Posts tagged math
Posts tagged math
Idaho math teacher Julianne Russell shares how she encourages her students to practice math, and how she thought about incentivizing them in a fair way.
Over the summer, Los Altos School District teacher Sheena Vaidyanathan shared the essay below with CSTA’s The Voice about using Khan Academy’s ever evolving and growing computer programming platform with her students. She also presented at the CSTA conference on July 16, 2013.
For more about Sheena’s classroom, check out this article with more details.
Curriculum in Action
Programming through Art and Math
By Sheena Vaidyanathan
Teaching computer science (CS) through art engages students and showcases the creativity behind programming. Connecting programming to math makes CS relevant to the school curriculum and ensures support and funding.
I combined CS with math and art to create a CS course called CSTEM for the Los Altos School District in California. Because CSTEM is a required class, every one of the over 500 sixth graders learns to code as a medium for creating art.
Students were surprised to see how the code on one side of the IDE translated into a design on the other. Students experimented with Processing functions to add windows, fences, chimneys, and other features to their houses. By the end of the first class, students had learned to use functions to create a variety of shapes. Important learning occurred around syntax, sequencing, and parameters.
Students at this age are just learning to graph coordinates. In the Khan Academy IDE, students can guess numbers for the parameters and then use the sliders to experiment. The program output is updated instantly. This form of playing with the x and y values makes the math exercise relevant and fun. In addition to coordinates, students explored other mathematical concepts, including functions, variables, and geometry. Once I had introduced iteration using the draw function, the students were able to create interactive art based on the mouse position variables.
Many students worked outside of class to create complex works of art through code. Using the cloud-based IDE made it easy for students to log in from home to continue working. To facilitate learning beyond the classroom and to manage a large number of classes, I made extensive use of Edmodo, a moderated online classroom, where I post messages and engage in discussions. Students used the environment to share their work, comment on other projects, and ask questions.
I asked the students what they would say to convince others to learn programming; their answers were inspiring.
• I would tell someone that coding is a type of art. There are no bounds to your creativity and you can create anything you want, it can be easy or hard.
• You should try coding! It’s really fun, but I’m not promising that it will be easy. It’s really useful and teaches patience.
• Coding uses all that I have learned in math and applies it to
the real world.
I have seen the value of connecting programming to both art and math; my students are enthusiastic about programming and my school administration is ready to expand the program. A recent, first-ever district coding competition attracted over 100 participants—and 58% were girls! CSTEM has convinced students in our district that CS can be challenging and fun. Required CS education at this age is both valuable and possible.
Let your child fail. That was my initial reaction to a recent message that showed up in my inbox. We live in a “little league” age of celebrating success. In t-ball, every player gets to bat. In little league, every player gets a trophy. I don’t disagree with instructional league rules by any means. However, at what age does failure begin to have value? I was sitting in a department meeting recently when a district-level administrator asked me if I had analyzed test scores of last year’s students to determine if Khan Academy actually had any effect on those students’ test scores. I replied honestly, and said that I had only checked on a handful of students’ scores. But as I continued to ponder her request, I lost my appetite for looking up any more test results. I realize that no matter what those test results may show, they don’t reveal one of the most important skills being taught in my class. They might reveal which students learned how to apply the Pythagorean Theorem in a real-life situation, but what is not tested is perhaps the most important. Tests of that sort do nothing to promote the value of failure. Upon reading that recent message from my inbox, I wanted to shout out “let your child fail.” The shouting was not due to frustration, rather to be sure that my voice was heard by many. And when I say fail, I mean fall. Let them fall. How can we learn to get back up if we never fall? Or if someone else always picks us up. Too often today, students are given every possible opportunity NOT to fail. But why? Why are we afraid of failure? Putting students in frustrating and uncomfortable situations is a tricky part of my job. I have to find that zone where students are frustrated enough to seek out a solution THEMSELVES. I hear this a lot, “Well I’ll just get my mom to help me.” There’s nothing wrong with phoning a friend or a mom. My message to parents, though, is to let your child fail. Sometimes teachers put students in a certain situation so they will fail. Because until they fail, they’ll never seek out that solution themselves. Tests don’t measure whether a student has developed the fortitude to seek out a solution himself, or whether they’ve developed persistence in problem solving. Even if a student doesn’t arrive at the correct solution, the journey or the number of attempts is often what is more important. I always try to make sure that I’ve directed my students to places and opportunities where they can develop, create, or find a solution. But I try to stop there. Too often are students lead, directed, and told which solution is correct. We call it “spoon-feeding”. And students know all about this. They know all about it, because it hits them like a brick wall the first time a teacher or parent shrugs their shoulders and refuses to help them at the first sign of adversity. I want my daughter to be a successful, hard-working citizen. I know that won’t come without learning to fail, get back up, and seek out a solution.
