Flow

Csikszentmihalyi mentions a study he conducted in 1956, where he found that 30% of US Americans were unhappy and increases in material well-being does not seem to affect how happy people are. This reminds me of the saying, “money can’t buy you happiness.” A deeper thought to contributions of one’s happiness more than materialistic things are emotional or spiritual; feeling welcomed and loved or feeling at home as a few examples.

Csikszentmihalyi describes flow as the effortless, spontaneous feeling you get when entering an ecstatic state (2004). He lists seven conditions for being in flow: 1) completely involved in what you are doing; 2) a sense of ecstasy; 3) great inner clarity; 4) knowing that the activity is doable; 5) a sense of serenity; 6) timelessness; 7) intrinsic motivation. One thing that makes me experience flow is when I skate on the ice playing hockey. Skating around feels so natural and calm; I become mesmerized by the puck and the sounds of skate blades cutting into the ice. All my worries seem to disappear for the time being as if I entered a different reality. Another moment I experience flow was when working at Science World and demonstrating science experiments on stage. I become so focused in the moment interacting with the audience and teaching science, I often lose track of time. I like to think of myself as being completely in “the zone.”

Csikszentmihalyi presents this diagram during his TEDtalk, where flow is in the area with the optimal mix of challenge and skill. Other areas like arousal, control, and relaxation could also be desirable. As a mathematics teacher, or any kind of educator, anxiety, boredom, worry, and apathy should be avoided. To promote this zone of flow in the classroom, I think teachers need to teach at a level that is not considered too difficult for students but challenging enough so they can use their previous knowledge to assist with learning. Some students might feel that music will help get into flow, so educators should consider allowing them to listen to music while working and “peeking” to make sure they are on task. Opportunities to discuss and share ideas students are interested in can also promote flow in the classroom as it is easy to have conversations about something one is passionate about. Math puzzles or relevant realistic problems could be a great activity to help students feel immersed in problem solving as it challenges their thinking outside of the box and forces them to ask questions.

 

Video:

Csikszentmihalyi, M. (2004). Flow, the secret to happiness. TED. Retrieved from https://www.ted.com/talks/mihaly_csikszentmihalyi_flow_the_secret_to_happiness?language=en

The new BC curriculum and secondary math course pathways structure

One thing that surprised me was how the BC curriculum was redesigned to provide more flexibility to educators to structure their lessons and teachings to reflect personalization of student learning. This is done through the creation of core competencies and big ideas educators should address when developing lessons; things students are expected to do and expected to understand. Core competencies are sets of intellectual, personal, and social competencies students develop to engage in deeper learning and support lifelong learning (BC curriculum, 2020). Big ideas do not require students to know specific pieces of factual information or isolated bits of information but are broad and abstract statements central to one’s understanding in an area of learning (BC curriculum, 2020). The second thing that surprised me was the inclusion of the definition for 21^st century skills, which was defined as, “a term used to describe the combination of specific skills, content knowledge, expertise, and literacies that are essential for today’s graduates” (BC curriculum glossary, 2020). I really liked this definition. I think it is crucial that secondary students be taught skills that are relevant to them and take advantage of how easily information can be acquired in this day and age.

This is my flowchart for the pathways structure of BC curriculum math courses. The one-way arrows shows where you could go to at the course given. Notice that courses like computer science 11 and history of mathematics 11 have many arrows going into it. I think that those courses could be taken at many stages of a secondary student's math career. The two-way arrows means you could take the course at the same time as another course. There might be a few arrows I missed for concurrent courses as it was hard to keep track of everything. 

Figure 1: My interpretation of BC secondary math course pathways

Readings:

BC Curriculum orientation guide: https://curriculum.gov.bc.ca/sites/curriculum.gov.bc.ca/files/Curriculum_Brochure.pdf

BC Curriculum glossary: https://curriculum.gov.bc.ca/sites/curriculum.gov.bc.ca/files/pdf/glossary.pdf

BC mathematics curriculum (K-12): https://curriculum.gov.bc.ca/curriculum/mathematics/core/goals-and-rationale

Geometric/numerical puzzle

Question: Thirty equally spaced points on the circumference of a circle are labelled in order with the numbers 1 to 30. Which number is diametrically opposite to 7?

To solve this geometric/numerical puzzle, I drew a circle and made diametric lines across from numbers 1 to 30. Using my image, I find that the number diametrically opposite to 7 was 22. After drawing my image, I noticed that there are 15 ‘spaces’ between the starting number and the number diametric from it. 

Figure 1: My drawing 

A puzzle related to this can be to rearrange the numbers so that they are not organized in ascending order around the circle and ask students to find numbers diametric and next to a number, etc. If this were a word problem, it would be lengthy just to set up the problem alone. An extension of this is to use numbers 1-24 to correspond with letters of the alphabet and students can use it to create coded messages.

