We're excited to welcome back guest blogger, Cathy Tran, a former producer at Scholastic. She's currently a Ph.D. student in Learning, Cognition and Development at the University of California, Irvine.
The New York Times Magazine this week published a series of articels about educational technology that are worth a read. Highlights include articles about transforming a classroom with video games, a history of classroom technology, and the 8-year-old programmer.
One article that particularly caught my eye was on computer tutors that respond to emotional cues. In my chats with teachers about technology, many have expressed concern about their roles being replaced. I wouldn't be surprised if some find this news frightening: researchers are creating computer tutors that can detect and respond to students who appear to be too bored or frustrated. Students are hooked up to sensors that monitor sweat, fidgety movements on seat cushions are recorded, and how hard students press the mouse is on the record as well. A tiny camera tracks facial expressions.
I find educational technology to hold huge positive potential and its research to be inspiring. The human brain is such an intricate, complex work of art that I bet no technological creations will ever make it obsolete. To me, it's exciting when technological gadgets can step in to do human tasks well because that means we can free up our brain (and time!) to do something else to improve the learning environment. Those effective tutor creators have quite a challenging task, though, because each biological response and muscle movement may have multiple meanings. For example, sweat can indicate excitement or anxiety - very different! It's tricky business to figure out how to take in all the different data, analyze what certain combinations may mean, and turn out the students' emotions on the other side. And even if the emotions are accurately identified, the question then becomes, how well can a virtual tutor assuage the negative ones? That's one big research ambition!
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Motivating students in mathematics class is often challenging because they fail to see the purpose of math and don't make connections among discrete mathematical topics. Recently, I read an article, From the Inside Out, that details the importance of developing students' intrinsic motivation. The teachers I encounter tend to recognize students' distaste for math and put forth effort to motivate students through rewards and positive comments. This article, however, stresses the need to increase students' self-motivation. You see, when teachers are the motivating force, students may lose that motivation when they enter another class. If the student is the source of motivation, he or she will carry the desire to be a mathematician to future classes and endeavors.
In this article, the authors highlight behaviors that indicate student-driven motivation, including a student initiating a connection to previous material, a student initiating a response beyond the original question, and a student initiating a conjecture. Each of these behaviors, if unprompted, implies that the student is making a connection to the mathematics at hand and is compelled to extend learning beyond what is being explicitly taught. While many students – especially those who struggle – do not initially engage in these behaviors, the authors suggest some methods for increasing students' internal motivation.
- Model desired behaviors — Pose questions to the class that will prompt students to make connections and conjectures.
- Recognize and acknowledge students' behaviors — Positively identify behaviors that indicate a student is thinking outside the math or beyond the content that is being presented.
- Encourage students — Help students think of themselves as mathematicians.
- Provide opportunities — Incorporate problem-solving and investigative activities throughout instruction.
It's great when teachers work hard to inspire their students to be great thinkers, but we must do more! We must inspire them to want to be great thinkers and mathematicians so they can succeed outside the walls of our classroom.
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As I've mentioned in earlier blog entries, I'm a big fan of introducing math concepts in ways that are interesting and motivating for students. It seems to be an obvious methodogy, but it can be a challenge when we're in front of the classroom feeling pressure to get so much done each day. I often suggest to my colleagues to start routines that squeeze math into various parts of the day. Many elementary teachers utilize daily math activities each morning such as talking about the day of the week, the temperature outside, and the schedule for the day. These are all great methods for getting young students to think numerically. However, implementing similar activities is a bit more challenging for older students.
One of my favorite tools that can be adapted for any age is a math calendar like the one shown here. Every teacher I know has a calendar in their classroom, but this one is special. Rather than using a traditional calendar with numerals, this calendar requires users to do a bit of math to figure out the date. I love this tool because it can be made quite simply and can be made appropriate for any grade level. I've seen some teachers go so far as to never use "traditional" dates on documents, and instead, they always create a mathematical date for students to figure out. This year I'm going to have students create their own math calendar. What a great differentiated project! Students can be given the directive to create a calendar for a month or even the whole year using non-traditional numbers. I think it would be challenging and fun for students but something that every level of student can complete successfully.
Inspire your students to do more math by thinking outside of the box and making a common daily tool more mathematical!
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This year, one of my district’s initiatives is to get teachers involved in more Professional Development (PD). As with any career, it is important that educators stay up-to-date on trends and teaching methods that can benefit their students. Unfortunately, budget issues have made teacher PD a bit of a challenge in many districts.
