IMPACT Live!

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

Your approach of integrating Desmos into teaching trigonometry through real-life applications like the Ferris wheel scenario is engaging. Using digital platforms like Desmos for visualizing complex mathematical concepts can indeed make learning more accessible and enjoyable for students. This method supports active engagement and allows students to explore and understand abstract concepts in a tangible way, potentially enhancing their journey toward proficiency.

However, while this strategy is impactful for engaging students and driving comprehension, it might also be beneficial to consider incorporating elements of inquiry-based learning or problem-based learning. For instance, you could give your students time to explore Desmos with sliders and seeing what they do to the function before or during class, then lead a group discussion where you end up summarizing what was found by watching that lecture video. Or you could have students attempt the Ferris Wheel activity outside of class and then start class by using the Snapshot tool to compare student answers. I love using a flipped classroom, but the flip doesn't always have to be direct instruction. By presenting problems that require students to apply their knowledge in new and unfamiliar contexts, we're showing students they have the tools and knowledge to tackle new problems without having seen a lecture and done a few examples first. 

So I guess my answer is this method is better than traditional direct instruction - you're using active learning, visualizations, making the most of class time by using a flipped approach... but it still has the feel of direct instruction where the instructor's voice is centered because you're showing students the video first. The beauty of playing with Desmos' graphing calculator is that your students could discover those things without any instructor input. I'd leave the lecture (consolidation) and sketched graphs on paper for the final exit ticket, rather than leading with them. 

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------

Thank you for your valuable feedback!

Here are some points of reflection and additional thoughts:

Preparation and Engagement:

The use of flipping and pre-tests provides a valuable insight into students' prior knowledge and helps in tailoring the teaching approach accordingly. The short video and low-key questions serve as effective warm-up, stimulating curiosity and preparing students for the challenges ahead.

Sketching and Graphing Challenges:

Focusing on the basic function f(x)=sin(x) for sketching is a foundational step, allowing me to understand students' approach and thought processes. Introducing more complex forms (1) and (2) opens up opportunities for deeper exploration and challenges, fostering critical thinking.

Real-Life Application:

Connecting trigonometric functions to real-life scenarios, like the Ferris Wheel problem, adds relevance and motivation for students. It also allows for practical application of theoretical concepts.

Inquiry-Based Learning:

Emphasizing the inquiry-based learning approach is essential, as it promotes engagement and deeper understanding. Highlighting this aspect helps students recognize the value of exploring concepts on their own. However, the key used here is proficiency, so it can be achieved through inquiry-learning approach.

Exit Ticket and Assessment:

Viewing post-Desmos activities as a short exam or exit ticket is a valid perspective. It serves as to view students' understanding and progress after the exploration phase.

Individualized Learning:

Acknowledging the time-consuming nature of graphing challenges, providing opportunities for students to work at their own pace, and offering additional practice outside class for those who need it are considerate approaches. This accommodates diverse learning needs.

Lecture Consolidation:

Breaking up Desmos activities with pauses for discussion and drawing major conclusions is an effective way to consolidate learning. The use of slides to pace the session keeps the flow structured and manageable.

Handout with Practice Problems:

Providing handouts with major definitions, formulas, and key points for practice problems is a good reinforcement strategy, helping students consolidate their learning outside of interactive activities.

·        ------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 09:23:31
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

Your approach of integrating Desmos into teaching trigonometry through real-life applications like the Ferris wheel scenario is engaging. Using digital platforms like Desmos for visualizing complex mathematical concepts can indeed make learning more accessible and enjoyable for students. This method supports active engagement and allows students to explore and understand abstract concepts in a tangible way, potentially enhancing their journey toward proficiency.

However, while this strategy is impactful for engaging students and driving comprehension, it might also be beneficial to consider incorporating elements of inquiry-based learning or problem-based learning. For instance, you could give your students time to explore Desmos with sliders and seeing what they do to the function before or during class, then lead a group discussion where you end up summarizing what was found by watching that lecture video. Or you could have students attempt the Ferris Wheel activity outside of class and then start class by using the Snapshot tool to compare student answers. I love using a flipped classroom, but the flip doesn't always have to be direct instruction. By presenting problems that require students to apply their knowledge in new and unfamiliar contexts, we're showing students they have the tools and knowledge to tackle new problems without having seen a lecture and done a few examples first. 

