Overall blog reflection

When I looked across the blog, I noticed that I have learned so many activities to teach math with fun such as solving puzzles, Math art projects, micro-teaching. all these activities help me to foster students to learn math by visualizing the concept and by making a connection with their prior knowledge and their real-life experiences. In fact, I have noticed that these all activities help me to change students' approaches to learn math.  

As a teacher, it is important for me to foster students’ metacognition behavior through my pedagogy. The use of student-centered,  think-pair-share and brainstorming strategies allows the students to make decisions about the way they explore the problem and come up with their own solution. 

reflection of math fair event

It was an excellent experience to see the concept through the students' perspective. I got the chance to talk to the students in person and asked them to share their learning experiences with me. I think it is important for math teachers to choose the student-centered activities that allow the students to interact more with each other and get involved in problem-solving activities. As a result, they will have a concrete foundation of math concepts.  

Reflection of Math (Un)fair

As a teacher, it was an excellent experience to observe students' work through student-centered activity. I have noticed that students were more excited to share their projects'ideas with their peers, teachers, and parents as well. I think the math (un)fair event is a perfect example for teachers on how to promote active learning and peer communication. 

Off the Grid

During the reading of the article about ‘Off the Grid’, I had 3 stops- the failures of the grid system, the alternatives to the grid, and how the indigenous thought generates the opportunity to open doors for new possibilities in mathematics.

The examples of the failures of the grid system mentioned that the limitations of the grid, and how hard for us to think beyond the grid even though we all aware of its limitation. The article mentions the reserve grids road system by giving some examples which highlight how people get confused when they are driving on the roads, where more than two different grids meet.

Reading about the alternatives to the grid, I realized how alternatives approach opens new learning doors for us to see the world in three dimensions (for example, the study of knots) instead to stick with only two dimensions (the grid). The article mentions “the geometry of curved string”. I learned how these alternatives are connected with ancient and modern traditions. I think that it is a really important alternative.

Lastly, I stopped at how the indigenous thought generates the opportunity to open doors for new possibilities to learn mathematics in school. I think that the new approach helps us to learn and to teach the indigenous mathematics curriculum, which helps us to see the world more openly. In other words, if we change our perspectives to see the world, we can see the reality of the situation from its root. This attitude opens the doors for new learning opportunities.

Re done : thinking about math textbook

When I was a student, I think that it was important for me to learn the math concept under the teacher’s guidance so that I understood the concept before started to apply it to my daily life experience. When I was a Grade 9 student, I did not feel comfortable to discuss the math concepts with other students but I was comfortable to share my opinion with the teacher. Like the article mentions exclusive imperative which is one of the “Rotman’s terms”.  I used to reflect my understanding with the teacher instead of my classmates because I used to use the textbooks and practiced the textbook’s examples. However, as a teacher, now I think that it is important for students to understand the concept through social interaction by doing problem-solving activities and by reflecting on their understanding with the other students. As the article mentions about Johansson who thinks that teachers and students can use the textbook in various ways.

As the article mentions about the Rotman’s terms: inclusive and exclusive imperatives. I think that using textbooks in school or not is all depends on the content and students’ needs. I mean, for some content, sometimes students have to use textbooks so that they stay on the right path and learn topics by doing lots of practice. However, most of the time students learn math concepts by explaining, proving and describing through social interaction instead of using textbooks only one way.  During my short practicum, I have noticed that students or teachers do not have to stick only to textbooks in the school due to technology and creating classroom structures. Both of them support students to take risks to engage in discourse and to see themselves as capable of learning Math. I have learned that students’ mathematical identities are connected to their participation in a set of productive practices and processes of doing mathematics. 

Draft 2: Unit lesson plan

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name: Hemlatta Engineer

School, grade & course: Seaquam Secondary School, Grade 12 & Calculus.

The topic of unit: Exponential and logarithm functions

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, and beautiful about this topic? (150 words)         The topic is included in the curriculum because Exponential and logarithm functions develop the concept of instantaneous rate of change. It is important that students learn the topic so that they can apply them to solve the growth and decay problems. I hope students will learn from the Exponent and logarithm functions unit that how to model real-world situations.         Exponential functions are helpful with phenomena that change very quickly or that grow or decay by percentage over a particular time period. In many of the sciences, certain quantities grow or decay at a rate that is proportional to their size. https://www.youtube.com/watch?v=0BSaMH4hINY.         Logarithm functions are helpful when working with phenomena that have a very wide range of values that students actually work within a smaller range. The Logarithm functions that are used to measure the magnitude of earthquakes. The magnitude of an earthquake is related to how much energy-related by the quake so that we can save human lives by predicting the after sock the earthquake’s effects.