To battle this problem, I am constantly keeping my eyes open for free PD opportunities. Surprisingly, there is a lot of it out there if you take the time to do some research. Free or low-fee PD opportunities give teachers a wonderful chance to learn and, often, the only cost to the district is for a substitute teacher. Here is a list of resources that sometimes offer low-cost PD:
- Your state Department of Education: On the NJ Website, there is a list of PD opportunities that are very timely in terms of what is going on in math education within the state.
- Your state math teachers association: Your state may have a group similar to the Association of Mathematics Teachers of NJ – such a group is likely to offer workshops for teachers. Many of these workshops are free and offered after-school via the internet. Therefore, these sessions don't even require the district to get a substitute.
- The National Council of Teacher of Mathematics (NTCM): NCTM offers similar professional development opportunities through e-seminars.
- Your textbook's website: Many publishing companies offer PD for program users. These sessions can be quite helpful, especially because they are often tailored to the program you are using.
If you have no luck with any of these resources, try doing an internet search. There are a lot of opportunities for teacher learning. Are there any other resources that you have found helpful? If so, share with your fellow colleagues!
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If you missed the New York Times article last week challenging conventional thinking about learning, follow this link immediately. It will point you to yet more research questioning the notion of children's learning styles. Yes, we have learning preferences, ways we're used to doing things, but there's no evidence that those preferences represent innate styles. And teaching to those styles hasn't resulted in improved performance.
How about the best way to study? Cramming is a bad idea, at least in the long term. Practice is best when it's distributed over time — even better when you mix up, or interweave, the content. Of course you want students to study in a quiet place with no distractions, right? Maybe not. A window to the outside world and a little bit of nature may improve retention. Practice tests can also help, especially if they prompt student to wonder why they got something wrong. Correcting a mistake or remembering something forgotten can really deepen learning.
We're big fans of systematic research, even when it busts some beloved assumptions of teaching and learning.
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Data-driven instruction: it's definitely been a buzz word over the past few years. Most educators know what it is and know why it's important. Few, however, have ever learned how to analyze data to improve student outcomes. As the year begins, one of my most important tasks is helping teachers analyze their state test results. I consider this a bit of a professional development activity because it doesn't just say something about student progress, it can be a window to the strengths and weaknesses of a teacher.
One strategy that is successful is to analyze each teacher's class list and highlight strands where students struggled or excelled. This can help the teacher determine areas of focus for the subsequent year. For example, if 80% of last year's class failed the Geometry portion of the test, the teacher can work to boost his or her Geometry unit. Next year, those results can be analyzed to see if changes were successful. Another strategy is to analyze students' growth from year to year. Using scores from the past two or three years, one can analyze which students are trending upward or downward. Again, this allows teachers to reflect on their practices the prior year to see if any of their teaching methods can be improved.
Of course we all know that state tests tend to be a "snapshot" of student ability and cannot be the only piece of data used to inform instruction. However, this data is very helpful as the year begins and we have a class full of students whom we may know very little about. As the process gets more comfortable for you, start looking at chapter or unit tests in the same way. This will enable you to tailor instruction to a particular class or student to increase achievement levels.
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Recently, a teacher colleague asked me for some ideas about how to implement math projects throughout the year. It got me thinking about the use of projects in math class and how they can enhance student learning. Many schools use math programs that implement both short- and long-term projects that will complement their curriculum while engaging students with the skills they are learning in class.
Like any new classroom initiative, implementing projects can be challenging at first. Decisions about the frequency, duration, and topics included in the projects must be made. Materials need to be collected and organized, and grading policies must be established. Thankfully, there are a plethora of resources available to help you get started. One source that is helpful is MATHGuide Projects. This site provides guidelines and suggestions for a variety of projects. One of my favorite project ideas is for students to create a puzzle. I've had students create a crossword puzzle using Geometry vocabulary words. Students may also want to create a "cross-number" puzzle that uses equations as clues and the solutions as the answers in the boxes. Depending on students' ability levels, these projects may take time, but they are fun and help students master the applicable skill.
Another resource that is helpful is a book titled Hands-On Math Projects with Real-Life Applications (J. Muschla and G. Muschla). This book is available for various grade spans and provides a multitude of ideas and resources for implementing projects in your classroom.
Start slow — try introducing just a few projects this year and then add a few more each year. Before you know it, you'll be motivating your students and giving them a reason why learning math can be fun!
