Category: Mathematics

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Formulate Questions to Advance Learning and Understanding of Course Content

Formulate Questions to Advance Learning and Understanding of Course Content

Diana Zhu

Mathematics/NYCCT

MAT1375 Pre-Calculus

Activity Description: Provide a brief description of the activity

Weekly discussion boards will be set up for students to ask questions from the class. Students can view and answer them. I will post feedback for the class to see, and I will take one or two good questions to discuss when I see them in the next class.

Learning Goals: What do you aim to achieve with this activity?

I want to create a learning environment where students are welcomed to ask and answer questions comfortably. I want students to know that their questions are being valued, and that plays a big role in their learning. It gives students another view of learning Math is not just working on Math problems, but formulating questions outside class is a key for deeper understanding of the course content.

Timing: At what point in the lesson or semester do you use this activity? How much classroom time do you devote to it? How much out-of-class time is expected?

A week before the first day of class, I sent students an email to inform them about this discussion board. To get started, I asked them to write a post on the following questions: “What is your view on Math learning?” “How do you learn the best? Independently or in groups?” and “What are your expectations for this class?” I have a few reasons for giving them this: first, I get to know students before the first day. Second, it helps me design my classroom setting according to class topics. Third, I can track how many students have access to Blackboard.
During the first day of class, I would go over the Blackboard with students to get them familiar with it and informed them about the weekly discussion boards would be set up for discussion questions. I usually spent up to 20-30 mins on questions they were still confused after the discussions on Blackboard with their peers.
Outside of class, students are expected 10-30 mins on discussion board as posting a question or replying to their peers' questions. For students who did not have questions, I would also encourage them to share the problems they encountered or learned with their peers. For me, I would spend about 40-60 mins weekly as reviewing students' questions and see if they are anything that need to be clarified. I also gave them feedback when they replied to questions on discussion board. Also, sometimes I would send the class an email if what they shared on Blackboard would be beneficial to students before next class.

Logistics: What preparation is needed for this activity? What instructions do you give students? Is the activity low-stakes, high-stakes, or something else?

Students would need to take good notes and use notes to work on their homework assignments. Sometimes, students will have questions by reading notes or working on homework questions. I was very flexible with questions they had from the class, and I just posted the weekly discussion board after each class. Also, I would send them a gentle reminder along with class update. When students got busy with their high school assignments or exams, I would remind and ask them to post questions after they finished with them. I think this activity can be low stakes if students ask very basic questions. It can be high stakes if students want to generate a question that requires deeper thinking. Sometimes, students may not understand others' questions because they did not have a good understanding of the content that the question is focused on. In general, formulating a question can be harder than answering a question.

Assessment: How do you assess this activity? What assessment measures do you use? Do you use a VALUE rubric? If not, how did you develop your rubric? Is your course part of the college-wide general education assessment initiative?

I counted this activity part of students' participation grades. In addition, students' in-class participation weighs more, but I did not tell that to the students. In class, I tried to cold call every student to get them engaged; I would ask students to come to board to show their work. I created a simple rubric that focuses on "initiative", but I did not make full use of it. Some topics may only require students to apply formulas that did not really give students much confusion where I did not expect questions from them. Therefore, it can be hard for me to assign specific points weekly based on students' discussion questions on Blackboard. Instead, I combined students' in-class participation and their participation on discussion board to assign participation grades for each student.

Reflection: How well did this activity work in your classroom? Would you repeat it? Why or why not? What challenges did you encounter, and how did you address them? What, if anything, would you change? What did students seem to enjoy about the activity?

*Being the first time implementing such activity, I think it went well as students got used to questions in my class.
*I would like to think about alternative ways to help students initiate questions because towards the end, many students would just post their screenshots of questions that they have from assignments. My original intension was helping students to generate questions not simply solving Math problems, but general questions related to the topics.
*Some students had the misunderstanding that if they knew the materials then no need to post questions. I had to have a class conversation to students that even if they understood everything, they were required to answer others' questions or share what they learned from each other's questions and responses. A student talked to me in office that he felt no need to post a question because his confusion can be answered during office hour. I told the student that team/group work is so important not just in school but in future career. I told the student about my expectations for him to share what he asked and learned from office hour to his peers, and he did. I think I would like to have a sheet of specific weekly discussion questions ready for future students and leave a question for students to write one. I think this way, I can check students for understanding and I can use students' common and meaningful questions for in-class discussions. This prevents the problem as no questions being posted on Blackboard occasionally.
*Students enjoyed the activity when they missed a class because they can ask each other questions on discussion boards. When they answered each other's questions, they also tried to be as specific as possible which made me very proud of. They did not rush to just giving out answers but explaining their work.