The picture below is a graph of a student’s last 35 problems on adding/subtracting negative numbers. You’ll find the number of problems completed at the bottom the bars. The red bars indicate a wrong answer was inputted first, but eventually the student arrived at the correct answer. You’ll also see that the student’s longest streak correct was 11. This particular student has been struggling adding and subtracting negative numbers for quite a while, but has just recently shown some progress. We’ve exhausted ourselves on learning strategies. We’ve talked about spending money, owing money, number lines, football plays, temperature, etc. The student has struggled to find a solution that works consistently enough to stick. However, it appears the student is finally getting it. This particular student has learned a lot about persistence in problem solving. The student has sought out the answer him/herself and used multiple resources along the way. Consider what this student learned throughout this journey, in addition to learning how to correctly add and subtract negative numbers. All because she was allowed to fail.
One of Khan Academy’s early pilot teachers, Suney Park, has been featured in the new book American Teacher. The book details the stories of 50 inspiring teachers from across the US. Congratulations Suney! Thank you for all that you do for your students!
Read about her inspiring story and learn more about how she uses Khan Academy here.
If you live in the California Bay Area, you can also hear her speak this Saturday, October 12 at the Barnes & Nobles in San Jose from 11:30-12:30 (more info here)
Last month, Khan Academy launched our Spanish website! We have been excited to hear from educators, parents, and students about the impact this has had on classrooms and learning around the globe.
For more details about the newly available resources, read on!
Spanish-speaking learners can now:
1. Grow with our personalized math experience
Using the new learning dashboard (launched in August), learners receive personalized recommendations on what to work on next, have access to over 100,000 math practice problems, and can track their progress.
2. Explore tutorials in other topics
Our tutorials cover a range of subject areas, including physics, chemistry, biology, art history and more. These tutorials are currently being translated into Spanish.
3. Learn with a mentor
Learners can sign up a parent, mentor, or teacher to help guide their path. These coaches can access real-time dashboards to identify where learners are and where they need help.
If you are a registered user and want to change your language to Spanish, just select “Español” as your preferred language at the bottom of the homepage. Please note that the Spanish website is a work in progress. As Khan Academy creates new content in English (which we do on a daily basis), translators will be working to translate this content to Spanish.
Help us spread the word! Share our Spanish website with Spanish-speaking individuals or educational organizations.
Want to help translate? Apply to become a translator for any language.
¡Khan Academy acaba de lanzar nuestro sitio en Español!
Hay aproximadamente 6 mil millones de personas que no hablan inglés en el mundo. Para proveer recursos libres a cualquier persona en el mundo hemos pasado el último año traduciendo la experiencia que ofrece nuestro sitio a cualquier idioma escrito del mundo.
Con el lanzamiento de la versión del sitio en Español, estamos ahora proporcionando acceso a 500 millones de personas que hablan Español alrededor del mundo. En los siguientes meses y años traduciremos nuestro sitio a otros idiomas.
Las personas que hablan Español ahora pueden:
1. Crecer con nuestra experiencia personalizada en matemáticas.
Usando nuestro nuevo panel de aprendizaje (lanzado en agosto), los estudiantes reciben recomendaciones personalizadas sobre qué trabajar, teniendo acceso a más de 100,000 problemas prácticos de matemáticas y pueden dar seguimiento a su progreso.
2. Explorar tutoriales de otros temas.
Nuestros tutoriales cubren una amplia gama de áreas, incluyendo física, química, biología, historia del arte y más. Estos tutoriales actualmente están siendo traducidos a Español.
3. Aprender con un tutor.
Los estudiantes pueden inscribirse con un tutor o maestro quién le ayudará a guiar su camino. Los tutores pueden acceder a paneles en tiempo real para identificar en donde están los alumnos y donde necesitan ayuda.
