Articles

9.1.1: The Student Experience - Mathematics


Kristen Mruk

When thinking about college, what comes to mind? Perhaps stereotypical images or misconceptions of college life, a friend or sibling’s story, or scenes from popular movies?

In popular culture, some movies depict college life as a party atmosphere in which students binge drink and waste their parents’ money to have a good time without consequence. Films including National Lampoon’s Animal House and Van Wilder as well as Accepted, to name a few, portray the student experience as a blatant disregard for education coupled with excessive drunken buffoonery. However, my party experience illustrates a side to college that is not generally in the limelight.

During my first weeks in college, I felt disconnected from the campus and feared that I would not make friends or find my niche. I was commuting from my family’s home and wanted to do more on campus than just go to and from class. I was enrolled in a First-Year Experience (FYE) course that was intended to provide a framework for a successful undergraduate career and beyond. In the class, we learned about student support services on campus (tutoring, personal wellness, academic advisement, etc.) as well as personal success skills (time and financial management, values exploration, etc.).

Being a new student, and a commuter, I was overwhelmed by the amount of new information, new territory, campus culture, and unfamiliar processes. I asked my FYE instructor after class one day if there was something I could do to feel more connected to campus. She opened my eyes to a side of college that I was missing—this was my invitation to the party.

My FYE instructor promptly led me to her office, introduced me to the staff, and explained the variety of involvement opportunities available through her office. I was amazed that there was so much to do on campus! Because of that meeting, I decided to apply for a job in the Student Union working at the information desk. This position was a catalyst for all of the additional parties I would be invited to throughout my time as an undergraduate student. With so many possibilities, I had to be diligent in prioritizing my time and energy.

Friends knew me to be much like the girl in the meme above. I was juggling extracurricular activities and two jobs all while maintaining a full course load. I had to be proactive and diligent to coordinate activities and assignments and make sure I had the time to do it all. Finding a system was a trial and error process, but ultimately I found a method that worked for me. I was an undergraduate student when apps didn’t exist and Facebook was just becoming popular, so my organizational system included a planner, a pen, and a lot of highlighters. Whatever that organizational system looks like for you does not matter as long as you use it.

There are a variety of organizational methods and tools you can use to stay on track with all aspects of your life as a student. Some of those are featured in the State University of New York (SUNY) blog: http://blog.suny.edu/tag/apps

It may be difficult to discuss your studies and educational experience with a parent or someone that has a significant interest in your academic achievement. This was the case for me; I was the first kid in my house to enroll in college, and my parents were under the impression that grades would be sent home like they were in high school. During the New Student Orientation program, my Mom learned about FERPA (Federal Educational Rights and Privacy Act) and what that meant for my grades. “FERPA gives parents certain rights with respect to their children’s education records. These rights transfer to the student when he or she reaches the age of 18 or attends a school beyond the high school level.” In essence, parents cannot access grades or other restricted academic information unless you provide it to them (http://www2.ed.gov/policy/gen/guid/fpco/ferpa/index.html?src=ft).

I was fortunate enough to have my parents’ financial support toward tuition, so they felt entitled to reviewing my grades at the end of each semester. I did not want to give them direct access to my grade report by filing a FERPA waiver, so after much deliberation, I agreed to share my grades once released at the semester’s end. If their standards were not met, there would have to be a conversation about repercussions.

In the fall of my sophomore year I took my first online course—Introduction to Computers and Statistics. All of the lectures and assignments were available online at anytime and exams were administered in a computer lab on campus. I thought having the ability to view lectures on my own time would be more conducive to my schedule as I was becoming more involved on campus. For the first few weeks of classes I watched the lectures regularly and did the assignments on time. Slowly but surely I found myself prioritizing my time differently, ultimately putting my online class on the back burner, because (I told myself) the work could be done anytime! By the end of the semester I realized that I was going to fail the class. No amount of extra credit, crying, or pleading could save my grade; I had earned an F.

Seeing a failing grade on my transcript taught me two valuable lessons. First, I discovered that I needed the routine and accountability of an in-person class to ensure my participation in the material. Second, I was responsible for the grades I received. I probably could have come up with a million excuses for why I didn’t watch the lectures or do the assignments, but the reality was I just didn’t do it. I did not seek my professor’s help during their office hours when I started to fall behind, I did not go to the tutoring center on campus to get extra help, and I did not reach out to my classmates to form study groups.

