Recently, I was tasked with developing and teaching two lessons to a group of peers over the course of two days. My lessons aligned with the Performance Criterion 3.2:Positive Social Interaction, which states, "Candidates design learning environments that support collaborative learning marked by positive social interaction". My lesson focused on teaching rates of change, more commonly referred to as slope in mathematics, and applied real world applications and utilized activities focused on group collaboration to reach our learning targets. My lesson meets PC 3.2 because of the formative assessment used on the second day, which involved the students to work together to solve and model a problem which would have been challenging to work on individually. Students shared their ideas, corrected each other, and worked together to complete the task. While I feel that I met PC 3.2, I could have gone further by including more questions in the activity, or creating more opportunities for think-pair-shares and turn and talks.
My experience teaching these lessons was a very informative one, and I learned a lot about adjusting my practice using student feedback. After the first lesson, in which I had a moment where students wrote on the board their ideas of examples of rates of change, my students informed me that they would have liked more opportunities to spend time at the board, and so I adjusted my formative assessment for the second day to be entirely at the board, as opposed to sitting in groups. Something I had also done during my first lesson was use student examples as discussion topics that we explored in the context of slope, and I learned that students become more engaged when they can play a role in providing specific examples, so I chose not to
have pre-written examples for the second lesson, and instead opted for student led examples again. Also, I realized that I have to write much larger than I think I do when writing on the board! It's very easy to think the writing is large enough when you're a few inches away, but students may have trouble seeing it. I also adjusted my second lesson to include a slide of the agenda and learning targets, which I also read aloud, as I only had written it on the board for the first lesson.
My formative assessments, in the form of exit cards and the group activity, allowed me to assess my students' understanding of slope, how it applies to real world models, and how to interpret a graph. I also provide opportunities for students to vocalize their questions or concerns, as well as giving them an opportunity to write their questions to me if a student was uncomfortable speaking up in class. During this experience, I realized how difficult it is to gauge how long an activity will take students, so I learned that it is beneficial to have optional activities planned which could also benefit student learning, but we do not necessarily need to do in order reach our learning target for the day.
I learned a lot about myself as a teacher during this experience. Something my peers and I noticed was that I tend to address students as "guys", which I realize is noninclusive for some students, and so I would like to start addressing students as "folks", "scholars", "mathematicians", or other gender inclusive words. I felt incredibly comfortable in front of the class even though I tend to be a quiet student, and my peers noticed my confidence and how comfortable I was, which only made me more confident in my abilities as a teacher. My experiences in my Literacy and Curriculum courses were very influential in the development of these lessons, as I was considering how to teach students new vocabulary, including y-intercept, slope, rate of change, increasing and decreasing, and other mathematical terms, while also differentiating instruction so that I can effectively reach all of my students. I am excited to teach lessons to larger groups of students and to see how effective of a teacher I am for students!
The Saint Michael's College Education Department's common read this year was a young adult novel titled George, written by Alex Gino. The book describes the story of Melissa, a fourth grader who thinks of herself as a girl, while those around her still view her as a male named George. The book tackles the ideas of struggling with one's gender identity, which includes moments of bullying and acceptance from one's family, and Melissa's desire to play Charlotte in her class' production of Charlotte's Web. I was lucky enough to be able to attend an author talk given by Alex Gino, and hear them answer questions from the audience and describe the process of writing Melissa's story.
The author talk led by Alex Gino was really fascinating and informative! I had little background knowledge of the process of writing a novel, and hearing Alex Gino describe their learning process throughout the writing and publishing periods was great to hear. Gino answered questions which had been in my mind since reading the story, such as why was the book titled George when the story is meant to represent Melissa's struggle to have others come to know her as Melissa. Gino was incredibly patient with the audience's questions, and their answers demonstrated how much time they had spent reflecting and learning. One moment of the discussion which stood out to me was when Gino urged teachers to avoid having students identify their pronouns in front of the class as an icebreaker. I have experienced this pronoun icebreaker in multiple classes since beginning my undergraduate education at SMC, and had thought that it was a progressive way to have students become aware and comfortable with how their peers identified. However, Gino noted that these kinds of situations can often be uncomfortable for gender-fluid and gender-nonconforming students, as declaring one's pronouns can cause them to feel "locked in" and unable to change their pronouns. Gino also reminded us that some students may still be struggling to determine their gender identity, and so asking them to declare pronouns in front of their peers may be challenging for them since they are still in the process of identifying themselves. Alex Gino encouraged educators, current and future, to find a more private and personal way for students to make their gender identity and pronouns known.