Si eres un usuario registrado y quieres cambiar tu idioma a Español, selecciona “Español” en la parte inferior de la página principal. Ten en cuenta que la página en Español es un trabajo en proceso. Como Khan Academy crea nuevo contenido en inglés (lo cual hacemos a diario) los traductores estarán trabajando para traducir estos contenidos al Español.
¡Ayúdanos a difundir ésta noticia! Comparte nuestro sitio en Español con personas u organizaciones educativas de habla hispana.
Derek kindly gave us permission to reprint his original post in its entirety below.
These pictures (below) are from one of our computer labs in the school. My students typically spend 2 days a week in a computer lab as part of a blended learning strategy. In addition to face to face time in my classroom, I have really enjoyed the time my students get to spend at a computer. There are some things a computer does really efficiently and Khan Academy provides me with a tremendous amount of data that I can’t imagine teaching without. Just from today, I can tell which students need extra time converting 1-digit repeating decimals to fractions and vice-versa. By tomorrow, 90% of my students will have demonstrated they are ready to move on to the next skill. Back in the classroom I will try to incorporate engaging activities that reinforce what we’ve learned, while building on the next skill or topic. It’s difficult to share in pictures or words, but already today I saw students helping other students. This isn’t something I ask them to do, they just do it. The atmosphere we create inside the computer lab is unmatched. I’ll try to share more about my students’ experience in math class. Ask your students about their experience thus far and feel free to contact me with questions or feedback.
Guest blog post by Alison Elizondo, 4th grade teacher at Burnett Elementary, a Title 1 school in Milpitas, CA.
Welcome to the 2013-2014 school year! During the summer, I attended (and spoke) at the KA workshop offered free of charge in Redwood City, CA. Maureen, from Khan Academy, encouraged participants to ‘just start’.
This is my third year using the KA platform in my fourth grade classroom. Because I want to constantly evolve, improve and create new learning experiences for myself and my students, I set a goal to begin KA on the first day of instruction.
I was amazed at what I witnessed in my classroom. The students were able to sign up, personalize their account, add me as a coach, take the new pretest and begin earning energy points on the very first day….and in 40 minutes.
First hand, I have experienced what kids can achieve if given the opportunity. I have 9 fourth graders that are still 8 years old. They were able to accomplish all of these tasks effortlessly. The message I took from this is that kids are open to new learning if the teacher is willing to try new ways of teaching.
Last year my class created the name ‘We <3 2 Learn’ for our KA rotation model. This school year, my fourth graders are going to innovate and collaborate in order to advance our program. Each student created an attainable math goal for themselves. We used the cool KA leaves found in the Coach Resources section of Khan Academy. These are now displayed on our ‘We <3 2 Learn’ bulletin board.
My students completed a survey today about the first week in fourth grade. Most every student reflected that the best part of the week was beginning Khan Academy. This is exciting! I can only imagine what we can achieve in 180 days together. Stay tuned :)
In his book The
Math Character Gap, Peter McIntosh shares his experience with how Khan Academy helped change his school’s math scores from the bottom 20th percentile on the California Standards Test to 11th in the state.
Read it for free!
When we made rebuilding student character (defined as responsibility, effort & confidence) our primary focus we achieved amazing results. Our average score on the California Standards Test (CST) for 9th grade algebra increased from 327 to 399, raising our state placement from the 20th percentile to the 99th percentile in just three years. We are now ranked 11th out of 1,377 high schools.
This is the story of how Oakland Unity High School, a small charter high school in the tough neighborhoods of Oakland, California, changed its math program and began the process of reversing the math gap. I am the algebra teacher at Oakland Unity High School. This book describes how diminished student character was the cause of that math gap and the specific steps we took to close it. An important part of our strategy was the use of Khan Academy. We describe the specific ways we use Khan and explain some of the reasons why Khan has been so effective. We also describe the specific policies we used to:
* increase student responsibility,
* improve effort on homework and classwork,
* address the total lack of student confidence on word problems.