(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words) The Process of the project: The project is all about comparing the Exponential function and logarithm function. The project helps students to connect math to real-world situations such as the growth of population, the growth of bacteria, sea level raise, temperature raise, weather forecasting, or university fees raise.   The students will be asked to choose one of the above-mentioned situations for the project. They will create an equation by using a story/word problem, draw a graph, present the PowerPoint presentation/model/poster and compare the exponential function’s equation with a logarithm function’s equation or vice a Versa. The project helps students to understand the topic by creating the equations, by comparing the properties of the two functions, and making scientific conclusions based on mathematical justification. When I will give the project to students, I will allow students to work either in pairs, or small groups or individually. I will give clear instructions on what is expected to do during the project and give a day to think about the project and ask them how they want to do the project, how they want to work. I will check the status of their process on the project regularly. They will submit the project after the week. I will assess the project by giving mark and feedback when they will share their projects with the class as a group.

(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words) I will build a fair and well-rounded assessments and evaluation plan for this unit by below mentioned three assessment modes. I will check their comprehension by giving homework for practice (1% marks/ lesson), by taking the midterm quiz (20 % marks), by giving project (35 % marks), and by taking the final exam at the end of the unit (35% marks). I will evaluate their understanding by reviewing the lesson at the end of each lesson. I will check in with each group when students are doing during the activities and during the project presentation. I will take the midterm test to evaluate students’ progress, and I will take the final test how well they understand the concepts of the unit.

Elements of my unit plan: Give a numbered list of the topics of the 10 lessons in this unit in the order I would teach them.

Lesson	Topic
1	Review: Laws of exponents and logarithms
2	Exponential of functions
3	Derivatives of Exponential functions
4	Properties of  the Derivatives of Exponential functions
5	Exponential growth & decay
6	The Midterm Test
7	Logarithmic functions
8	Derivatives of logarithmic functions
9	Natural logarithm and common logarithm
10	Properties of the derivatives of logarithmic functions
11	Logarithmic differentiation
12	The Unit Test

b) 3 detailed lesson plans:

MATH LESSON PLAN 1: Exponential of functions

Subject: Math	Grade: 12	Date: Feb. 25, 2020	Duration: 80 Minutes
Lesson Overview (What this lesson is about)	This lesson will help students understand the concept of the Exponential of functions and its importance. It will also help the students to build a concrete foundation on Exponential functions by using/ analyzing the graph.
Class Profile	The class has 30 students including 5 ELL learners, 16 girls, and 14 boys.

Big Idea

Differential calculus develops the concept of instantaneous rate of change.

Curriculum Competencies (What the students will do)	Students are expected to: ·       Explore, analyze, and apply mathematical ideas using reason, technology, and other tools ·       Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about the number ·       Visualize to explore and illustrate mathematical concepts and relationships ·       Apply flexible and strategic approaches to solve problems
Content (What the students will know)	Determine the Exponential of functions by using the graphs and by using the laws of exponents Determine the types of Exponential of functions
Language Objectives (What new language students will learn)	Define Exponential of functions, in academic and in layman terms Sketch the Exponential of functions’ graphs in small groups Explain & State the domain, the range, and the asymptote of the Exponential of functions to the class, both orally and in writing.

Materials and Equipment Needed for this Lesson

·       Calculus 12 textbook ·       Colored pens, pencils, eraser, grid papers, and ruler ·       Whiteboard with markers ·       Exponential of functions Worksheets including problem-solving activity