Additional Information: Please share any additional comments and further documentation of the activity – e.g. assignment instructions, rubrics, examples of student work, etc. These can be links to pages or posts on the OpenLab.

I only used the OpenLab to share the reflection because I could not attach it here. I finally found a way to make the file onto OpenLab with tables shown. Overall, it was a great learning experience for me. Without attending the workshop, I could never come up with discussion board idea for my class to help students form the habit of generating questions and share with their peers. Very appreciate this opportunity.

Please share a helpful link to a pages or post on the OpenLab

https://openlab.citytech.cuny.edu/mat1375cn05/reflection-on-discussion-boards/

Posted on

Tell Me About Infinity

Tell Me About Infinity

Jonas Reitz https://openlab.citytech.cuny.edu/members/jreitz/

Mathematics/ School of Arts and Sciences

MAT 2675 Calculus II https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/

Activity Description: Provide a brief description of the activity

In this low-stakes writing assignment, students create a blog post exploring the concept of infinity. The post must respond to one of several prompts focusing on personal experiences of infinity, and must include a photo that illustrates infinity in some way. Extra credit is offered for providing a thoughtful comment on another student’s post.

Learning Goals: What do you aim to achieve with this activity?

This activity is introduced in the course MAT 2675 Calculus II as we prepare to embark on the study of infinite sequences and series, the first rigorous introduction of infinity in a mathematical context. Before students begin to wrestle with the (challenging!) technical details of the subject, I want them to reflect on their preconceptions about this pervasive and slippery notion of “infinity”. I want to give them the opportunity to make connections between infinity as it appears in other areas of life – philosophy, art, religion – and as it appears in the curriculum. In addition, I use this activity to build or reinforce technical skills – how to create a blog post, upload images, and add tags. I want to get students writing in a low-stakes environment, where their focus is on the content. Finally, I want to give students a chance to respond to one another, building community and trust in my class.

Timing: At what point in the lesson or semester do you use this activity? How much classroom time do you devote to it? How much out-of-class time is expected?

This activity is tied to a particular topic in Calculus II, infinite sequences and series, which traditionally makes up the last third of the course. The assignment is given just before we begin this topic, around week 9 or 10, and it is due two weeks after it is assigned. I spend 5-10 minutes discussing the project in class when it is assigned, and in subsequent classes I will provide a little time for students to ask questions or raise concerns. I expect students to devote 2-4 hours to this activity, over the course of 2 weeks.

Logistics: What preparation is needed for this activity? What instructions do you give students? Is the activity low-stakes, high-stakes, or something else?

I post the assignment, including detailed instructions, on the course OpenLab site (see below). I will spend a very short time in class discussing the assignment and answering questions – but I will NOT go over every detail (they are expected to carefully read the assignment and follow all instructions). I try to make the assignment stand-alone, with links to appropriate resources (including, for example, how to create a blog post, how to upload an image, and so on).

High-Impact Educational Practices: Which of these practices based on George Kuh’s High Impact Educational Practices (and other innovative approaches) does this activity incorporate? Choose all that apply.

Open Digital Pedagogy (the OpenLab), Wrriting-intensive projects/assignments

Assessment: How do you assess this activity? What assessment measures do you use? Do you use a VALUE rubric? If not, how did you develop your rubric? Is your course part of the college-wide general education assessment initiative?

The assignment includes a list of 5 specific expectations (“You should create a new blog post including the following”), and I use this as a checklist. The assignment is worth a certain number of points, and a student’s score is based solely on the checklist. I want this to be low-stakes in terms of writing — grammar and spelling are not evaluated, and the structure and content of the written work need only loosely fit the instructions. I write a response to each student’s post, and while I don’t share their point score at that time, I will point out if there are significant problems or missing items and encourage the student to make revisions.