Students today are not struggling in math because of poor content delivery. They struggle despite the best efforts of many good teachers because many of them are increasingly resistant to absorbing any content. They are stuck in a vicious cycle because they lack three character elements: responsibility, effort and confidence. I am not suggesting a diminution of the teacher’s role; I am suggesting a shift to emphasize leadership and inspiration over explanation. Any teacher that has survived in some of our tougher classrooms has the necessary leadership skills, and I believe that online learning makes this shift more effective.
These are good kids, who used to be enthusiastic learners, who have gotten off track for a variety of reasons. Many of the factors that caused them to lose their way may not have been their fault, but it is their responsibility to rebuild their own character. It is our responsibility as teachers to create the environment for that rebuilding effort. This is the blueprint for creating that environment.
The book is manageable to read at 21,000 words, but filled with useable, real-world solutions that brought our urban math classroom from the bottom of California high schools to the very top.
“Khan Academy helped me a lot because I didn’t know a lot about ratios and expressions, but with Khan Academy and the help of my teacher and TA I learned to love math and have fun.” – ALearn middle school student
For many students, summer is a time to play outside, sleep in, and watch TV. School and learning become a blurred memory. Many of these students, especially low income students, then suffer “summer learning loss” and actually lose 2-3 months of math proficiency over the summer, falling further behind their peers—and accounting for over two-thirds of the achievement gap between low income and their higher income peers..
But for 1,200 first generation-to-college middle and high school students in Santa Clara and San Mateo Counties, the summer of 2013 offered a great opportunity to improve their skills in math and get on track to go college as they enrolled in ALearn’s Math Acceleration and Catalyst to High School programs.
ALearn is a non-profit organization founded in 2007 that is committed to help more low-income, underrepresented students prepare for and complete college. Since then, ALearn has provided rising 6th, 7th, and 9th graders access to academic support programs and a college-going culture that has helped increase the number of college-bound students in the Silicon Valley.
The majority of the students that ALearn serves come mostly from Title I schools, with high percentages of English Language Learners and students who qualify for the Free and Reduced Lunch Program. They often come with significant gaps in their math knowledge. They also lack the self confidence that they can do math well, and sometimes have given up on themselves.
To face these challenges, ALearn uses a blended learning approach based on the new Common Core standards. Experienced, credentialed math teachers and energetic college student Teaching Assistants (TAs) use small groups, interactive hands-on activities, games, and Khan Academy computer modules to help students realize that math is not only necessary, but it can be fun as well.
From all the resources and tools ALearn used this summer, Khan Academy stands out as one of the favorites for teachers, teaching assistants and students. When asked what he liked best about the program, an ALearn high school student responded that it was “Khan Academy because it was like having a personal math tutor in class and at home. I could just go to Khan [Academy] whenever I need help”.
"…it was like having a personal math tutor in class and at home. I could just go to Khan [Academy] whenever I need help”. - ALearn high school student
To most teachers, Khan Academy was new. To help them better reach their full potential using Khan Academy, ALearn included a comprehensive training session during its professional development that showed teacher and TAs how to use Khan to help students understand the math concepts better and at their own pace. “Incorporating the online resource of Khan Academy was engaging and fun for students while also allowing students to continue building their skills at home” commented an ALearn high school teacher.
“Incorporating the online resource of Khan Academy was engaging and fun for students while also allowing students to continue building their skills at home” commented an ALearn high school teacher.
Furthermore, teachers and TAs were able to monitor student progress using Khan Academy’s diagnostic features and intervene where necessary, a feature that allowed them to better meet the specific needs of their students. An ALearn middle school TA mentioned how “students were able to connect the lessons and test their knowledge with the exercises on Khan. They got excited to leave the classroom and go work on something else”.
More importantly, students enjoyed using Khan Academy since they were in control of their progress and they even competed against each other to see which student got the most energy points. “I think that Khan Academy helped me the most because it would make sure you I did well and understood math completely. You would not be able to move on unless Khan [Academy] is completely sure you are ready to go to the next step” commented an ALearn middle school student.
ALearn is glad to have such an effective and popular resource available at no cost to help more of its students achieve proficiency in math. For the third year in a row, ALearn has integrated Khan Academy into its academic curriculum, serving 100% of the students enrolled in its programs with significant practice using KA. ALearn students showed remarkable results and success using Khan Academy to supplement the curricula used in the classroom. Rather than losing competency in math over the summer, these students gained significantly. In the words of an ALearn middle school TA, “Khan Academy was definitely a major strength in this program.”