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Now that school has started, I'm working on new tasks and initiatives to ensure that our students have the best year possible. For many of us, success is measured by mandatory state assessments. If we had it our way, this would not be the case, but due to state and federal mandates our administrators, teachers and students are often judged by those pesky test scores.
When I taught high school, I didn't understand the pressure that elementary and middle school teachers are under to prepare students for the test. The words "teach to the test" frustrated me tremendously. If you're teaching the standards successfully, shouldn't the kids pass the test? I've learned that it's not that simple. Preparing students for the test isn't just about covering the standards, it's about covering the standards before the test in early May – our schools don't close until late June – and it's about preparing students for the various types of questions on the test.
Ideally, all of this is done without spending the entire month of April on test-prep activities, but this is a challenge due to pressure on teachers to increase scores. This year, I'm starting a new initiative titled ASK Aerobics (NJ's test is titled Assessment of Skills and Knowledge, or NJ ASK). All teachers in Grades 3-8 will assign a daily warm-up based on one of the four major mathematical strands, along with an open-ended question for the fifth day of the week. The goal is for students to complete one test-prep question each day for the entire year. As the math specialist, I will gather the work, compile data, and return to teachers a simple report showing students' strengths and weaknesses. Although it will be a lot of work, I feel that the data we collect can really inform instruction while consistently presenting students with a variety of NJ ASK-like problems. We're all keeping our fingers crossed that this will eliminate some of that last-minute pressure that teachers and students feel in the month before the test.
I'd love to hear about the pressures you feel with standardized tests and how you help students and teachers meet this challenge. Please share.
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Many teachers begin the school year by implementing lessons to improve students' abilities to solve problems. Unfortunately, problem-solving is one of the areas of great weakness for students and an area that consistently decreases student test scores.
I spend a lot of my time working with teachers to strategize about how to help students in this area.
First, this is definitely an area where practice makes perfect. Students need consistent exposure to rich problem-solving scenarios that have meaning and require them to use a combination of computational strategies. Second, students need to see a great variety of problem types. Perhaps this is why it's critical to teach problem-solving lessons from Day 1. Students of all levels should be challenged by problems that differ from what they've previously encountered. Struggling in math class is not the worst thing in the world — it improves students' critical thinking skills and ability to reason through an unknown situation.
For younger students, it's often the process that presents a challenge. Last year, I began using the STAR problem-solving technique with elementary students in my district:
Search the Problem (read the problem and identify important information)
Translate the Problem (translate the words into an equation to be solved)
Answer the problem (work through the problem and find a solution)
Review the Solution (a critical step – make sure the answer makes sense)
I developed a motivating problem-solving poster with star graphics and an accompanying template that students used as they worked through each step. I've found that this technique makes the process less intimidating for students and encourages them to want to solve problems. Have you used any similar strategies? Please share what's worked for you!
I mentioned in an earlier post that one of my goals for this school year is to re-think my homework policy. Although I don't teach in a class where I would assign homework, I'd like to come up with some recommendations for my colleagues. We've consistently seen that kids' marking period grades are tremendously affected by their homework grade. In my experience, the majority of the influence is in the negative direction because the kids are bright and do well in class but just don't do their homework. Most of my colleagues do grade homework on effort as opposed to correctness, but I still feel uncomfortable giving a student a 75 in a course when he or she has received much higher grades on every test and quiz.
To commence my research efforts, I read the book Rethinking Homework: Best Practices to Support Diverse Needs by Cathy Vatterott. This book discusses the merits of both sides of the homework debate and focuses on giving students quality homework, as opposed to a large quantity of homework. I think this might be a challenging endeavor for math teachers because the tendency is to give lots of computation problems for student to practice. I certainly feel strongly that students need to practice math to achieve mastery, but I also feel that we must be strategic about how students practice. Vatterott suggests giving students more flexibility in terms of homework assignments by letting (older) students choose which problems they'd like to do and giving students more than one night to complete an assignment. Students have busy lives and often their out-of-school responsibilities are out of their control. Penalizing such students is only going to turn them away from education. Also, I think giving students just a few high-quality, rich problem-solving opportunities as opposed to many computation problems will help students bring meaning to what they are learning and even make it a bit more interesting.
I am just at the beginning of my research on this topic, but as we begin a new school year, it is a topic that I am eager to address with my colleagues. Do you have an "out of the ordinary" homework policy? If so, please share!
Vatterott, C. (2009). Rethinking Homework: Best Practices to Support Diverse Needs; ASCD.
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