So I guess my answer is this method is better than traditional direct instruction - you're using active learning, visualizations, making the most of class time by using a flipped approach... but it still has the feel of direct instruction where the instructor's voice is centered because you're showing students the video first. The beauty of playing with Desmos' graphing calculator is that your students could discover those things without any instructor input. I'd leave the lecture (consolidation) and sketched graphs on paper for the final exit ticket, rather than leading with them. 

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------

I'm not sure if you edited your reply from what you original posted (what I have in my email is different and more clear). So to summarize it for others, I was confused about the pre-work students were doing, but it isn't a lecture and pre-assessment on graphing transformations of trig functions, the video and sketches by hand were graphing the base functions and ensuring all students came into the lesson with that common knowledge. So we were advocating for the same progression of a lesson and the initial "watched a video on graphing sine and cosine functions before coming to class" was literally only about graphing sin(x) and cos(x).

I do want to tag @Luke Walsh as the master of amazing Desmos activities for trig! If he's willing to share the collection - it's the best.I used a ton of his stuff similarly to how Lucie's response in the email version discussed - using pacing and student snapshots to help students conceptualize the topics. I also had a ton of fun moving students from the graphs of sine and cosine using this activity: https://teacher.desmos.com/activitybuilder/custom/5f6b448202a5380c957c29e3 watching students struggle with how those points might translate to a graph was the absolute best time. 

I am a little unclear about the prompt for the discussion though. Is it about how we use technology to accomplish active learning? Or can it be about just innovation with tech or just innovation with active learning? I realize I took the entire discussion in another direction trying to make sense of the provided example.

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-05-2024 11:31:00
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

Thank you for your valuable feedback!

Here are some points of reflection and additional thoughts:

Preparation and Engagement:

The use of flipping and pre-tests provides a valuable insight into students' prior knowledge and helps in tailoring the teaching approach accordingly. The short video and low-key questions serve as effective warm-up, stimulating curiosity and preparing students for the challenges ahead.

Sketching and Graphing Challenges:

Focusing on the basic function f(x)=sin(x) for sketching is a foundational step, allowing me to understand students' approach and thought processes. Introducing more complex forms (1) and (2) opens up opportunities for deeper exploration and challenges, fostering critical thinking.

Real-Life Application:

Connecting trigonometric functions to real-life scenarios, like the Ferris Wheel problem, adds relevance and motivation for students. It also allows for practical application of theoretical concepts.

Inquiry-Based Learning:

Emphasizing the inquiry-based learning approach is essential, as it promotes engagement and deeper understanding. Highlighting this aspect helps students recognize the value of exploring concepts on their own. However, the key used here is proficiency, so it can be achieved through inquiry-learning approach.

Exit Ticket and Assessment:

Viewing post-Desmos activities as a short exam or exit ticket is a valid perspective. It serves as to view students' understanding and progress after the exploration phase.

Individualized Learning:

Acknowledging the time-consuming nature of graphing challenges, providing opportunities for students to work at their own pace, and offering additional practice outside class for those who need it are considerate approaches. This accommodates diverse learning needs.

Lecture Consolidation:

Breaking up Desmos activities with pauses for discussion and drawing major conclusions is an effective way to consolidate learning. The use of slides to pace the session keeps the flow structured and manageable.

Handout with Practice Problems:

Providing handouts with major definitions, formulas, and key points for practice problems is a good reinforcement strategy, helping students consolidate their learning outside of interactive activities.

·        ------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 09:23:31
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

Your approach of integrating Desmos into teaching trigonometry through real-life applications like the Ferris wheel scenario is engaging. Using digital platforms like Desmos for visualizing complex mathematical concepts can indeed make learning more accessible and enjoyable for students. This method supports active engagement and allows students to explore and understand abstract concepts in a tangible way, potentially enhancing their journey toward proficiency.