We’re excited to announce that Khan Academy is creating new content to rigorously and comprehensively cover the Common Core Math Standards, a set of K-12 math standards that most of the states in the US have adopted. Like the authors of the Common Core Standards, we believe that conceptual understanding, procedural fluency, and application are all critical and complementary components of an excellent math education.
As the Standards become more widely implemented, we want to make it easy for students, teachers, and parents to find the content they need on our site.
An up-to-date mapping of our content to the Common Core Standards is available here.
Nice! What type of content are you creating?
For several years we’ve had math problems on our site that address many of the topics in the Common Core. These problems are grouped into problem sets, which we call exercises. Rather than simply retroactively map our existing exercises to the Standards, we’re proactively creating new math problems and modifying some of our existing content to rigorously and comprehensively cover the Standards. This is a significant effort, but a worthwhile one, as it will make our content much richer and will help students learn concepts more deeply.
Students always find out immediately if they answered a question correctly or incorrectly, and every question has a complete worked solution. Sal’s also making videos to show how to reason through and solve our new questions.
Our questions are computer-gradable, but they’re not just multiple choice; many questions ask students to write equations, create graphs, or fill in values on a table.
Can I see an example?
Yep! Here are a few examples of the thousands of questions that have been written based on the Common Core Standards:
Interpreting features of functions - Maps to Common Core Standard HSF-IF.B.4
It’s one thing to know what an even function is. It’s even cooler to understand what it means in a real-world physics, statistics, or finance problem. Try your hand at it in our interpreting features of functions exercise.
Understanding place value - Maps to Common Core Standard 4.NBT.A.1
One of the many magical things about the base ten number system: you can write the same number in lots of different ways. We hear the kind of thinking students do in our understanding place value exercise may come in handy when subtraction with regrouping comes along…
Units - Maps to Common Core Standard 6.RP.A.3d
In our units problems, students use proportions to solve real-world unit conversion problems. Sometimes it’s a matter of life or death, as in the case of the squirrel in the question above
Like our existing math practice problems, these new practice problems are grouped into exercises (problem sets) and can be found on our knowledge map, in our tutorials, and by searching on our site.
Who’s creating this content?
We’ve brought on a team of experienced math teachers, tutors, and professors to write math problems that rigorously cover the Common Core Standards. In addition to drawing on their own experience teaching students, team members also regularly utilize other great resources on Common Core Standards, like sample problems from Illustrative Mathematics, Common Core progressions documents, and sample items from Smarter Balanced and PARCC, the main consortia developing Common Core assessments.
It’s important that our content is high-quality and always improving, so all questions are peer reviewed to ensure they address the relevant standards and are clearly written. We also seek input from several advisors and partner organizations that are well-versed in the Common Core Standards.
To ensure the quality of our content, we continuously refine our math problems based on feedback from students and teachers who use our site. We regularly run analytics to determine whether certain questions are too challenging or too simple, and modify our content accordingly. Since millions of problems are done on Khan Academy each week, we can gather significant data quickly and iterate rapidly.
Sounds cool, but I’m pretty sure Common Core has nothing to do with me.
Of course, we recognize many of our users are not affected by the Common Core. Many adults use our site to brush up on their math skills, and lots of folks use Khan Academy to study math that goes beyond the Common Core (lots of our content addresses concepts outside the scope of the Standards). Still others attend schools that don’t use the Standards or live outside the US. Even for those folks, the new content we’re creating will provide a richer, deeper learning experience on Khan Academy, and we truly believe this effort will benefit everyone who uses our site.
How do I find all this new content?
All of our Common Core content is integrated into our site and searchable by keywords and topic names like fractions, proportions, and functions. You don’t need to know anything at all about the Common Core Standards to find content on our site or to benefit from these new resources.
And though it goes without saying, we want to be super clear: Khan Academy has always been all about meeting people wherever they are, not about dictating what you can or can’t learn just based on your age. We’ll never restrict the content you can see based on what grade level you’re in or prevent you from exploring.
We’re excited to offer content that rigorously and comprehensively covers the Math Common Core Standards and that makes the quality of the content on our site better for everyone. This is still very much a work in progress, and we’d appreciate your feedback. You can suggest ideas for new content or share updates to our Common Core mapping here.