I feel like all problems can be logic problems, but a problem is considered “geometric” when there are aspects that allow for visualization of the problem geometrically. When I read this problem, I immediately thought of it as a geometric problem because I began visualizing a circle with the numbers arranged around it. I drew diametric lines to help me think of the solution and did not make the logical connection between half of 30 and properties of a circle.

I think there is more value to give students problems with no single correct answer (in an academia, these are considered wicked problems). This encourages discussion and conversation amongst students to share their reasoning and logic when arriving at their answer. 

Updated Microteaching Topic: Introduction to the Guitar

Some feedback I received from my guitar microteaching lesson was to shorten some content so that I could ensure that my teaching pace was slowed down to fit into the 10 minute window while also emphasizing vocabulary and reviewing the different parts of the guitar. If this were an in-person lesson, one way to address the issue of not everyone having a guitar would be to pass my guitar around the class so that students can hold it and make connections between my presentation and embodied learning.

For my updated microteaching guitar lesson plan, I have chosen to omit the section on teaching the C major scale. I had also intended to play a short song at the beginning and end of the lesson, however, I did not do this during the actual lesson because of the short time constraint. 

Following along on the power point , I will be omitting slide 4. 

Subject: Introduction to the Guitar	Grade:	Date: Oct 14/20	Duration: 10 mins
Lesson Overview (What this lesson is about)	This lesson will provide students an introduction to the guitar.
Class Profile   Construct a hypothetical class profile, in which you specify how many students are in your class, their learning challenges, and their levels of English proficiency	EDCP 342A: Curriculum and Instruction in Secondary Mathematics (~27 post-secondary students)
Content Objectives (What the students will know)	By the end of the lesson, students should be able to: ·        Identify different parts of the guitar. ·        Define pitch and correctly label note associated with each (open) string. ·        Read chord charts and tabs.
Language Objectives   (What new language the students will learn)	·        Pitch: how high or low a musical sound is. ·        Tab: Short for tablature, which is a form of writing down music for the guitar, which mainly uses numbers instead of music notation.   ·        Chord: Set of harmonic pitches/frequencies consisting of multiple notes heard simultaneously.

Materials and Equipment Needed for this Lesson

Guitar

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up   Get students’ attention, connect to previous knowledge and explain why the topic is important to learn.	·        Ask if anyone has picked up and tried to play a guitar before.	1 minute
2.	Presentation   Teach the new content and language.	·        Show students the different parts of the guitar.         ·        Name the pitch associated with each string.         ·        Reading tabs.         ·        Reading chords.	5 minutes
3.	Practice and Production       Practice, reinforcement, and extension of the new content and language.	·        Practice reading tabs.         ·        Practice reading chords.	2 minutes
4.	Closure	·        Summary of vocabulary from Language Objectives.         ·        Open the floor to questions.	2 minutes

Three curricula all schools teach

I think it is interesting that students spend 480 weeks or 12,000 hours in school by the time a child graduates from secondary education. If they continue to post-secondary immediately after graduation, they will typically add on another 110-140 weeks or approximately 2600-3000 hours in school. That is a long time to spend in an academic institutional setting consecutively.

The big point from this reading was the implicit curriculum that schools teach, one of them being to set up students for the real-world outside of secondary education. Eisner mentions how “children will not have jobs in adult life that is interesting; most jobs do not provide for high degrees of intellectual flexibility; most jobs depend on routine” (n.d., p.90), which implies that secondary education is purposely designed to set up students for that lifestyle afterwards. Secondary education prepares students for one-way communication and hierarchical organizational structures in the workforce. It is also mentioned that the current design of the curriculum fosters competitiveness through grading of students. Something I have noticed while in schooling is that students are very competitive amongst each other when it comes to grading, with some students even going as far as “sabotaging” classmates by not helping or lying when asked questions about assignments. Eisner mentions that grading “fosters differentiation of classes into ability groups” (n.d., p.91). This is the idea that students who achieve higher grades get placed into honours classes and programs. Some honours programs offer different credit track systems within the school curriculum speeding up a student’s progress. This now becomes unfair as it does not give students an opportunity to be part of this program. In an example from my high school experience, I have seen some students who excelled in mathematics opt out of the honours mathematics program and take “normal” math to get a better grade as the content is not as challenging. Implicit curriculum also teaches students how to be cognitively flexible, ie. be able to shift problems and adapt to new demands on schedule; teach intellectual and social virtues such as punctuality and willingness to work hard on tasks; and defer immediate gratification in order to work for distant goals. Interestingly, I have noticed these implicit curricular teachings through my elective classes in high school through mechanics, automotives, and even home economics. The teachers I had for these courses talked to us like adults and taught life-lessons in the classroom and made me realize that my courses were training us to be able to manage busy homework and study schedules and conform to authority.