Although the F that I received will never disappear from my transcript, it is an important reminder of the gruesome conversation I had with my parents and the feeling of failure in the pit of my stomach. Needless to say, that was the only online course I took during my collegiate career, but it was absolutely worth the lessons learned.

Professors do care about how you are doing in their class; they genuinely want you to succeed, but they will give you the grade you earn. There are people and resources on campus for you to utilize so you can earn the grade you want.

Your professors are one of those resources, and are perhaps the most important. Go see them during office hours, ask them questions about the material and get extra help if you need it. The caveat here is that you cannot wait until the last week of the semester to visit your professors to get help. Tears and pleading will not help you at the eleventh hour.

Another resource to utilize can be found in the campus learning center. I frequented my campus’ writing center for assistance with papers and research projects. Initially, I was scared to be critiqued, thinking my work would be perceived as inadequate. The first time I took a paper there, I recall standing outside the door for about ten minutes thinking of an excuse not to go in. Thankfully I saw a classmate walk in and I followed suit. The experience was less dramatic than I imagined it to be; no one ripped my paper to shreds and told me that I would never graduate. Instead I sat with an upper-class student who coached me through some pointers and suggestions for improvement. Thanks to that first visit, I received an A- on the paper!

I thought I knew exactly what I wanted to do when I started college, but that changed three times by the time I graduated. Initially I started as an International Business major but ended up receiving a degree in Communication and continued on to graduate school. My greatest advice to you is to embrace feelings of uncertainty (if you have them) with regard to your academic, career, or life goals. Stop into the Career Services office on your campus to identify what it is that you really want to do when you graduate or to confirm your affinity to a career path. Make an appointment to see a counselor if you need to vent or get a new perspective. Do an internship in your field; this can give you a first-hand impression of what your life might look like in that role.

When I chose International Business, I did not do so as an informed student. I enjoyed and excelled in my business courses in high school and I had hopes of traveling the world, so International Business seemed to fit the bill. Little did I know, the major required a lot of accounting and economics which, as it turned out, were not my forte. Thinking this is what I wanted, I wasted time pursuing a major I didn’t enjoy and academic courses I struggled through.

So I took a different approach. I began speaking to the professionals around me that had jobs that appealed to me: Student Unions/Activities, Leadership, Orientation, Alumni, etc. I found out I could have a similar career, and I would enjoy the required studies along the way. Making that discovery provided direction and purpose in my major and extracurricular activities. I felt like everything was falling into place.

I would like to pause for a moment and ask you to consider why you are in college? Why did you choose your institution? Have you declared a major yet? Why or why not? What are your plans post-graduation? By frequently reflecting in this way, you can assess whether or not your behaviors, affiliations, and activities align with your goals.

What you actually do with your student experience is completely up to you. You are the only person who can dictate your collegiate fate. Remind yourself of the reasons why you are in college and make sure your time is spent on achieving your goals. There are resources and people on your campus available to help you. You have the control—use it wisely.


For potential Ph.D. students

Over the next few years, I may take on a few additional Ph.D. students, although times may come when I'll be too full (e.g. a time that ended recently). This page is intended for those considering working with me, although it also contains some tips for graduate students in general, as well as an idea of what I expect.

Algebraic geometry (or at least my take on it) is a technical subject that also requires a good deal of background in other subjects, as well as geometric intuition. So before I take you on as a new student, you should be comfortable with the foundations of the subject, which means having done the majority of the exercises in Hartshorne or my course notes, and being able to explain them on demand. (You shouldn't do this on your own I'm happy talking with you through this process.) You should also be actively interested in learning about nearby subjects that interest you. Which subjects they are is up to you. If you're not interested in regularly attending talks, and being broadly interested in mathematics outside of your thesis topic, or if you don't feel like getting technical in a rather serious way, I'm probably not a good fit for you.

If you are interested in some of the ideas of algebraic geometry, you should also consider a number of other advisors. In this department there are a good number of people interested either directly or indirectly in algebro-geometric ideas. You can read about them here. I will of course be happy to talk with you no matter whom you are working with.