The SMC Education Department Mission Statement says that "Our graduates are change agents committed to social justice and sustainability." As gender identity continues to be a topic of discussion in this current progressive-leaning world, educators are learning how to approach these sensitive topics to make all students feel included, welcome, and safe in their classroom environment. Events such as the author talk given by Alex Gino provide opportunities for us future educators to grow our understanding of these sensitive topics, and allow us to reflect on how we can best create a respectful and safe environment for students to develop and grow in over time.
The process of reading George and listening to Alex Gino were very informative and eye opening for me. I previously had little knowledge of what members of the LGBTQ+ community truly experience, and Melissa's story described bullying, coming out to one's family and friends, and looking for acceptance not only from peers but from themselves. I now feel that I have a greater understanding of the LGBTQ+ community, and realize that implementing inclusive practices means more than just hanging up posters. It means fostering a classroom community of respect and understanding, where students can feel free to express themselves and share. The common read made me more conscious of how I use gendered terms in the classroom, including "guys", "men and women", and "boys and girls", since these terms could isolate a particular student and cause them to feel "different" from their peers. I also believe that establishing class norms at the start of the term is beneficial, so that students can understand what is expected of them and what would not be acceptable in the classroom, such as discrimination or other hateful practices.
I am thankful for the opportunity to hear Alex Gino speak about George and inform me even further on how to create an inclusive classroom environment. This opportunity has provided me with a lot to reflect on.
Recently, I was tasked with developing a pre-reading lesson plan and teaching it to a small group of peers. My lesson involved us taking a critical eye to statistical studies by discussing how sample sizes can influence statistical studies, which can cause the study's results to be skewed. While developing my lesson, I wanted to have a way for students to think about sample sizes themselves, which I introduced by conducting a survey using our class as the sample size. I decided that the majority of the lesson would be discussion based, and that I would assess student learning from the mini-lesson using an exit card.
My lesson connects with the Saint Michael's Educational Departments Mission Statement, specifically the pillar stating that "Our learners are passionate and curious scholars", as this lesson is meant to instill a curiosity and understanding of statistics in students. When presented with statistical data in the future, I would like my students to question how the data was found, and to be critical when examining such data. This lesson would also ideally lead into a small assessment where students can examine statistical studies of their own choosing, which creates an opportunity for student choice to find a study which is interesting to them and observing how the study was conducted and where faults may lie.
I really enjoyed developing and teaching this lesson, and learned a lot in the process. One thing which I had the most trouble with was estimating how long an activity would take during the planning period. While I relatively accurate in estimating the length of the activities, my peers and I agreed that there were moments in which I spoke to fast and could have slowed down to take more time with. Another opportunity for improvement would be that I could have given the students a written definition of sample sizes, as their understanding of sample sizes came from our discussion during the lesson. To improve for next time, I will do my best to slow down every now and then to spend more time on some activities and ideas being discussed, while also ensuring that any new vocabulary is being accurately defined for students. I believe that I was successful in reaching my pre-reading goals as well, in which I hoped that students would be able to identify studies which might be influenced by specific aspects of sample sizes. The exit cards showed me how well students understood the lesson through creative responses. I learned a lot about pre-reading and teaching from this lesson, and will improve in these areas moving forward!
In our "What is Literacy?" assignment, we were tasked with identifying and analyzing the meaning of literacy, and what literacy means for students in this digital age. Within the assignment, we also made connections with literacy in our content area, with my focus being on literacy in a mathematics focused classroom. The Education Department's Mission Statement offers five main pillars describing the goal of the education department for its students, and while I believe literacy skills are interwoven into each pillar of the mission statement, some pillars represent my ideas of literacy better than others. For example, "Our graduates are passionate and curious scholars" emphasizes my belief that literacy skills incite curiosity in students, and in using one's literacy skills to gain information from visual, printed, or digital media, students exercise their curiosity and are capable of exploring topics which they are passionate about. Allowing students to present to each other in small groups also focused on the "Our graduates are collaborative and knowledgeable instructional leaders" pillar, since students were allowed to learn from each other's presentations, and specifically were able to converse with other students specializing in their content area, furthering their understanding of how literacy applies to their focus.
In the context of this assignment, we were working under the pillar stating, "Our graduates are creative and integrative educators", since many students utilized digital media tools which they had little experience in, they were allowed to go outside of their comfort zone to explore the tool of Adobe Spark Page, learning both the benefits and drawbacks of such a medium. In creating their presentation, students exercised their creativity in how they represent and describe literacy. In my presentation, I considered practical applications of literacy skills in mathematics, and what type of information mediums students may be tasked with interpreting and understanding. For example, students may be asked to read maps, graphs, and mathematical symbols to interpret equations. I believe that this closely matches the "Our graduates are change agents committed to social justice and sustainability" pillar from the mission statement, as having students consider how mathematical models are applied to the real world could be the first step to solving sustainability problems, carbon emissions, and a diminishing water supply. Students are encouraged to think about tomorrow, instead of focusing on the facts of today, and are able to apply their learning to problems that will be around as they grow older.
