Catch!
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| How does our brain compute the complex trajctory of a ball when taking a catch? Changing the size of the ball can really mess up the calulations - learned that the hard way this summer! |
We don't need no education!
"Hey, Sakura! you have almost used up the whole class, may be just give up and let Mr. Kakashi teach." whispered Naruto from the front row.
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| Let's learn from the experts - image generated by AI |
Sakura was not yet ready to give up. She knew that her classmate Sasuke was wrong. She also believed that her teacher, Mr. Kakashi, was wrong as well. Mr. Kakashi was wrong to assign a homework problem on a topic that he did not teach, and now his mistake was in accepting the incorrect solution posted by Sasuke on the board.
"I still don't agree, Mr. Kakashi!" Sakura piped up for the fourth time today, "I have read the whole chapter on projectile motions a few times to try to understand how to solve this problem. You definitely cannot just apply the acceleration due to gravity to the initial velocity, you need to first split it into horizontal and vertical..."
Kakashi shook his head. "Seventh graders are as dumb as rocks," he thought, "but this student is probably the densest of them all."
"I may not have a degree in Physics young lady, but I am sure too on how to apply Newton's laws." retorted Kakashi.
May be on any other day Sakura would have backed down, but today was different. She felt resolute in her mission. Even if it took the entire class period, she would keep on arguing her points.
Hey! Politicians! Leave our kids alone!
In 2024, at the time of writing this post, the provincial government of Mantioba, Canada, has removed all subject requirements for certications to teach K-8 (kindergarten to grade eight). Teaching at public schools in Canada requires a certification process designed and accredited by the respective provinces (and territories). While that does create a job barrier, this system is supposed to ensure that the teachers at public schools know what to teach and how to teach the students at this level. Do you believe that the removal of subject requirements for the certification helps maintain this purpose?
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| A quick summary of the relevant changes that were made in the Manitoba K-8 teaching certificate requirements - information obtained from the Government of Manitoba website, modified and reproduced under the OpenMB Information and Data Use License |
There are a lot of nuances to this topic. For example, eventhough the province does not require a teacher to have any math courses for the certificate to teach K-8, it may not mean that schools will start hiring, say, French teachers — with absolutely no background in higher level Mathematics — to teach math classes. After all, school administrators have a duty of due care and due diligence to the pupils. However, school budgets can be funny sometimes, and economic viability may tend to a future where someone with no math background may need to teach a math class.
A follow up question then asks: "why do kindergarten teachers need to know Calculus?" This is not a fair question, since the curriculum for K-8 covers upto, and including, grade eight. Having been taught Physics by a Physical Education teacher in grade seven, and Biology in grade eight by an Accounting teacher, I can attest to the difference it makes to have a non-specialist teach specialized subjects at these levels. Despite their best effort, these teachers are often missing foundational knowledge to properly respond to student questions about the subject. This may also exacerbate a dire situation where the teacher is not keen about the subject that they are teaching, regardless of their motivation towards teaching itself. Consequently the students may become frustrated with the experience and the subject.
Finally, when it comes to math, an assumption is often made that math specialists do not suffer as badly from math anxiety as non-specialists do. It is not far-fetched to assume that a non-specialist may be more intimidated about teaching math, although I have not yet come across research articles which have definitive tests for this hypothesis. Ramirez et al. tells us that "many elementary teachers have higher math anxiety than individuals in other fields of study, such as business, physical science, and health sciences". Nevertheless, this post will try to shed light on how teacher math anxiety may affect student learning in math classes, with a slight bias towards the ansatz that teachers who have never taken math classes at the University level may experience higher levels of math anxiety than those who have done so.
All-in-all, you're NOT just another brick-in-the-wall!
It is certainly concerning to note that the level of math anxiety is the highest amongst Elementary education majors compared to any other college majors, mentioned by both Yanuarto and Ramirez et. al. What would happen if one of these education majors was suddenly thrust in front of a classroom full of young inquisitive minds and asked to teach math? My son, who just started kindergarten this year, often asks deep questions about the math that his sister — in grade five — is learning. Yes, it is important to remember that even kindergarteners are not brought up in isolation; many-a-times they have an older sibling who they try to emulate. If his teacher were to have general math anxiety, then how would they have responded to my son's questions? Negative experiences with learning math at home or in class can lead to poor understanding and development of math skills (Yanuarto). As Beilock and Willingham puts it quite succinctly, "regardless of a student's gender, his or her teacher's math anxiety seems to carry implications for the student's level of math achievement."