My personal style as an advisor

I'll suggest problems to think about, starting from small toy problems (which have a habit of growing into interesting serious research). You'll have to pick what to work on, and find your own thesis problem. Mathematics isn't just about answering questions even more so, it is about asking the right questions, and that skill is a difficult one to master.

I like to meet my students every week (except for exceptional weeks, of which there are many). You may prefer not to meet in a given week if you have nothing much to report, but those weeks are particularly important to meet.

The disadvantage of being a student of a young parent is that you'll have to be prepared to be more independent.

I will be a demanding advisor, more demanding than most.

I have pretty broad interests in and near algebraic geometry. To get an idea of the things I think about, see some of the things I've written. However, some of those subjects may not be ideal for a Ph.D. student for a number of reasons. I'm interested in lots of things. I may however not be the ideal person to supervise lots of things. For example, I will not supervise a thesis in a nearby field. But I definitely do not require that you work on problems directly related to my own research.

General advice (which would apply particularly to my own students)

Think actively about the creative process. A subtle leap is required from undergraduate thinking to active research (even if you have done undergraduate research). Think explicitly about the process, and talk about it (with me, and with others). For example, in an undergraduate class any Ph.D. student at Stanford will have tried to learn absolutely all the material flawlessly. But in order to know everything needed to tackle an important problem on the frontier of human knowledge, one would have to spend years reading many books and articles. So you'll have to learn differently. But how?

Don't be narrow and concentrate only on your particular problem. Learn things from all over the field, and beyond. The facts, methods, and insights from elsewhere will be much more useful than you might realize, possibly in your thesis, and most definitely afterwards. Being broad is a good way of learning to develop interesting questions.

When you learn the theory, you should try to calculate some toy cases, and think of some explicit basic examples.

Talk to other graduate students. A lot. Organize reading groups. Also talk to post-docs, faculty, visitors, and people you run into on the street. I learn the most from talking with other people. Maybe that's true for you too.

  • Older graduate students will verify that there is a high correlation between those students who are doing the broadest and deepest work and those who are regularly attending seminars. Many people erroneously conclude that those who are the strongest students therefore go to seminars, while in fact the causation goes very much in the opposite direction.
  • Go to research seminars earlier than you think you should. Do not just go to seminars that you think are directly related to what you do (or more precisely, what you currently think you currently do). You should certainly go to every single seminar related to algebraic geometry that you can, and likely drop by other seminars occasionally too. Learning to get information out of research seminars is an acquired skill, usually acquired much later than the skill of reading mathematics. You may think it isn't helpful to go to a seminar where you understand just 5% of what the speaker says, and may want to wait until you are closer to 100% but no one is anywhere near 100% (even the speaker!), so you should go anyway.
  • Try to follow the thread of the talk, and when you get thrown, try to get back on again. (This isn't always possible, and admittedly often the fault lies with the speaker.)
  • At the end of the talk, you should try to answer the questions: What question(s) is the speaker trying to answer? Why should we care about them? What flavor of results has the speaker proved? Do I have a small example of the phenonenon under discussion? You can even scribble down these questions at the start of the talk, and jot down answers to them during the talk.
  • Try to extract three words from the talk (no matter how tangentially related to the subject at hand) that you want to know the definition of. Then after the talk, ask me what they mean. (In general, feel free to touch base with me after every seminar. I might tell you something interesting related to the talk.)
  • New version of the previous jot: try the "three things" exercise.
  • See if you can get one lesson from the talk (broadly interpreted). If you manage to get one lesson from each talk you go to, you'll learn a huge amount over time, although you'll only realize this after quite a while. (If you are unable to learn even one thing about mathematics from a talk, think about what the speaker could have done differently so that you could have learned something. You can learn a lot about giving good talks by thinking about what makes bad talks bad.)
  • Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind.
  • Here's a phenomenon I was surprised to find: you'll go to talks, and hear various words, whose definitions you're not so sure about. At some point you'll be able to make a sentence using those words you won't know what the words mean, but you'll know the sentence is correct. You'll also be able to ask a question using those words. You still won't know what the words mean, but you'll know the question is interesting, and you'll want to know the answer. Then later on, you'll learn what the words mean more precisely, and your sense of how they fit together will make that learning much easier. The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone this is much easier to do than learning "forwards". (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)
  • Your thesis problem may well come out of an idea you have while sitting in a seminar.
  • Go to seminar dinners when at all possible, even though it is scary, and no one else is going.
  • Go to colloquia fairly often, so you have a reasonable idea of what is happening in other parts of mathematics. It is amazing what can become relevant to your research. You won't believe it until it happens to you. And it won't happen to you unless you go to colloquia. Ditto for seminars in other fields.
  • There is a huge amount to say about giving talks. For now, I'll first direct you to Terry Tao, who reminds us to be considerate of our audience, and that Talks are not the same as papers.
  • Advice from Jordan Ellenberg.
  • How to give a colloquium. (First line: "Most colloquiua are bad".)