While listening to my small group's presentations, I was given new ideas for how literacy is considered beyond mathematics. I was reminded that for students today, literacy skills include navigating social media, biased resources, and unknown digital tools. In the classroom, effectively instructing how to recognize bias is essential to developing thoughtful and reflective students who question the information in front of them. Throughout my inclusion class, I've learned that equity is not always equality, and that some students may need more support than others in order to learn. As such, employing a variety of differentiated instruction methods, including visual models, hands-on work, group work, and student choice-led assignments will ensure their success in a rapidly evolving world where literacy skills are constantly evolving.
Q: Some teachers believe that preparing students to be “more still, more compliant, more conforming...” (never forgetting a pencil) will prepare them for the world. What are some of the dangers of that kind of belief system? How do you prepare children for the way the world works or should work? A: When teachers act as the "end-all and be-all" authoritative figure in the class, they tend to project their own ideal qualities on their students, and when students don't follow the behavioral guidelines that they believe appropriate, the students are punished. As a result, students learn to sit behind their desks in silence, working on assignments. This may improve standardized testing scores, but is it improving the quality of our students? Is it preparing them for the real world? When students grow up learning to do as their teacher says, they are being taught not to question authority, even if they disagree with how something is being done. In the real world, when something is done incorrectly, one would hope that someone would speak up with an improved method of performing the same task. Students should feel comfortable speaking up and discussing new ideas, so as to create a better and more efficient world. Teachers who aim for compliant and silent students are merely suppressing the energy-filled students who long to work on hands-on projects and in the field, which is what they would be doing in the "real world" when working a new job. Teachers should promote and encourage all types of students, so that education is accessible to each and every one of them.
“Do not worry about your difficulties in mathematics. I can assure you mine are still greater.” -Albert Einstein
Throughout the world, the presence of mathematics is clear and visible. Mathematics can be seen in the price of clothing, the measurement of land, and especially the work of astronauts and space exploration. So then why do students feel as though they’ll never need mathematics in their lives? According to the National Assessment of Educational Progress (NAEP), the percentage of eighth graders in 2015 who were proficient in mathematics was only 25%, a dip from the previous year of 27% proficiency. What factors are contributing to this low proficiency level in students, and can teachers effectively cultivate students with an interest in math?
Mathematics has long since been a topic of discussion in education. For some students, mathematics has been a topic of interest that they have explored and developed their skills in for many years. Unfortunately, many students struggle with mathematics more than other subjects, and struggle to stay motivated to further their mathematics education. Students often ask themselves and their teachers “When are we going to use this in real life”, and too often these students are not given a proper answer to the question. As a child, I remember my teacher telling me that we study mathematics to such an extent in order to become the highest level thinkers we can possibly be. While satisfied at the time, as I have grown older, and my education has become more reflective of the world around me, mathematics still maintains this disconnected feeling from the world that I have grown up in. Throughout my life, and the lives of many students, teachers have approached mathematics very similarly: through lecture-based classroom teachings and student note taking, with a subsequent quiz or test. Since the approach that educators routinely use to teach mathematics only caters to one type of learner, many students feel left behind in math courses, and become anxious of all topics regarding mathematics. How can educators develop thoughtful curriculum to approach all types of learners, with the goal of engaging all students and relieving the anxiety that many feel, while still maintaining the core curriculum and standards that need to be taught?
What is math anxiety? In order to resolve it, educators should understand where it comes from and how to identify it. While some students may be more vocal than others about their disdain for mathematics, others may attempt to hide it from their teachers. Edutopia has come up with a great piece for recognizing and alleviating math anxiety, and some of their listed symptoms are as follows:
Avoiding the classroom, teacher, or work in order to avoid mathematics at all costs.
A lack of responses in class, even if given the proper amount of time to think and develop an
answer.
Anger or frustration at themselves or their peers.
A low self-esteem regarding math, often reinforced when they cannot come up with answers as
quickly as other students.
Low grades in mathematics, which reinforces their low self-esteem belief that they are “not
good at math”.