If the [explicit] curriculum of secondary education is to teach students to have English literacy, numeracy, and academic knowledge to prepare them for post-secondary education, then the mandated BC Provincial Curriculum achieves this. The mandated BC Provincial Curriculum also includes some aspects of the implicit curriculum that Eisner discusses in this paper. The BC curriculum tries to connect academic learning to life skills for students to succeed if they choose not to further their education after secondary. The BC curriculum also includes some of Eisner’s idea of the “null curriculum.” Eisner defines the “null curriculum” as information schools do not teach. For example, most students complain about not knowing how to do their taxes however, I think this is taught in a BC mandatory graduation class; it could use further emphasis so students can retain this information longer than from a single lesson on taxes and finances. There are some skills schools may not offer completely as they do not have the resources to teach such as an automatives program. BC curriculum should work with school districts to try and accommodate this by bringing in guest presentations of people who work in those fields to educate students and provide opportunities to learn more through apprenticeship or volunteer programs.

Reading:

Eisner, E.W. n.d, The Three Curricula That All Schools Teach. The Educational Imagination On the Design and Evaluation of School Programs. 3rd Edition. Stanford University. Pp. 87-107

Microteaching Topic: Introduction to the Guitar

 Next week, I will be microteaching an introduction to the guitar. 

Lesson plan adapted from LLED 360 Lesson Plan Template: 

Subject: Introduction to the Guitar	Grade:	Date: Oct 14/20	Duration: 10 mins
Lesson Overview (What this lesson is about)	This lesson will provide students an introduction to the guitar.

Content Objectives (What the students will know)

By the end of the lesson, students should be able to: ·        Identify different parts of the guitar. ·        Define pitch and correctly label note associated with each (open) string. ·        Read chord charts and tabs.

Language Objectives   (What new language the students will learn)

·        Pitch: how high or low a musical sound is. ·        Scale: any set of musical notes ordered by fundamental frequency or pitch. ·        Tab: Short for tablature, which is a form of writing down music for the guitar, which mainly uses numbers instead of music notation.   ·        Chord: Set of harmonic pitches/frequencies consisting of multiple notes heard simultaneously. ·        Octave: series of 8 notes occupying the interval between two notes.

Materials and Equipment Needed for this Lesson

Guitar

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up   Get students’ attention, connect to previous knowledge and explain why the topic is important to learn.	·        Ask if anyone has picked up and tried to play a guitar before/familiarity with music theory.          ·        Play a short song (Serene of Water from OoT)	1 minute
2.	Presentation   Teach the new content and language.	·        Show students the different parts of the guitar         ·        Name the pitch associated with each string         ·        Introduce the C Major note scale         ·        Reading tabs         ·        Reading chords	5 minutes
3.	Practice and Production   Practice, reinforcement, and extension of the new content and language.	·        Practice reading tabs         ·        Practice reading chords	2 minutes
4.	Closure	·        Open the floor to questions         ·        Play a closing song? (Lost Woods)	2 minutes

https://drive.google.com/file/d/1KaEka-xEBx7ovP7ZsFU5e6-_D3TG_-QD/view?usp=sharing 

Battleground Schools

I really liked how this article was like a brief history of mathematics education throughout the 20^th century. Starting with the Progressivist Movement led by John Dewey from 1910-1940, New Math reform movement of the 1960s, and present-day Math Wars. Dewey advocated for a shift in math education where students should form and test hypotheses and perceive patterns and relationships through experimentation, inquiry and interpretation. Dewey is a very influential person and strong advocate for educational reform. Dewey challenged the system of impractical solutions derived from complicated steps to solving math problems. Another moment that made me stop during reading was through the introduction of the Bourbaki math group. They were a secret-invite only group of French-mathematicians publishing work under the pseudonym Nicholas Bourbaki. They published mathematical textbooks and introduced new math notations. I thought it was funny that there existed a secret group of mathematicians in which entry was invite only; like a superhero organization. The last section that made me stop was on the discussion of New Math. New Math was introduced following the Soviet Union’s successful launch of Sputnik in the great space race. The goal of New Math was to introduce abstract concepts earlier from K-12 so that students can develop into rocket scientists and engineers to help US win the space race. Teachers and parents who learned math previously did not understand New Math and was not able to teach it effectively. New Math was highly conservative and reflects traditional university style teaching such as lecturing, presentations, favouring deductive methods and viewed math as infallible. This reminded me of the scene from the movie Incredibles 2, where Bob was trying to teach Dash “new math” and was getting frustrated questioning, “why would they change math? Math is math.”

 

Paper:

Gerofsky, S. 2008. Mathematics Education. Battleground Schools Volume 2 (L-Z). Greenwood Press. Westport, Connecticut, London. Pp. 391-400

Movie Scenes. 2018. Incredibles 2 – ‘Math is Math’ Scene. Retrieved September 29, 2020 from https://www.youtube.com/watch?v=3QtRK7Y2pPU.