Here's a great story from Mark Meckes that simultaneously illustrates a number of points. By chance, I recently saw a PhD thesis whose acknowledgements ended with the sentence "Finally, I would like to thank Dr. Mark Meckes, whose talk in Marseille in May of this year [2008] provided the final insight I needed to completely answer Kuperberg's Conjecture." What is interesting about this is that not only had I never heard of Kuperberg's Conjecture, but my talk was completely unrelated to the subject of the thesis, and even after reading the relevant section of the thesis I still couldn't see the connection. So one truly never knows where useful insights will come from. One of the many things I love about this story is that I don't find it at all surprising! So go to talks --- and give talks --- and talk to people!

  • For people writing research papers for the first time (or not for the first time), here is a lecture by Serre, one of the best mathematical writers of all time, with some opinions on good (and bad) writing.
  • Terry Tao on writing.

When thinking about advisors, talk to past and current graduate students. (My former and current students: Eric Katz 2004, Rob Easton 2007, Andy Schultz 2007, Jarod Alper 2008, Joe Rabinoff 2009, Nikola Penev 2009, Jack Hall 2010, Dung Nguyen 2010, Atoshi Chowdhury, Yuncheng Lin, Daniel Litt. I also collaborated with Kirsten Wickelgren 2009, who worked with Gunnar Carlsson.)

  • You find some advice and discussion at the secret blogging seminar (by Noah Snyder and others) quite interesting.
  • Steven Weinberg wrote a fantastic piece in Nature about graduate school.
  • Terry Tao's blog is essential, and includes career advice.
  • Here is a page at UC Davis of useful things to know when starting graduate school . as contributed by experienced grad students.
  • John Baez has advice for the young scientist, which includes advice on giving good talks, as well as an important discussion on keeping your soul.
  • Click on "TSR" here for advice collected by Dan Margalit for graduate students in topology (which is universal).

Specific advice about algebraic geometry at Stanford

Sign up for the algebraic geometry mailing list.

Go to the Western Algebraic Geometry Seminar, a twice-yearly conference.

Occasionally go to Berkeley when you hear about something particularly interesting.

When you are up to it, subscribe to the daily mailing of abstracts of algebraic geometry papers posted to the arXiv. Then most days, just delete them, but when you have some time, browse through them, and read the abstracts that catch your eye. You'll gradually get a sense of what is going on in the field. Caution: this can be psychologically damaging, as you'll feel "here I am stuck on this simple problem, and thousands of papers are coming out. ". So only do this if and when you're ready. I might delete this paragraph at some point if I realize it is counterproductive. (Thanks to many people for advice about this page, including Yvonne Lai, Daniel Erman, and Mark Meckes.)
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Importance of Productive Struggle in Math

The process of productive struggle has encouraging applications to math education in particular. Only 33% of US eighth-graders scored “proficient” or “advanced” in math on the National Assessment of Educational Progress in 2015, leading many students to feel like they are not a “math person”, even though research shows everyone is capable of mathematical thinking.

It’s often the quick calculators and good memorizers who are praised the most in math class. However, Stanford professor Jo Boaler warns that instruction based solely on memorization and arithmetic can lead students to misunderstand and dislike math. Test results show that the highest achievers are those who can see the bigger picture and make connections between different mathematical concepts. There’s a growing body of research that shows that getting students to the point of productive struggle is one of the keys to achieving deeper learning and creative problem solving.