For many students struggling with mathematics, the root of their problem lies in the fact that they don’t understand why certain steps are being taken to solve a problem. This problem stems from students not understanding how to read and interpret mathematics. For example, let’s take the following statement: ∀x∈ℤ, ∃y∈ℤ such that P(x)=y. Unless you have taken a mathematical proofs course, you would most likely have difficulty understanding the given statement. When broken down into words, the statement becomes more clear: “For every x value within all integers, there exists a y value within all integers that satisfies P(x)=y, where P(x) is some function”. While this example is still abstract, it demonstrates the idea that if mathematics is broken down into its core components, where the vocabulary and symbols can be explained, students will feel more capable when approaching math problems.
In order to combat math anxiety, Jo Boaler, a Mathematics professor at Stanford University, created Youcubed, an online resource for students and teachers to use in order to gain a more math-positive mindset. Youcubed offers a wide range of activities for students to engage in, including videos, lessons, and quizzes. One such activity that Youcubed offers is the Week of Inspirational Math, a week of courses and problems available for students to explore in depth and creative problems, with encouraging messages and inspirational videos to motivate their continual growth in mathematics. According to the Youcubed website, 96% of students who were surveyed and used Youcubed reported that they felt motivated to continue working even when the problems were difficult or they made mistakes.
Real World Applications:
“When are we going to use this in the real world” students will ask themselves and their teachers repeatedly. To this, teachers should be able to answer with “Right now!” It is important for teachers to relate their teachings to the world around their students, and this is especially true for math. In a lesson plan I designed with another future mathematics educator, we related two step linear equations to common issues of water, including water pollution and water usage, in order to draw our students into the lesson. Instead of giving students problems that consist of only numbers, which feel disconnected from everything else in their life, educators are encouraged to provide students with contextual mathematics lessons. By providing students with real world applications of the mathematics being taught in class, students will feel more connected to what they are learning and will understand the context of the lesson, as opposed to feeling as though the lesson is disconnected from the issues they see in the world. Geometry lessons can be likened to partitioning land for designing a farm, designing structures such as buildings and bridges, or designing complex and abstract art pieces. Algebra lessons can be used to discuss pollution issues, food shortages, and population densities across varying states or countries.
According to the survey of Math Relevance to U.S. Middle School Students, 48% of students prefer learning about math outside of school, and 48% of students prefer learning new subjects with hands-on activities. So, it should be clear to educators that one crucial way to engage students in new math lessons is to utilize hands-on, outdoor activities. One example of outdoor activities comes from the Edge program, where students participated in sugaring activities and worked in multi-age groups to work on a variety of different math infused activities that stemmed from working in nature and the sugaring process. From measuring the contents of a local pond, to designing and implementing a classroom farm, teachers have the opportunity to provide students with real and meaningful interactions, which not only encourage them to develop and grow their mathematical skills, but also encourage collaborative work between students and peers to reach a greater goal. This is best exemplified through the SLOPE project, which encourages students to pursue careers in STEM fields by allowing them to work on exploratory projects that suit their interests.
Conclusion:
When approaching mathematics as a real world tool, with positive applications capable of bettering the world around them, students are no longer focused on the disjointed equations that they have trouble reading given on a quiz, but instead focus on collaboratively working with other students to solve the real world issue that has been given to them. Educators should focus their attentions on making mathematics an accessible subject to their students, instead of making it feel like a subject that only “some people can be good at”. By encouraging group collaboration, students learn to work together on problems and can reach a greater understanding mathematics as a whole through their work with peers. Educators can create a math friendly environment where students feel as though their work is significant and can cause a change in the world by providing them with real world applications of mathematics.
Summary: The information taken from the blog post was only that of the infographic given by the Math Relevance to US Middle School Students, a reliable source of information for survey data on mathematics as a subject. The reason this infographic is relevant to my research is that it emphasizes the idea of teaching mathematics outside of the classroom, and how students view math as a whole.
“Sugaring, STEM, and the Community Part 2: Teaching Others.” Innovation: Education, 19 Apr. 2018, tiie.w3.uvm.edu/blog/sugaring-and-the-community-part-2-students-become-teachers/#.XJ_EN-JKiT8.
Summary: This blog post shows real world applications that one can provide their students with to make mathematics more accessible. The Edge Program’s combined use of mathematics, hands on activities, technology, and real world applications created an accessible outlet for students to learn and understand mathematics, while focusing on a project based learning experience.
Summary: This video from the SLOPE program shows how project based learning experiences can be applied to STEM fields, and offers yet another option for educators to consider when designing their curriculum.
Summary: The information provided here from the National Center for Education Statistics shows clearly the performances of students in the United States in mathematics. The data provided from this source emphasizes the idea that mathematics is not reaching all students as well as it could be, and how teachers approach their math curriculum need to be adjusted.