However, while this strategy is impactful for engaging students and driving comprehension, it might also be beneficial to consider incorporating elements of inquiry-based learning or problem-based learning. For instance, you could give your students time to explore Desmos with sliders and seeing what they do to the function before or during class, then lead a group discussion where you end up summarizing what was found by watching that lecture video. Or you could have students attempt the Ferris Wheel activity outside of class and then start class by using the Snapshot tool to compare student answers. I love using a flipped classroom, but the flip doesn't always have to be direct instruction. By presenting problems that require students to apply their knowledge in new and unfamiliar contexts, we're showing students they have the tools and knowledge to tackle new problems without having seen a lecture and done a few examples first. 

So I guess my answer is this method is better than traditional direct instruction - you're using active learning, visualizations, making the most of class time by using a flipped approach... but it still has the feel of direct instruction where the instructor's voice is centered because you're showing students the video first. The beauty of playing with Desmos' graphing calculator is that your students could discover those things without any instructor input. I'd leave the lecture (consolidation) and sketched graphs on paper for the final exit ticket, rather than leading with them. 

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------

I did edit it to open up the discussion and generalize it a bit with the purpose of giving a chance for everyone to bring new innovative ideas. The prompt is about Innovative Teaching and Learning with additional focus but not limited to Using Technology for supporting active learning. It is open to introduce any active innovative approach that you may use. So, please feel free to bring any new ideas.                 I am sharing the link to AMATYC Conference Demo. I created it with parts from my activities just to get a flavor of different types activities for various purposes of use https://student.desmos.com/join/uv5u6u

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 15:45:20
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

I'm not sure if you edited your reply from what you original posted (what I have in my email is different and more clear). So to summarize it for others, I was confused about the pre-work students were doing, but it isn't a lecture and pre-assessment on graphing transformations of trig functions, the video and sketches by hand were graphing the base functions and ensuring all students came into the lesson with that common knowledge. So we were advocating for the same progression of a lesson and the initial "watched a video on graphing sine and cosine functions before coming to class" was literally only about graphing sin(x) and cos(x).

I do want to tag @Luke Walsh as the master of amazing Desmos activities for trig! If he's willing to share the collection - it's the best.I used a ton of his stuff similarly to how Lucie's response in the email version discussed - using pacing and student snapshots to help students conceptualize the topics. I also had a ton of fun moving students from the graphs of sine and cosine using this activity: https://teacher.desmos.com/activitybuilder/custom/5f6b448202a5380c957c29e3 watching students struggle with how those points might translate to a graph was the absolute best time. 

I am a little unclear about the prompt for the discussion though. Is it about how we use technology to accomplish active learning? Or can it be about just innovation with tech or just innovation with active learning? I realize I took the entire discussion in another direction trying to make sense of the provided example.

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-05-2024 11:31:00
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

Thank you for your valuable feedback!

Here are some points of reflection and additional thoughts:

Preparation and Engagement:

The use of flipping and pre-tests provides a valuable insight into students' prior knowledge and helps in tailoring the teaching approach accordingly. The short video and low-key questions serve as effective warm-up, stimulating curiosity and preparing students for the challenges ahead.

Sketching and Graphing Challenges:

Focusing on the basic function f(x)=sin(x) for sketching is a foundational step, allowing me to understand students' approach and thought processes. Introducing more complex forms (1) and (2) opens up opportunities for deeper exploration and challenges, fostering critical thinking.

Real-Life Application:

Connecting trigonometric functions to real-life scenarios, like the Ferris Wheel problem, adds relevance and motivation for students. It also allows for practical application of theoretical concepts.

Inquiry-Based Learning:

Emphasizing the inquiry-based learning approach is essential, as it promotes engagement and deeper understanding. Highlighting this aspect helps students recognize the value of exploring concepts on their own. However, the key used here is proficiency, so it can be achieved through inquiry-learning approach.

Exit Ticket and Assessment:

Viewing post-Desmos activities as a short exam or exit ticket is a valid perspective. It serves as to view students' understanding and progress after the exploration phase.

Individualized Learning:

Acknowledging the time-consuming nature of graphing challenges, providing opportunities for students to work at their own pace, and offering additional practice outside class for those who need it are considerate approaches. This accommodates diverse learning needs.

Lecture Consolidation:

Breaking up Desmos activities with pauses for discussion and drawing major conclusions is an effective way to consolidate learning. The use of slides to pace the session keeps the flow structured and manageable.