9.1.1: The Student Experience - Mathematics

To improve the math learning experience of you or your child, it might be wise to consider retaining the services of a math tutor. There are several factors that you should keep in mind when choosing the right tutor:

A good math tutor will need to have mastery of the material that he or she is teaching. Thus, it is important that they have a strong formal background in mathematics. When teaching young children, completion of at least a high school diploma would be recommended. Teaching older students, in high school or college, the ideal tutor would have at least an undergraduate degree, with emphasis on mathematics (engineering or science degrees often have solid math requirements too).

Experience and Training

Helping others learn requires great communication skills, and the ability to identify the best way to convey the material in a way that matches the individual needs of the learner. Prior experience in either tutoring or in teaching is highly recommended when seeking out a math tutor, and that experience should ideally include the grade-level of the material you are covering. The best tutoring companies invest resources in continually training their staff on the latest educational methods to help learners master the material.

Location and Availability

To minimize time and travel expense wasted in transit, the math tutoring location will ideally be near you. A large math tutoring company with many locations will have better odds of a location near you. Some tutoring companies do telephone or online tutoring, either as their main method of communications or as a complement to traditional classroom-style settings.

Some tutors are available only at pre-scheduled times, whereas others can be reached outside those hours, or even around-the-clock in some cases (e.g. some of the online services). Depending on your needs, this may or may not be important.

Many academic studies have documented that students learn best when they have more attention to their individual needs. Thus, smaller classroom sizes, or even one-on-one learning, are advisable to maximize the benefits of the math tutoring. Typically, the youngest children in particular benefit from small classroom sizes, but this can also be the case for older ones.

The best way of learning is through practice, practice, and more practice. This can be done through homework assignments, or in-class practice sessions. Regular testing is important to ensure that the material is being mastered. Math tutoring companies are often of help to prepare for specific standardized tests (e.g. SAT, GRE, GMAT, LSAT), so having access to tests in the same format as the expected standardized exams is useful.

Tutors need to be compensated for their time (they have families to feed also), so it's unrealistic to expect good math tutoring for free. To get smaller classrooms or individualized tutoring, it will naturally need to cost a little extra. Whether that is a good investment will depend on the individual needs of the learner, and the degree of their enthusiasm to succeed at math. Some math tutoring companies offer financial aid or discounts, so it doesn't hurt to ask whether those are available (a discount at a better math tutoring company might make it a better value than full-price at a lesser company). Educational expenses might be able to be deducted from your income taxes, depending on where you live, so be sure to save receipts and ask your accountant for more information.


Language-Specific Courses

Beyond the introductions above which use Python, here are several introductions to other programming languages. Many are taught during MIT&rsquos four-week Independent Activities Period (IAP) between the fall and spring semesters.

6.092 Introduction to Programming in Java


This course is an introduction to software engineering, using the Java programming language. It covers concepts useful to 6.005 Elements of Software Construction. Students will learn the fundamentals of Java. The focus is on developing high quality, working software that solves real problems.

Prerequisites: Designed for students with some programming experience.

18.S997 Introduction to MATLAB Programming


This course teaches MATLAB® from a mathematical point of view, rather than a programming one. The idea is that by thinking about mathematical problems, students are prodded into learning MATLAB for the purpose of solving the problem at hand. Topics include variables, arrays, conditional statements, loops, functions, and plots.

Prerequisites: There are no formal prerequisites for this course.

6.057 Introduction to MATLAB


This course is an accelerated introduction to MATLAB and its popular toolboxes, and is great preparation for other classes that use MATLAB. Lectures are interactive, with students conducting sample MATLAB problems in real time. The course includes problem-based MATLAB assignments.

Prerequisites: There are no formal prerequisites for this course.

6.S096 Introduction to C and C++


This course provides a fast-paced introduction to the C and C++ programming languages. You will learn the required background knowledge, including memory management, pointers, preprocessor macros, object-oriented programming, and how to find bugs when you inevitably use any of those incorrectly.

Prerequisites: Designed for students with some programming experience.


