Introduction:
“Do not worry about your difficulties in mathematics. I can assure you mine are still greater.”
-Albert Einstein
-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 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?
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:
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.
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.
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.
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.
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.
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.
Annotated Bibliography
“Math, Middle Schoolers and Real-World Relevance (Infographic).” Innovation: Education,
30 Nov. 2018,
tiie.w3.uvm.edu/blog/math-middle-schoolers-real-world-relevance-infographic/#.XHhs1OJKi00
30 Nov. 2018,
tiie.w3.uvm.edu/blog/math-middle-schoolers-real-world-relevance-infographic/#.XHhs1OJKi00
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.
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.
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.
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.
be applied to STEM fields, and offers yet another option for educators to consider when designing
their curriculum.
DeSilver, Drew. “U.S. Academic Achievement Lags That of Many Other Countries.” Pew Research
Center, Pew Research Center, 15 Feb. 2017,
www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/.
Center, Pew Research Center, 15 Feb. 2017,
www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/.
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.
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.
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.
Picha, Gina. “Recognizing and Alleviating Math Anxiety.” Edutopia, George Lucas Educational
Foundation, 17 May 2018, www.edutopia.org/article/recognizing-and-alleviating-math-anxiety.
Foundation, 17 May 2018, www.edutopia.org/article/recognizing-and-alleviating-math-anxiety.
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.
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.
This blog post really hits home for me. I can remember experiencing math anxiety as early as first grade, and the problem compounded each year following me all the way through high school. Incorporating concepts like math as a language and PBL just might be the solution to remove some of those barriers that prevent students from seeing themselves as "good at math." It's amazing that mindset can have such a large impact on student success!
ReplyDeletePowerful post, Austin! I was particularly struck by your emphasis on making math an accessible subject for students in a similar way to teachers of foreign languages. It seems so self explanatory, but I can remember how often I struggled with understanding math until a high school teacher of mine applied mathematics to other subject areas with ease. When math became a relevant part of my historical studies, my math teacher was quite literally speaking my language. The idea of approaching math education with the goal of connecting it to real-world application is so important, and I think your research reflects how this is not only doable, but essential to student learning.
ReplyDeleteHi, Austin! As a fellow aspiring mathematics teacher, I completely agree that there is a disconnect between math classes and the real world. The central question you addressed regarding how to engage all learners in various approaches while still meeting CCSMS standards is something I grapple with in my college courses. Listing the signs of math anxiety was a great call and I am excited to check out Youcube! The real world applications you outlined were powerful and I hope to use them in a future classroom. Overall, great job!
ReplyDeleteHey Austin, I really like how you argued that success largely depends on mindset, in both math and pretty much any other field of study. Of course this mindset depends on how the course material is being presented, and I loved your emphasis on project-based-learning as a way of combatting math anxiety. Math for me was always a drag due to endless worksheets and a lack of purpose, and I wish that I had been taught by someone as passionate as you are about making math real. Great job!
ReplyDeleteHey Austin. First of all, I would like to give you a round of applause for talking about what others are afraid to say about mathematics curriculum. As a fellow aspiring math teacher, I relate to the struggles of teaching in a modern day math class. Math anxiety is very real and not addressed as often and it is hard to get students engaged when they don't understand how it applies to the real world. I would just like to say that this is an overall amazing post!
ReplyDeleteWhat's good Austin - so math anxiety was interesting to read about because I never really experienced it in middle or high school. I didn't like math but was good at it, which is an odd phenomenon because usually you like what you're good at. Thank you for enlightening me on it, though. Anyway, the idea of real-world applications is so important in math because that's definitely the subject you see it the most in. I liked the example you gave of your lesson plan - good work, my friend. In middle school I definitely felt more connected to a math lesson if I felt like it had a real world application. One of my favorite projects to this date I ever did was in 7th grade math regarding volume and surface area of a box. We got to write to food companies and tell them how to better package their food items with these new surface areas we found for their products that were more efficient. It was fun, especially when we got responses from real companies. Cheez-Its said no to my ideas but it was still a cool project in that we got to apply what we were learning to the real world. That's probably the most engaged in math I've ever been!
ReplyDeleteThis blog post is such an important one when thinking about math education. I believe you have found the underlying issue - it’s not that math is too hard for some kids to grasp, rather it is the teaching methods and the learning experiences that make math too hard/disengaging/irrelevant. I am so glad to see the answer of “right now” to the question, when are we ever going to use this. It is very possible to design relevant, engaging, hands-on math lessons. It just requires a paradigm shift for the adults that are creating the instructional lessons. I really appreciate the link to the lesson you created as a concrete example of this shift. Thanks Austin! - Lindsey
ReplyDeleteTook me time to read all the comments, but I really enjoyed the article. It proved to be Very helpful to me and I am sure to all the commenters here! It’s always nice when you can not only be informed, but also entertained! how to do division
ReplyDelete