Handout with Practice Problems:

Providing handouts with major definitions, formulas, and key points for practice problems is a good reinforcement strategy, helping students consolidate their learning outside of interactive activities.

·        ------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 09:23:31
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

Your approach of integrating Desmos into teaching trigonometry through real-life applications like the Ferris wheel scenario is engaging. Using digital platforms like Desmos for visualizing complex mathematical concepts can indeed make learning more accessible and enjoyable for students. This method supports active engagement and allows students to explore and understand abstract concepts in a tangible way, potentially enhancing their journey toward proficiency.

However, while this strategy is impactful for engaging students and driving comprehension, it might also be beneficial to consider incorporating elements of inquiry-based learning or problem-based learning. For instance, you could give your students time to explore Desmos with sliders and seeing what they do to the function before or during class, then lead a group discussion where you end up summarizing what was found by watching that lecture video. Or you could have students attempt the Ferris Wheel activity outside of class and then start class by using the Snapshot tool to compare student answers. I love using a flipped classroom, but the flip doesn't always have to be direct instruction. By presenting problems that require students to apply their knowledge in new and unfamiliar contexts, we're showing students they have the tools and knowledge to tackle new problems without having seen a lecture and done a few examples first. 

So I guess my answer is this method is better than traditional direct instruction - you're using active learning, visualizations, making the most of class time by using a flipped approach... but it still has the feel of direct instruction where the instructor's voice is centered because you're showing students the video first. The beauty of playing with Desmos' graphing calculator is that your students could discover those things without any instructor input. I'd leave the lecture (consolidation) and sketched graphs on paper for the final exit ticket, rather than leading with them. 

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------

Hi Lucie,

 This is a great prompt. This is my first time teaching Calculus, which has a lab element in it. I am constantly on the lookout for fun activities and active learning, to keep students engaged. We meet for nearly 3 hours on one day, beside 75 minutes on another day. I've used desmos activities from AMATYC library archives as well as Geogebra ones from colleagues. One active/inquiry based learning, without much technology was for students to graph a position and velocity graph given partial information as follows,

Neil starts jogging on straight path and runs faster and faster for 4 minutes, then he walks for 6 minutes. He stops at an intersection for 3 minutes, runs quickly for 5 minutes, then walks back for 8 minutes. How far is he from the starting point?

The critical piece missing was any of the speeds - walking or running, or acceleration, but I handed them a measuring tape and sent them into the hallway. So, they had to measure themselves walking and running and come up with a reasonable estimate. Since their initial acceleration was unknown, how would they plot? it had them thinking long... They were to plot the graphs. Excel tends to either make straight lines between points or curve fit all points, it cannot easily make piece wise continuous plots. I have yet to grade this work, which was just turned in.

------------------------------
Manisha Ranade
Associate Professor
Santa Fe College
Gainesville FL
http://www.sfcollege.edu

Original Message:
Sent: 02-05-2024 16:24:09
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

I did edit it to open up the discussion and generalize it a bit with the purpose of giving a chance for everyone to bring new innovative ideas. The prompt is about Innovative Teaching and Learning with additional focus but not limited to Using Technology for supporting active learning. It is open to introduce any active innovative approach that you may use. So, please feel free to bring any new ideas.                 I am sharing the link to AMATYC Conference Demo. I created it with parts from my activities just to get a flavor of different types activities for various purposes of use https://student.desmos.com/join/uv5u6u

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 15:45:20
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

I'm not sure if you edited your reply from what you original posted (what I have in my email is different and more clear). So to summarize it for others, I was confused about the pre-work students were doing, but it isn't a lecture and pre-assessment on graphing transformations of trig functions, the video and sketches by hand were graphing the base functions and ensuring all students came into the lesson with that common knowledge. So we were advocating for the same progression of a lesson and the initial "watched a video on graphing sine and cosine functions before coming to class" was literally only about graphing sin(x) and cos(x).