About Math Camps

Each summer, CMS math camps provide students with an interest in mathematics with a unique and unforgettable experience. The camps take place in universities and CEGEPs across Canada and range from day camps to week long events. Students who attend the camps leave with new friends, new ideas, and a new outlook on mathematics. CMS math camps are a great opportunity to:

Enhance skills and knowledge

CMS camps provide an enrichment experience for students who have shown an interest in and an aptitude for mathematics. Advanced math concepts are presented in a manner that is challenging yet still accessible. Students are also coached on how to approach problems and have the opportunity to develop their group problem solving skills.

Gain a new perspective

CMS camps allow students to experience math as never before through games, projects, experiments, and other fun activities. The camps also highlight the role math plays in everyday life. In surveys taken after the camps, students consistently report an increased interest in math and science careers.

Make new friends

CMS camps are a great way to connect students with similar interests. Many campers go on to form Facebook groups, stay in touch as ‘math camp alumni’, and even try their hand at one of the CMS national competitions


TESTIMONIALS

AwesomeMath doesn’t just teach you math, but they invoke the curiosity inside you, until a stage where you start to push yourself higher. My love for math explodes during the course, and it’s just so fulfilling!

AwesomeMath truly offered me a remarkable experience, even with the difficulties by being online. The classes were fun, the instructors were easy to get along with, and they teach you with materials of just the right difficulty, providing not only theory, but many examples and practice problems. It is nice to be able to communicate with math lovers around the world for three weeks. Overall, this has been definitely one of the most memorable experiences I have ever had in my life. Spend your summer with AMSP!

AwesomeMath is one of the best math enrichment programs for mathletes! The unique and challenging content is matched by equally substantive teaching. The program would not spare you the rigor or beauty of competitive math.

AwesomeMath is one of the best places I have gone to for competitive math. The explanations in class were clear, and the examples given in class were challenging and intriguing. Thanks to AwesomeMath, I’ve greatly improved in my problem solving skills and math skills in just over a few months.

I would enroll in the AwesomeMath Online Summer Program because the Instructors are really doing a great job of teaching via the virtual medium. I enjoyed having collaboration with other students.


College of Education

The Florida State University College of Education offers a unique combination of global-class academics and a close-knit, student-focused community for an exclusive educational experience. Here, you will work as peers with some of the finest minds in the educational world. You will engage in leading educational research and technology and emerge with an educational advantage from an institution that holds the Carnegie Foundation’s highest designation - Doctoral/Research University-Extensive.

Join a world-class institution committed to challenging and nurturing each student.

See how we have earned our reputation as a respected innovator in education.

Build strong, lifelong bonds with friends and faculty alike.

Start your career surrounded by the state’s educational movers and shakers.

I chose higher education because it is my calling to give back to students from similar (and even more disadvantaged) backgrounds like me. The vast nature of education allows me to transform the minds of students and the policies affecting their success.

Our students are our one and only priority. Everything we do is driven by our commitment to creating the best possible student experience across all aspects of their lives – academic, social, and personal. As a student in the FSU College of Education, you have direct access to some of the best minds in the education field. You are challenged through innovative programs and unique teaching methodologies. You are given almost limitless opportunities within an educational setting that no other school can offer. Your entire student experience is what prepares you to become the educational leaders of tomorrow.

As quickly as the world of education evolves, students in the FSU College of Education are uniquely trained to adapt and set the standards by which tomorrow’s educators will be measured. We have a commitment to sending the best, most-prepared educational professionals into the world, and we will provide all the support and guidance you need. But you will also be challenged and pushed to achieve things you never dreamed you could do. Innovative programs, exceptional facilities, and unparalleled resources give you the ideal setting to take your educational career in any direction you can imagine.

Dig deeper with faculty who have built a preeminent research institution.

Hit the real world running (and better prepared than almost everyone else).

Explore our high-tech facilities and affect how your children’s children will learn.


2019 Mathematics Survey Questionnaire Results

NAEP mathematics survey questionnaire results are highlighted below for selected topics, including students' Internet access and digital technology at home content emphasis or coursetaking in mathematics students' confidence in their mathematics knowledge and skills (grades 4 and 8 only) teachers' satisfaction and views of school resources (grades 4 and 8 only) and postsecondary plans (grade 12 only).