Reflection: How well did this activity work in your classroom? Would you repeat it? Why or why not? What challenges did you encounter, and how did you address them? What, if anything, would you change? What did students seem to enjoy about the activity?

This has been one of my most successful writing prompts – I was excited and impressed with the variety of creative and thoughtful responses. Asking them to write about their personal experience provided freedom to talk about the subject without fear of “being wrong,” and gave a rich source of material from which they could draw. Many posts spurred great comments, and I noticed in several cases the comments developed into real conversations (although the extra credit offered for commenting on another post did not extend to multiple comments).
I think this assignment could adapt quite easily to many disciplines. It is often the case that certain words, familiar from our daily lives, take on a specific and technical formal meaning in an academic context which gives students trouble – especially as the “formal” and “informal” definitions may be at odds with one another. I can imagine this activity applying to many such cases – by asking students to explore their existing experience of a word or concept, they begin to focus on the meaning of it in an intentional way, which prepares them to compare and contrast their informal definition with the formal usage.

Additional Information: Please share any additional comments and further documentation of the activity – e.g. assignment instructions, rubrics, examples of student work, etc. These could be in the form of PDF or Word files, links to posts or files on the OpenLab, etc.

Link to Assignment: https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/2012/04/04/openlab-assignment-7-tell-me-about-infinity/

Link to Student Work Examples: https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/?s=infinity

Posted on

“How Long is the Brooklyn Bridge?” – Field Trip

“How Long is the Brooklyn Bridge?” – Field Trip

Jonas Reitz (with Ezra Halleck) https://openlab.citytech.cuny.edu/members/jreitz/

Mathematics/ School of Arts and Sciences

MAT 1175 Fundamentals of Mathematics https://openlab.citytech.cuny.edu/mat1175fa2011/

Activity Description: Provide a brief description of the activity

In this introductory mathematics course students are exposed to a variety of mathematical ideas in the abstract, with relatively few built-in applications or connections to the “real world”. By taking students out of the classroom, exposing them to a local New York Landmark (walking across the Brooklyn Bridge), and asking them to use the mathematical knowledge in the course to estimate the length of the bridge, we allow them to make a concrete connection between their own experience and the ideas in the text. The field trip itself provides plenty of opportunity for informal interaction among students and faculty, and overcoming the practical difficulties (staying together, navigating the New York streets, following instructions, accomplishing the goals of the day) gives the class a shared experience that builds community and trust. We paused at the halfway point of the bridge to participate in an icebreaker activity (a bingo variant, which encouraged meeting and talking to many different classmates). Finally, students were asked to take a photo of themselves on the bridge.
Following the trip, students completed a followup assignment on the OpenLab in which they posted the results of their calculations (how long is the Brooklyn Bridge), their photo from the trip, and a reflection on the process.

The field trip combined two MAT 1175 sections (my own section and a one taught by my colleague, Ezra Halleck), and provided a great opportunity for students in both sections to make connections.

Learning Goals: What do you aim to achieve with this activity?

This activity uses an abstract idea (proportions) to answer a concrete real-world problem, “How long is the Brooklyn Bridge?”. Students compare the time it takes them to talk a known distance (the length of the City Tech block of Tillary Street, from Jay Street to Adams Street) with the time it takes them to walk across the Brooklyn Bridge. By solving a proportion, they are able to use their time measurements to estimate the length of the bridge. This demonstrates the underlying idea of proportions in a familiar, outside-the-classroom context, and provides perspective on the abstract notions presented in the text.

In addition, this activity (which took place early in the semester) provided a great way to help establish a sense of community in the class. We took advantage of this activity as a way for students to form groups that included members from both participating sections, which went on to complete a larger group project over the course of the semester.

Finally, this activity was a great way to introduce technical skills – creating a blog post, uploading photos, adding tags, and so on.

Timing: At what point in the lesson or semester do you use this activity? How much classroom time do you devote to it? How much out-of-class time is expected?