Lesson Stages	What students are going to do?	What teacher is going to do?	Time Allotted
Warm-up	Students will do the problem-solving activity by completing the table, by drawing the graphs, and by comparing the graphs, based on the examples are provided by the teacher. Students will give answers to the questions. *If students struggle to do the activity, more time will need to be allotted to do the activity before introducing the Exponential functions*	I will start the topic by letting them know why is it important to understand the concept of Derivatives of the functions by showing the video clip from the YouTube https://www.youtube.com/watch?v=0BSaMH4hINY. (Note: the video is around 5 minutes long, however, I will show them only first 2 minutes video so that students can visualize the topic). I will give problem solving activity to Graph f(x) = 2x  and f(x)=(1/2)x.  I will ask questions: “What happens to f(x) as x increases?”  “What happens to f(x) as x decreases?” Based on students’ answers response, ask further questions to gather more information about the graphs.	10 minutes
Presentation Teach the new content and language.	Students will ask the questions if they need more explanation to understand the definition. Students will write the notes as well as answers to the questions. They will take a look at the similarities and differences between the two graphs so that students can recognize the types of Exponential functions.	I will explain the definition of the Exponential Function. I will use the same graphs which students have drawn during the activity. I will ask questions for assessing understanding: “Does the graph intersect the x-axis? Explain how you know.” “What are the domain and range of f(x)?” “How does the domain and range of f(x) = (1/2)x Compare to the domain and range of f(x) = 2x?” “What do you notice about the y-intercepts of the graphs of f(x) = (1/2)x and f(x) = 2x?” “What is the asymptote of the function?”	20 minutes
Practice and Production Practice, reinforcement, and extension of the new content and language.	Students will work on the given worksheet in groups. Students will solve examples by graphing the exponential function.	I will give the worksheets to the entire class so as to ensure all students work on it. I will make sure ELL students are paired with non- ELL students during classwork as groups in order to ensure that they are able to work on their understanding of the exponential functions. I will walk around and give hints to groups, help them to correct any errors made. If mistakes are made by most groups, I will gather all students and explain the concept.	30 minutes
Closure	Students will review the topic by recognizing the types of Exponential functions and solving example on the separate paper. They will share their perspectives with the class to review the concept learned.	I will review the topic by asking students to predict that if the resulting graph would be exponential growth or exponential decay, how can we correctly answer the question without actually drawing the graph? I will give homework to solve the Examples: 2, 4 (a, b, c, d, & e), 7, and 8 from the textbook.	20 minutes

Assessment/Evaluation of Students’ Learning

I will walk around during the problem-solving activity at the beginning of the class to ensure that all students are participating. Students will share their perspectives with the class to review on the concept learned in the class, so their level of understanding can be increased. Students will be assessed on participation and understanding during the class and in-class work. I will make sure that students have a concrete understanding of an exponential function by reviewing the topic at the end of the class. I will give homework for practice and it will be collected in the next class and marked for completion and I will reflect on what students do not understand generally, and then review it again in the next class.

 MATH LESSON PLAN 2: Derivatives of Exponential functions  

Subject: Math	Grade: 12	Date: Feb. 26, 2020	Duration: 80 Minutes
Lesson Overview (What this lesson is about)	This lesson will help students understand the concept of the Derivatives of Exponential of functions and its importance. It will also help the students to build a concrete foundation on the Derivatives of Exponential of functions by using/analyzing the graph.
Class Profile	The class has 30 students including 5 ELL learners, 16 girls, and 14 boys.

Big Idea

Differential calculus develops the concept of instantaneous rate of change.

Curriculum Competencies (What the students will do)	Students are expected to: ·       Explore, analyze, and apply mathematical ideas using reason, technology, and other tools ·       Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about the number ·       Visualize to explore and illustrate mathematical concepts and relationships ·       Apply flexible and strategic approaches to solve problems
Content (What the students will know)	Determine the Derivatives of Exponential of functions by using the graphs   Determine the Derivatives of Exponential of functions by using the lows of exponents
Language Objectives (What new language students will learn)	Define  the Derivatives of Exponential of functions, in academic and in layman terms Apply the product and chain rules for the derivatives of the exponential of functions to the class, both orally and in writing.

Materials and Equipment Needed for this Lesson

·       Calculus 12 textbook ·       Colored pens, pencils, eraser, grid papers, and ruler ·       Whiteboard with markers ·       Worksheets including review activity and exit slips

Lesson Stages	What students are going to do?	What teacher is going to do?	Time Allotted
Warm-up	Review activity: Students will review the definition of Derivative based on the example provided by the teacher. They will use their prior knowledge and experience to review the product rule and the chain rule.	I will start the topic by introducing the history of the math behind the topic: The use of a value approaching zero to study rates of change can be found in Indian mathematics, perhaps as early as 500 AD, when the astronomer and mathematician Aryabhata (476–550) used a value approaching zero to study the orbit of the Moon. I will give review activity by providing the example. f(x) = 2x  I will ask students “What happens to f(x + h) as we put x =2x?”  “What happens to f(x) as we put x= 2 x?” Based on students’ answers response, ask further questions to gather more information about the graphs.	10 minutes
Presentation	Students will ask the questions if they need more explanation to understand the definition. Students will write the notes as well as answers to the questions.	I will explain the derivatives of an Exponential Function. I will solve the derivatives of  Exponential Function’s examples on the whiteboard by asking inquiry questions to them such as:  “What is the difference between the product rule and chain rule?” “How do you know that you are going to apply the product rule or the chain rule?”	20 minutes
Practice and Production Practice, reinforcement, and extension of the new content and language.	Students will work on the given worksheets in groups. Students will solve examples of the derivatives of the exponential function.	I will give the worksheets to the entire class so as to ensure all students work on it. I will make sure ELL students are paired with non- ELL students during classwork as groups in order to ensure that they are able to work on their understanding of the derivatives of exponential functions. I will walk around and give hints to groups, help them to correct any errors made. If mistakes are made by most groups, I will gather all students and explain the concept.	30 minutes
Closure	Students will review the topic of how to determine derivatives of Exponential function by filling up the exit slips and solving examples on the whiteboard.	I will review the topic by giving the exit slips to students and by asking students to demonstrate their understanding by solving examples on the whiteboard. I will assign homework to solve examples for practice from the textbook (calculus a first course) ex.4 (a - j), 6 on page 367.	20 minutes