NAEP survey questionnaire responses provide additional information for understanding NAEP performance results. Although comparisons in students' performance are made based on student, teacher, and school characteristics and educational experiences, these results cannot be used to establish a cause-and-effect relationship between the characteristics or experiences and student achievement. NAEP is not designed to identify the causes of performance differences. Therefore, results must be interpreted with caution. There are many factors that may influence average student achievement, including local educational policies and practices, the quality of teachers, available resources, and the demographic characteristics of the student body. Such factors may change over time and vary among student groups.

NAEP reports results using widely accepted statistical standards findings are reported based on a statistical significance level set at .05, with appropriate adjustments for multiple comparisons. Students are always the unit of analysis when reporting NAEP survey questionnaire responses. The percentages shown are weighted and represent students or students whose teachers or school administrators indicated a specific response on the survey questionnaire. Some student responses are missing as a result of an inability to link students to their teachers' or school administrators' responses to the survey questionnaire or as a result of nonresponse from students, teachers, or school administrators. The denominator of the percentages presented excludes all students with missing information in the data for the analysis. The percentage distributions of reported survey response categories could change when students with missing data are included in the denominator. To find missing rates and explore student, teacher, and school questionnaire data further, use the NAEP Data Explorer.

Eighty-one percent of fourth-grade students in 2019 have Internet access and a computer or tablet at home

In 2019, eighty-one percent of all fourth-grade students in the nation reported that they had both Internet access and a computer or tablet that they could use at home. Grade 4 students who reported having both Internet access and a computer or tablet at home had a higher mathematics score on average (245) than those who reported having only Internet access (234), only a computer or tablet (223), or neither (226) at home.

FIGURE | Percentage of fourth-grade students assessed in NAEP mathematics, by whether they have Internet access and digital devices available at home for them to use: 2019

The percentages of fourth-graders who reported having both Internet access and a computer or tablet at home in 2019 varied across states/jurisdictions and across participating Trial Urban District Assessment (TUDA) districts. While 81 percent of grade 4 public school students in the nation reported having both Internet access and a computer or tablet at home, across states/jurisdictions, the percentages of grade 4 public school students who reported having both resources at home ranged between 57 and 87 percent. While 79 percent of grade 4 students in large city public schools reported having both Internet access and a computer or tablet at home, across TUDA districts, the percentages of grade 4 public school students who reported having both resources at home ranged between 68 and 89 percent. To see detailed results by state/jurisdiction and by TUDA district, use the NAEP Data Explorer tables linked below.

See the detailed results for this question in NAEP Data Explorer:

Teachers of higher-performing fourth-grade students place heavy emphasis on measurement, geometry, and algebra in class

The chart below shows the percentages of fourth-grade students by the level of emphasis their teachers placed on five mathematics content areas in class. Percentages are compared between lower-performing students (scoring below the 25th percentile) and higher-performing students (scoring at or above the 75th percentile) on the 2019 NAEP mathematics assessment. Note that not all emphasis categories are shown for each mathematics content area.

Compared to lower-performing students, a larger percentage of higher-performing students at grade 4 had teachers who reported placing heavy emphasis on measurement (32 percent versus 28 percent), geometry (36 percent versus 31 percent), and algebra and functions (60 percent versus 57 percent).

FIGURE | Percentage of fourth-grade students assessed in NAEP mathematics whose teachers reported placing heavy emphasis on various content areas of mathematics, by percentiles: 2019

The percentages of fourth-graders whose teachers placed heavy emphasis on the five mathematics content areas in class varied across states/jurisdictions and across participating TUDA districts. For example, in 2019, sixty percent of grade 4 public school students in the nation had teachers who reported placing heavy emphasis on algebra and functions. Across states/jurisdictions, the percentages of grade 4 public school students whose teachers reported placing heavy emphasis on this content area ranged between 39 and 75 percent. In 2019, sixty-four percent of grade 4 students in large city public schools had teachers who reported placing heavy emphasis on algebra and functions. Across TUDA districts, the percentages of grade 4 public school students whose teachers reported placing heavy emphasis on this content area ranged between 38 and 86 percent. To see detailed results by state/jurisdiction and by TUDA district for the full list of mathematics content areas, use the NAEP Data Explorer tables linked below.