Summary: I chose to include this TED Talk because it offered an idea about mathematics that I don’t believe many people consider, that which is math is a language. I believed this video to be informative because it shows that mathematics doesn’t necessarily need to be explained to be understood.
Summary: This article provided from Edutopia highlights the idea of math anxiety, something that many students and teachers can understand, and offers advice to teachers on how they can reduce their students’ anxiety about mathematics. Teachers can take the ideas in the article and implement them in their own classrooms, and subsequently take those ideas that work best for them and their students.
Throughout this semester, I've had the opportunity to work with a conversational partner from Haiti. We have met multiple times to have conversations with each other, where we share our experiences and ask each other questions about the other's life. He has shared pieces of his writing with me in hopes that I could help him improve his writing and his English. After discussing with my colleagues about the WIDA levels of their conversational partners, I believe that my partner is at the fourth level of reading, the expanding stage, because, in his writings that he has shared with me, he is capable of writing stories and reports based on facts that he has learned, while defending those ideas, and then subsequently is able to revise his work after I've given his feedback. During our conversations, my partner has even taught me new English words that I've never heard before, which causes me to believe that he is at the fourth level of listening as well. Although, he and I have joked around and been sarcastic with each other on occasions, which leads me to believe he is somewhere between the fourth and fifth level of listening on the WIDA scale. When speaking with my partner, he has shared many stories of his life in Haiti, along with the lessons that he has learned throughout his life. He has defended his ideas through evidence he has lived through, which lead me to believe he is also at the fourth level for speaking. Throughout the semester, I have also texted my partner to arrange meetings and have brief conversations with. As a result of his ability to understand my messages, and how he can locate information that I've sent him within a relatively large paragraph, I believe he is at the third level, the developing stage, of his reading skills on the WIDA scale. Overall, my partner is incredibly funny, genuine, and has taught me a lot of life lessons. He is very intelligent and is capable of growing even further than where I believe he currently places.
Recently, my PLC group finished our reading of Troublemakers by Carla Shalaby. When examining the novel, we recognized that there is no coming of age moment in the book, which has led us to believe that this novel does not necessarily qualify as a YA novel. This novel is important for educators and parents to gain a better understanding of what causes children to act out, and what their actions are trying to tell us.
Characteristics of YA Lit
Protagonist
Zora, Lucas, Sean, Marcus
Developmental Stage of Protagonist (Handouts or charts in Week 3 & 4 labeled “Stages”)
Early Adolescence for all 4 protagonists
Key Conflict
Students labeled as “troublemakers” and how that label can affect them in their education and how others treat them. Shalaby examines how the label of “troublemaker” can create a negative atmosphere around those students and, instead of listening to their cries for attention and looking for the source of the issue, teachers push aside the rambunctious energy those students display as a way to silence them in hope for conformity amongst students.
Point of View Telling Story
Carla Shalaby observing these four children in their current learning environment.
Evidence that this is written for YA
Written about middle school aged kids about common issues that they face
Ending: “storybook” or no?
No, there isn’t a complete ending, each POV ends on a different “takeaway” for teachers and how they can help students like Zora, Lucas, Sean, and Marcus.
Evidence of parents
Shalaby details the dynamics between each “troublemaker” and their parents in their respective chapters.
Coming of Age Issue
There isn’t a coming of age issue presented because the observations only take place over a few weeks, so there isn’t enough content to see the change in characters.
Number of Pages & Reading Level
187 pages.
Examples of “Windows and Mirrors”
Windows= teachers who still teach in the classic “lecture” style
Mirrors= for students who are considered “troublemakers” and are constantly being nagged on for doing things wrong, when in reality they just need a friend or a teacher to understand what is going on in their lives outside of the classroom. Also, for parents who are concerned with the current school systems and the accommodations for students who have trauma.
After reviewing twovideos on the topic of designing questions for students, I have come away with a greater understanding for how one can structure their classroom and the questions being given to their students to promote the greatest level of learning. I have come to recognize that teachers often work collaboratively when designing their questions, building off one another's ideas with the goal of reaching every type of student in their curriculum. The questions being asked of students are meant to build off one another. First, by giving students a question that is easy to answer, they feel confident in discussing their thoughts in the classroom. When a followup question that is more in depth is posed, the students are challenged to think and have greater expectations set for them. Teachers may pose a question that relates their teaching to the everyday world around their students and their lives so that students may relate to what they are learning and feel more compelled to study, learn, and grow within these disciplines. Teachers have been designing questions so that they can slowly and deliberately give their students more responsibility and, in turn, set higher expectations for what those students can achieve.