Assessment/Evaluation of Students’ Learning

I will walk around when students are going the review activity at the beginning of the class to ensure that all students are participating. Students will be assessed on participation and understanding during the class and in-class work. Students will review the concepts learned in the class by filling up the exit slips at the end of the class, so their level of understanding can be increased. I will collect the exit slips at the end of the class and I will review the slips and reflect on what students do not understand generally, and then review it again to the following class. I will give homework for practice and I will collect students’ homework in the next class and mark for completion.

MATH LESSON PLAN 3: Properties of the Derivatives of Exponential functions

Subject: Math	Grade: 12	Date: Feb. 25, 2020	Duration: 80 Minutes
Lesson Overview (What this lesson is about)	This lesson will help students understand the concept of the Properties of the Derivatives of Exponential of functions and its importance. It will also help the students to build a concrete foundation on Exponential of functions by applying its properties to the real world situations.
Class Profile	The class has 30 students including 5 ELL learners, 16 girls, and 14 boys.

Big Idea

Differential calculus develops the concept of instantaneous rate of change.

Curriculum Competencies (What the students will do)	Students are expected to: ·       Explore, analyze, and apply mathematical ideas using reason, technology, and other tools ·       Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about the number ·       Visualize to explore and illustrate mathematical concepts and relationships ·       Apply flexible and strategic approaches to solve problems
Content (What the students will know)	Determine the 8 Properties of the Derivatives of Exponential of functions by sketching the graphs
Language Objectives (What new language students will learn)	Define the 8 Properties of the Derivatives of Exponential of functions, in academic and in layman terms by sketching the Exponential of functions’ graphs Explain & State the domain, the range, the asymptote, the interval of increase or decrease, the extreme value, concavity, and the sketch of the curve of the Exponential of functions to the class, both orally and in writing.

Materials and Equipment Needed for this Lesson

·       Calculus 12 textbook ·       Colored pens, pencils, eraser, grid papers, and ruler ·       Whiteboard with markers ·       Worksheets including problem-solving activity and exit ticket activity handouts

Lesson Stages	What students are going to do?	What teacher is going to do?	Time Allotted
Warm-up    Get students’ attention, connect to previous  knowledge and explain why the topic is  Important to learn.	Students will do the problem solving activity by sketching the graphs. Students will complete the table, draw the graphs, and compare the graphs by using their prior knowledge and experience. *If students struggle to do the activity, more time to be allotted to do the activity before introducing the Exponential functions*	I will introduce the topic by giving the problem solving the activity. I will provide the examples for the activity: f(x) = 2x and f(x) = ex I will ask students “Does the curve symmetry to any axis?” “Does the graph of f(x) have  Y-intercept?” Based on students’ answers response, ask further questions to gather more information about the graphs. Questions for assessing understanding: “Does the graph intersect the x-axis? Explain how you know.”	15 minutes
Presentation Teach the new content and language.	Students will work on the properties of the derivatives of Exponential function by answering the questions.	I will explain the Properties of the Derivatives of an Exponential Function: the domain, the range, the asymptote, the interval of increase or decrease, the extreme value, concavity, and the sketch of the curve. I will use the same graphs that students sketch during the activity. I will try to foster their critical thinking by asking the enquiry questions such as: “What are the domain and the range of f(x)?” “What is the asymptote, the interval, the extreme value, the concavity of the function”	20 minutes
Practice and Production Practice, reinforcement, and extension of the new content and language.	Students work on the given worksheet in groups. ELL students will work with non- ELL students during class work.	I will give the worksheets to the entire class so as to ensure all students work on it. ELL students will be paired with non- ELL students during class work as groups in order to ensure that they are able to work on their understanding of the derivatives of exponential functions. I will walk around and give hints to groups, help them to correct any errors made. If mistakes are made by most groups, I will gather all students and explain the concept.	30 minutes
Closure	Students will do the exit ticket activity. Students will explain their ideas in a class by sharing at least one scenario that they think can be modeled with a function. Students will get a general idea about the project that “What”, and “How” they are expected to do during the project.	I will give the exit ticket activity which is a brainstorming activity.  I will ask students to identify three different real world scenarios that can be modeled by functions. After a few minutes, I will ask each pair of students to share at least one scenario that they think can be modeled with a function. I will give the chance for the class to provide feedback. Do you agree that this context can be modeled with a function? Do you have any constructive ideas about how? The goal is to motivate students’ thinking for a collaborative project that they will work on as groups. I will assign a project due to the date, it would be a week later.	15 minutes