See the detailed results for this question in NAEP Data Explorer:

Higher average scores for fourth-graders who are more confident in their ability to do mathematics-related tasks

Fourth-grade students answered questions about their confidence in performing a variety of mathematics-related tasks, such as estimating the weight of five apples using pounds, or finding the amount of carpet needed to cover a floor if its length and width are known. Students' responses to these questions can be combined to create an index that focuses on their confidence in their mathematics knowledge and skills.

In 2019, fifty-three percent of all fourth-grade students in the nation reported low to moderate levels of confidence in their mathematics knowledge and skills. Grade 4 students who reported higher levels of confidence in their mathematics knowledge and skills had a higher mathematics score on average than those who reported lower levels of confidence.

See the detailed results for this question in NAEP Data Explorer:

Teachers' views of the quality of their schools and resources vary across states and jurisdictions and across districts

As part of the 2019 mathematics assessment, teachers of fourth-grade students answered questions about their satisfaction with being a teacher. In 2019, five percent of fourth-grade public school students in the nation had teachers who reported that the statement "I am frustrated as a teacher at my school" described them exactly. Across states/jurisdictions, the percentages of grade 4 public school students whose teachers reported this response ranged between 2 and 10 percent. In 2019, six percent of fourth-grade students in large city public schools had teachers who reported that the statement "I am frustrated as a teacher at my school" described them exactly. Across TUDA districts, the percentages of grade 4 public school students whose teachers reported this response ranged between 1 and 12 percent.

Teachers also answered questions about their views on the physical status of their schools and resources. In 2019, six percent of fourth-grade public school students in the nation had teachers who reported that school buildings in need of significant repair were a serious problem. Ten percent of fourth-grade public school students in the nation had teachers who reported that overcrowded classrooms were a serious problem. Finally, six percent of fourth-grade public school students in the nation had teachers who reported that a lack of adequate instructional materials and supplies was a serious problem. Teachers' views about the physical status of their schools and resources also varied across states/jurisdictions and across participating TUDA districts. For example, across states/jurisdictions, the percentages of grade 4 public school students whose teachers reported that overcrowded classrooms were a serious problem ranged between 4 and 25 percent. In 2019, twelve percent of fourth-grade students in large city public schools had teachers who reported that overcrowded classrooms were a serious problem. Across TUDA districts, the percentages of grade 4 public school students whose teachers reported this response ranged between 2 and 31 percent. To see detailed results by state/jurisdiction and by TUDA district, use the NAEP Data Explorer tables linked below.


Should I Major in Mathematics?

Actually, that's a question only you can answer. Some people have a passion for the intellectual challenge: solving difficult problems and proving conjectures are true. Others understand the versatility of a degree in math. If you decide to major in math, the question you will most be asked is, "What will you do with your degree, teach?" For many math majors, teaching is their goal. If you want to know what else is out there, take a look at the MAA Career Page.

A couple of statistics: In The Jobs Rated Almanac 1999, "mathematician" ranked #5 out of 250 job studied in terms of income, stress, physical demands, potential growth, job security, and work environment The National Association of Colleges and Employers 2005 Salary Survery states that mathematicians earned a starting salary 37.7% above the national average. A 2009 study showed that the top three best jobs in terms of income and other factors were careers suited for math majors.

What classes are out there for a math major? Well, every math major takes a three-semester sequence in calculus. Afterwards, there are classes in discrete math, differential equations, linear algebra, abstract algebra, and real analysis to take. Electives can include operations research, topology, cryptography, number theory, geometry, probability theory, statistics, and numerical analysis. Many schools ask their students to do a senior research project or take a capstone course.

Outside of class in college, there are often MAA student chapters or math clubs. Some schools sponsor their students to take the Putnam Exam, administered by the MAA . Usually to get ready for the Putnam, prospective test takers go over past problems and discuss strategy at a weekly meeting. Faculty supervised student research is an exciting way to delve further into a topic you find exciting. Such work may be for college credit, or as an extra-curricular activity. Researchers have plenty of opportunities to give a talk either at their home institution, at MAA Sectional Conferences, Regional Undergraduate Conferences, or at MathFest. Also, students can present their findings on a poster at the Joint Mathematics Meeting.


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