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| The working memory can be overwhelmed by the presence of math anxiety -photo generated by AI |
Research has shown that brighter minds often suffers the most disruption in math performance due to math anxiety (Beilock et. al.). Just to clarify, the stronger students would not necessarily have the highest level of math anxiety, rather that their math learning would suffer the worst from the presence of math anxiety. While this may be counterintuitive, Beilock and Willingham provides a very natural explanation: students with highest level of working memory often adopt advanced problem solving strategies that are cognitively demanding, and math anxiety simply disrupts these strategies. Once caught in the cycle of being anxious about math, students' performance in math may continue to go down due to a self-fulfilling route, where, in the words of Yanuarto:
"...person who feels as if they are going to fail with math, which builds anxiety, which then leads to failure. Failure fosters the idea that they are not good at math which then creates even more math anxiety, creating more failure..."
As always. I request the reader to consult the source materials and to take everything in these blog posts with a grain of salt. The topic of Math Anxiety is something I enjoy learning about, and these blog posts are simply companions to my journey.
There is a dedicated page for the bibliography containing citations to the papers mentioned in this blog. This is a living document that gets updated as I publish newer entries for the blog. The hope is to expand this list to a recommended reading set for scholars of Math Anxiety knowledge.
Catch!
Ramirez et. al. carried out a study in 2018 to investigate how teacher's math anxiety may affect student math performance. The subject of their study was ninth grade mathematics. Their paper is a fascinating read and I highly recommend you to read the source material for unique insights into the matter. However, be forewarned, the authors lean a bit too heavily on fixed versus growth mindset to my liking. Some recent developments into the theory of mindsets indicate the need for a closer look at this concept. Furthermore, as Max Lionel mentions so eloquently in episode one of his podcast, there may be other types of mindsets to consider when it comes to teaching and learning methodology.
Let us look at the objective teaching deficiencies that arise from teachers having math anxiety. Combining ideas from Yanuarto and Ramirez et. al., we can summarize that math teachers with math anxiety may
- be less confident about successfully carrying out their teaching responsibilities,
- respond angrily to students request for help with mathematics, or spend less time attending to students' questions
- project their anxiety on students,
- have a tendency to accept responses quickly without checking solutions and correcting mistakes, which may create an environment that devalues sense-making,
- ask for a single solution to a problem, with emphasis on rote learning and algorithmic thinking.
Ramirez et. al. have shown that higher teacher math anxiety leads to lower student math performance, regardless of students' prior math achievements. Furthermore, students can quickly pick up on the teacher's attitude towards math, and this has a significant affect towards their math learning. This resonates with Yanuarto's viewpoint that "math anxiety is taught in the classroom". Well then, what can be done to ensure that teachers feel confident in their preparation to teach math? Beilock provides a simple suggestion that has been proven effective in addressing math anxiety amoing pre-service teachers: get the teachers to take a course focused on how to teach math concepts. In fact, this strategy works better than requiring teachers take a course focused directly on math concepts themselves.
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How will the removal of the core-requirements of languages, sciences, and history and geography affect math teaching? In my experience, a well-rounded math teacher needs to have some understanding of these subjects as well. The relation between the sciences and mathematics is fairly obvious, mathematics being the lingua-franca for modeling scientific phenomenon. History and geography benefit from many mathematical concepts such as graphs, maps, trees, etc. However, the most crucial connection may be between the languages and mathematics. The theory of Mathematics is rich with linguistic features, and the struggles of learning mathematics run parallel to those of learning a second language. In fact, I believe that the phenomena of "Foreign Language Anxiety" and "Math Anxiety" are closely related. This is a broader topic that I wish to investigate in the future, but for now, in my opinion, math teachers not taking language courses at the University level may be a bigger loss than anticipated. What are your thoughts on this? |
Where does this leave us in our criticism of the Manitoban government's change in the requirements for K-8 teaching certificates? As with every idea, there are pros and cons. The obvious positive of this change is reflected by the reason this change was introduced: to make it easier to qualify for the Manitoba K-8 teaching certificate. Whether that will increase the
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