Assessment/Evaluation of Students’ Learning

I will walk around when students are doing the problem solving activity and the exit ticket activity to ensure all students are participating. Students will be assessed on participation and understanding during the class and in-class work. Students will share their perspectives with the class to review on the concepts learned that day, so their level of understanding can be increased. I will collect the exit ticket activity handouts at the end of the class and I will review the handouts and reflect on what students do understand generally, and then review it again in the following class if necessary.

Worksheet (link), Exit ticket activity for the Project and project's rubric:

Exit ticket activity: What’s Your Function

We are going to work on a project with a partner today. The project is about creating our own functions to model different scenarios in our communities.

For today’s exit ticket, please work with a partner and brainstorm at least 3 different scenarios that could be modeled with a function. Identify the variables in the function and hypothesize what type of function would best model the scenario.  An example is provided below:

Example:

Scenario: Average temperature by month in Vancouver, BC.

Variables: Month (x-axis) and Temperature (y-axis)

Type of Function: I think this function is best modeled by an exponential function because the temperature is low in January, gradually increases as we get to April and July.

Your Work:

1.       Scenario:

Variables:

Type of Function:

2.       Scenario:

Variables:

Type of Function:

3.       Scenario:

Variables:

Type of Function:

What’s Your Function – Performance Task List (10 Points)

Group Members: ____________________________________________________

We have spent the beginning of the unit learning how to create and apply different types of functions to better understand our world. This project will be part of the demonstration of your understanding of the unit concepts.

Each project must contain the following elements:

1.       Typed up written response (11 points total) that includes the following:

-Clear Title for the project (1 point)

-Identification and explanation of the variables in your function (2 points)

                             -Explanation of the domain and range for your function (2 points)

                             -Description of the relationship in the function (1 point)

-Identify what type of function best describes your function (exponential, or logarithmic) and why (2 points)

-ReflectionCritique of the process (3 points)

                                           -What the group did well on the project (relative strengths)

                                           - What the group can work on/improve upon for next time

                                           - What the group learned about functions and themselves

2.           Display of your function AND its inverse function using function notation (4 points)

3.           Graph of your function (5 points) – include title, label axes, appropriate scale and units

4.           Table of values for your function (5 points)

Group members: _________________________________________                                         Date: ________________

What’s Your Function Project Rubric
	4	3	2	1
1. Elaboration and Clarification	Presentations demonstrate excellent elaboration and use of relevant detail to clarify the main points in presentation	Most parts of the presentation elaborate and use evidence to clarify the main points of the presentation	Few parts of the project are elaborated on and only main ideas are presented without proper clarification and/or follow-up	Many parts of the presentation fail to elaborate on or identify the main idea being made in the project.
2. Justification and use of evidence	Detailed evidence is given to support answer and all of the information and analysis is correct, insightful, AND relevant to the project	Gives evidence to support the presentation, but only minimally analyzes the evidence AND/OR  is off-topic at times	Gives evidence to support the presentation, but some of the information is incorrect or the analysis is weak	Gives inappropriate evidence to support the presentation OR fails to support the presentation
3. Group Work	The group demonstrated excellent collaboration and interpersonal skills in completing the project.	The group demonstrated collaboration and interpersonal skills in completing the project.	The group demonstrated limited collaboration and interpersonal skills in completing the project.	The group demonstrated minimal collaboration and interpersonal skills which interfered with the completion of the project.

4. Content (10 points – see Performance Task list for details): ________

Total Points (out of 35):                                                                                          Grade:

Strengths:                                                                                                                               Areas for revision: