION
Office of the Registrar: http://registrar.uwo.ca
Student Development Services: www.sdc.uwo.ca
Please see the Psychology Undergraduate web site for information on the following:
http://psychology.uwo.ca/undergraduate/student_responsibilities/index.html
- Policy on Cheating and Academic Misconduct
- Procedures for Appealing Academic Evaluations
- Policy on Attendance
- Policy Regarding Makeup Exams and Extensions of Deadlines
- Policy for Assignments
- Short Absences
- Extended Absences
- Documentation
- Academic Concerns
- 2020-2021 Calendar References
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.
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4). https://doi.org/10.1038/nrn2334
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
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
Sarnecka, Barbara W, Goldman, M.C, Slusser, E. B. (2015). How counting leads to children’s first representations of exact, large numbers. In A. Cohen Kadosh, R., Dowker (Ed.), Oxford Handbook of Numerical Cognition. Oxford Univ Press.
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
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