I do want to tag @Luke Walsh as the master of amazing Desmos activities for trig! If he's willing to share the collection - it's the best.I used a ton of his stuff similarly to how Lucie's response in the email version discussed - using pacing and student snapshots to help students conceptualize the topics. I also had a ton of fun moving students from the graphs of sine and cosine using this activity: https://teacher.desmos.com/activitybuilder/custom/5f6b448202a5380c957c29e3 watching students struggle with how those points might translate to a graph was the absolute best time. 

I am a little unclear about the prompt for the discussion though. Is it about how we use technology to accomplish active learning? Or can it be about just innovation with tech or just innovation with active learning? I realize I took the entire discussion in another direction trying to make sense of the provided example.

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-05-2024 11:31:00
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

Thank you for your valuable feedback!

Here are some points of reflection and additional thoughts:

Preparation and Engagement:

The use of flipping and pre-tests provides a valuable insight into students' prior knowledge and helps in tailoring the teaching approach accordingly. The short video and low-key questions serve as effective warm-up, stimulating curiosity and preparing students for the challenges ahead.

Sketching and Graphing Challenges:

Focusing on the basic function f(x)=sin(x) for sketching is a foundational step, allowing me to understand students' approach and thought processes. Introducing more complex forms (1) and (2) opens up opportunities for deeper exploration and challenges, fostering critical thinking.

Real-Life Application:

Connecting trigonometric functions to real-life scenarios, like the Ferris Wheel problem, adds relevance and motivation for students. It also allows for practical application of theoretical concepts.

Inquiry-Based Learning:

Emphasizing the inquiry-based learning approach is essential, as it promotes engagement and deeper understanding. Highlighting this aspect helps students recognize the value of exploring concepts on their own. However, the key used here is proficiency, so it can be achieved through inquiry-learning approach.

Exit Ticket and Assessment:

Viewing post-Desmos activities as a short exam or exit ticket is a valid perspective. It serves as to view students' understanding and progress after the exploration phase.

Individualized Learning:

Acknowledging the time-consuming nature of graphing challenges, providing opportunities for students to work at their own pace, and offering additional practice outside class for those who need it are considerate approaches. This accommodates diverse learning needs.

Lecture Consolidation:

Breaking up Desmos activities with pauses for discussion and drawing major conclusions is an effective way to consolidate learning. The use of slides to pace the session keeps the flow structured and manageable.

Handout with Practice Problems:

Providing handouts with major definitions, formulas, and key points for practice problems is a good reinforcement strategy, helping students consolidate their learning outside of interactive activities.

·        ------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY

Original Message:
Sent: 02-05-2024 09:23:31
From: Kelly Spoon
Subject: IMPACT Discussion - Digital Platforms

Your approach of integrating Desmos into teaching trigonometry through real-life applications like the Ferris wheel scenario is engaging. Using digital platforms like Desmos for visualizing complex mathematical concepts can indeed make learning more accessible and enjoyable for students. This method supports active engagement and allows students to explore and understand abstract concepts in a tangible way, potentially enhancing their journey toward proficiency.

However, while this strategy is impactful for engaging students and driving comprehension, it might also be beneficial to consider incorporating elements of inquiry-based learning or problem-based learning. For instance, you could give your students time to explore Desmos with sliders and seeing what they do to the function before or during class, then lead a group discussion where you end up summarizing what was found by watching that lecture video. Or you could have students attempt the Ferris Wheel activity outside of class and then start class by using the Snapshot tool to compare student answers. I love using a flipped classroom, but the flip doesn't always have to be direct instruction. By presenting problems that require students to apply their knowledge in new and unfamiliar contexts, we're showing students they have the tools and knowledge to tackle new problems without having seen a lecture and done a few examples first. 

So I guess my answer is this method is better than traditional direct instruction - you're using active learning, visualizations, making the most of class time by using a flipped approach... but it still has the feel of direct instruction where the instructor's voice is centered because you're showing students the video first. The beauty of playing with Desmos' graphing calculator is that your students could discover those things without any instructor input. I'd leave the lecture (consolidation) and sketched graphs on paper for the final exit ticket, rather than leading with them. 

------------------------------
Kelly Spoon
Associate Professor
San Diego Mesa College
San Diego CA

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

Dear Lucie,

Thank you for sharing your pedagogical approach with us.

Starting with the pre-tests as a formative assessment prior to class time, going through the lesson with the real-life applications and concluding with the exit exam, all permeated with Desmos visualization foster students' deep engagement during their learning process.

It looks like you are guiding the students to develop their own learning-to-learn ability by pausing the Desmos activities for discussion about the curriculum topics covered, stressing, and clarifying the lessons learning objectives.

I do think this method increases students' engagement which drives them toward proficiency in mathematics. 

Just wondering if you incorporate any paper and pencil, i.e., by hand graphing during your lessons?

------------------------------
Bukurie Gjoci
Assistant Professor
CUNY - LaGuardia CC
Long Island City NY

Original Message:
Sent: 02-04-2024 20:49:35
From: Lucie Mingla
Subject: IMPACT Discussion - Digital Platforms

What is your innovation in using technology and active learning?

As educators, we always think of the learning outcomes, and proficiency levels in learning a topic, or skill in class. To become proficient means to become an expert. However, mastering the concepts and skills can only be developed in a scalable way. In education we often refer to Bloom's Taxonomy followed by Anderson and Krathwohl's 2001. The taxonomy (Remembering; Understanding; Application; Analyzing; Evaluating; Creating) continues to shape education, with other frameworks like Marzano's, Gardner's, Hattie's, Fink's, Wiggins, etc.

Proficiency can only be achieved through a great teaching and Engagement of students in the learning process, which is another IMPACT's pillar. This discussion is focused on creating comprehensive activities that ensure students' engagement towards reaching a higher level of

proficiency. Also, it is worth discussing ways to use the digital platforms actively and effectively (in our favor) to engage our students in a way that helps them achieve the desirable proficiency levels.

In my teaching, I've been actively incorporating Desmos, an online graphing calculator, to help students grasp the connection between real-life problems and different types of functions, computations, and graphing. My focus is on using visualizations to enhance understanding and interpretation of solutions. The goal is to make learning mathematics more enjoyable, equitable, and inclusive by addressing challenges and providing effective resources. As an example, I can bring the topic on teaching real life applications and graph the trigonometric functions of sine and cosine. I crafted a well-structured lesson plan that seamlessly integrated technology and real-life applications to enhance the understanding of trigonometric functions. The use of Desmos in conjunction with a real-life scenario, such as the Ferris wheel rotation, was a brilliant way to make abstract concepts more tangible for students.

Students watched a video on graphing sine and cosine functions before coming to class. As a pretest, students were given to graph sine and cosine functions from scratch on paper. During the Desmos activity, students engaged with the Ferris wheel rotation, connecting theoretical concepts to a practical, relatable situation. The real-life problem, finding the reference angle of a person on the Ferris wheel, served as a meaningful connection between trigonometry and everyday scenarios. This not only deepened their understanding but also reinforced the relevance of mathematical concepts in real life. The incorporation of sliders for transformations enabled an interactive and enjoyable dimension to the learning process.

Students explored graphing trigonometric functions of the form:(1) 𝑓(𝑥)=𝑎·𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑, (2) 𝑔(𝑥)=𝑎·𝑐𝑜𝑠(𝑏𝑥−𝑐)+𝑑, where a, b, c, d can be any real number. Students observed the rotation on Desmos which enabled modeling of continuous counterclockwise (positive), and clockwise (negative) rotation, which led to the concept of the domain of sine and cosine in the interval (−∞,∞). To graph, students created a table of values for each function by evaluating for values in the interval of any period (Ex. [0,2𝜋]). They observed key points and the behavior of the graph such as max, min, zeros, domain, range and amplitude, intercepts, intervals of increasing, decreasing, etc. They practiced manipulating the graph by changing a, b, c, and d constants and observed their role in the functions. Students were able to graph functions of sin and cos from simpler forms to the more complicated forms (1), or (2), and draw conclusions for each of the basic transformations. Students were assessed and provided feedback in multiple ways. I have used this method for many lessons such as graphing parabolas, exploring limits, implicit differentiation, and tangent line, etc.

Do you think this method is effective to engage students and drive toward proficiency and mastering the targeted concepts and skills?

------------------------------
Lucie Mingla
Lecturer
LaGuardia CC at CUNY
Queens NY
------------------------------