This activity took place very early in the semester – the second or third week of class. It was a great way to break the ice, to get students engaged with the material and interacting with one another, and to establish a new perspective on the material at hand and on the college experience generally (especially since this course has many first-time freshman students). This meant that planning had to take place very early – distributing field trip instructions, completing necessary paperwork, and preparing the class for day of the trip. We devoted about 15 minutes in class to discussing the trip (prior to the trip itself), one day of class for the trip, and about 15 minutes in class discussing the results of trip (the week following). We expected students to spend about an hour outside of class writing completing the followup assignment on the OpenLab.

Logistics: What preparation is needed for this activity? What instructions do you give students? Is the activity low-stakes, high-stakes, or something else?

Any City Tech field trip requires proper paperwork to be completed, including permission forms for any students under the age of 18. We provided detailed logistical instructions for the day of the trip, including directions (in case students came late and wanted to catch up with us) and suggestions of what to wear and bring (comfortable walking shoes, weather-appropriate attire, water bottle, camera, stopwatch). We also created written instructions for the mathematical part of the trip, detailing where and how to time themselves walking and emphasizing the importance of maintaining a steady walking pace. The activity is low-stakes but is counted towards their grade – we did not deduct points for wildly unrealistic estimations of the bridge length, for example, as long as they were supported by data recorded on the trip, and calculations were shown clearly. Students that missed class that day were allowed to make it up by following the instructions on their own and completing the followup assignment on the OpenLab.

High-Impact Educational Practices: Which of these practices based on George Kuh’s High Impact Educational Practices (and other innovative approaches) does this activity incorporate? Choose all that apply.

Open Digital Pedagogy (the OpenLab), Place-Based Learning, Brooklyn Waterfront

Assessment: How do you assess this activity? What assessment measures do you use? Do you use a VALUE rubric? If not, how did you develop your rubric? Is your course part of the college-wide general education assessment initiative?

The field trip itself was not assessed, beyond checking attendance. The followup assignment included a list of 5 specific expectations (“Create a new blog post responding to the field trip.”), and this was used as a checklist. The assignment was worth a certain number of points, and a student’s score is based solely on the checklist. We wanted this to be low-stakes in terms of writing — grammar and spelling are not evaluated, and the structure and content of the written work need only loosely fit the instructions.

Reflection: How well did this activity work in your classroom? Would you repeat it? Why or why not? What challenges did you encounter, and how did you address them? What, if anything, would you change? What did students seem to enjoy about the activity?

This is the first time I took students out of the classroom, and I was gratified by the energy and excitement that this simple change of scenery infused in the class. It was great to see students interacting with each other (and with me) in an informal setting, and I believe that the connections that were made that day had a lasting impact on the students’ experience.

I was surprised at the amount of planning and logistics that were involved in even a simple field trip, and in the future I will aim to have my planning absolutely complete prior to the start of the semester. It was difficult to carve out time in our overfull departmental syllabus to allow the trip to take place. While we did not cover a great deal of mathematical content on this day, I still believe it was a worthwhile investment of time – the mathematical content that we incorporated was presented in a way that drove home the efficacy and wide applicability of the underlying ideas, which I think our students will remember beyond the end of the course (unlike the vast majority of the other content).

I think this kind of activity is widely adaptable to many disciplines – for me, this is not a project about studying proportions, but instead about allowing students to experience a connection between course content and the outside world. Asking students to step out of the classroom immediately creates new perspective, and giving them something “hands on” to do involves them in the course content in a way that is difficult to do inside the classroom walls, in the context of a traditional textbook. In addition, the social and emotional impact on the class can be profound – especially in large, “non-major” courses in which students are not already incorporated into a discipline-specific cohort, and may not be predisposed towards engagement in the material.

Additional Information: Please share any additional comments and further documentation of the activity – e.g. assignment instructions, rubrics, examples of student work, etc. These could be in the form of PDF or Word files, links to posts or files on the OpenLab, etc.

Field trip instructions:
https://openlab.citytech.cuny.edu/mat1175fa2011/assignments/day-5-brooklyn-bridge-field-trip/

Followup assignment:
https://openlab.citytech.cuny.edu/mat1175fa2011/brooklyn-bridge-trip-followup-assignment/

Student work: https://openlab.citytech.cuny.edu/mat1175fa2011/?s=field+trip+response

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