San Diego math teacher Osvaldo Soto has set out to address why so many students struggle in math at the middle and high school levels, according to an article in the San Diego Union-Tribune. Even students who excel in elementary school may later fall behind, lacking the necessary foundations to move on to Algebra, Geometry, and upper-level math. Soto believes that teachers are too quick to show their students short cuts to solve problems. These tricks and shortcuts may be effective in the short run, but students fail to develop the analytical skills to solve the problems on their own. And too often, they don’t even understand how they came to the answer.
While tutoring middle school students in math recently, I have noticed that many of them try to rush to get to the answer without really understanding what the problem is asking. When I ask them to show and explain their steps, many times they are unable to justify what they are doing. One student was trying to plug numbers into the Pythagorean Theorem but did not know the definition of the hypotenuse. This student clearly had some critical gaps in his knowledge of geometry. He was trying to plug numbers into a formula he had memorized, but he had not mastered the essence of the concept.
While adults who are more familiar with math may rely on quick shortcuts, it is important for students to employ analytical and quantitative thinking skills when approaching problems. These skills will help build the foundations for success in math. Soto, a member of Math for America San Diego, is trying to revive math instruction by encouraging students to think and to be curious about math.
What are some strategies you use to develop students’ conceptual understanding? And how do you promote curiosity in the math classroom?
Officials in South Korea are tracking down "cram schools" that go past their 10 p.m. curfew and have students in uniforms working on math problems deep into the night. The Education Ministry even offers rewards to tipsters. The Washington Post reported that more than three quarters of students in Korea enroll in private tutoring, the highest rate in the world. More than $19 billion was spent on private tutoring in 2009, more than half the amount spent on public education.
Some wonder if Korea's impressive statistics in education come at too high of a cost. Korea regularly ranks near the top in international math exams, such as the PISA. Their high school dropout rate is less than four percent. College completion is at 56 percent, among the highest in the world.
However, Korea's Minister of Education, Lee Ju Ho, expressed his concern to the Post that much energy "has been spent on raising test scores, not nurturing creativity or any other aspect of human nature." This sentiment jibes with conversations that I've had with colleagues who say many families in other countries want their kids to do their primary and secondary schooling in the states to develop into more well-rounded individuals with talents outside of academics and that have social lives.
If the international exams tested creativity and other 21st century skills, do you think the U.S. would be at the top of that ranking?
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Most educators, especially math teachers, are passionate about mathematics. However, not all students have the same respect for the subject. Cossondra George recently published an article in Education Week providing tips about how to build students’ aptitude and engagement with mathematics. “While it is considered unacceptable for the average person to lack basic reading and writing skills,” she writes, "people often brag about their inability to ‘do math.’ It is almost a badge of honor to be numerically challenged.” Here, George highlights the reality that society often believes it is acceptable not to be good at math.
In her article, George provides six suggestions to increase students’ level of confidence with mathematics.
- Purchase a set of whiteboards for your class – These help students engage with the lesson and practice concepts with their easy-to-erase tools. Even reluctant students can have fun solving problems on the whiteboards.
- Create real-life examples of concepts you are learning – Go beyond story problems offered in textbooks and create problems that relate directly to students’ lives.
- Teach the power of “Is your answer logical?” – Students need to understand that math isn’t just about a process but also about a logical solution. Always require that your students look back at the original problem to be sure their solutions make sense.
- Integrate technology to capture student interest – Students live in a technological world, so bring that world into the classroom through interactive games and activities.
- Encourage, require, and demand re-dos – By correcting missed problems, students identify their mistakes and take pride in working through the correct solution.
- Use small groups and presentations where students teach each other – Students learn better when they teach a topic and other students are likely to be highly engaged when learning from their peers.
Each of these suggestions will help improve the disposition of your students. Try some of these suggestions to make your classroom one where the inability to do math isn’t acceptable, and instead, students are urged to be true mathematical thinkers.
When dealing with elementary and middle-school students, it’s often difficult to help them see further into the future than the next weekend. However, students at this young age should be setting long-term goals and begin thinking about potential career options. While we all know that their plans are likely to change many times before they head out into the work force, it is beneficial for them to at least come up with a few options. This will allow them to set the short-term goals necessary to head in the right direction, and in many cases it will give more meaning to what they are learning in school.
Recently, CareerCast.com published the Top Best Jobs of 2011 based on work environment, stress, physical demand, and hiring outlook. The top spot was secured by Software Engineer, but the number two spot is Mathematician, the number three spot is Actuary, and the number four spot is Statistician. Based on this information, it seems that being a motivated, hard-working math student in the early grades can lead to more than just a good grade on a report card. Students who master elementary math content are likely to do better in higher-level math courses. These courses are the ones that are necessary to secure our nation’s top jobs.
The challenge for teachers is getting students to look into their future and think about potential careers. It’s especially difficult to get them to understand jobs such as “mathematician” and “actuary” because these aren’t careers that they are likely to be familiar with. Start hosting a math career day to help students learn about such jobs, as well as to gather more information about how math is used in more familiar jobs like an accountant or engineer. They may have to do a bit of research, but it’s a great opportunity to help kids make connections, write in math class, and perhaps even stumble upon a future career.
As another school year nears the end, reports tend to surface about graduation rates and, subsequently, drop-out rates. I began reading an article about drop-out rates when I remembered a report I read several years ago regarding this subject. The report, Approaches to Dropout Prevention: Heeding Early Warning Signs With Appropriate Interventions, details some factors that may indicate a higher chance of student drop-out in high school and provides interventions for decreasing drop-out rates. Of particular interest to me, is the information provided about the correlation between early math success and future drop-out rates.
Among other indicators, the report states that low performance in core subjects such as math may lead to a greater likelihood of a student dropping out of high school. One study mentioned in the article indicated that "more than half of sixth graders with the following three criteria eventually left school: attend school less than 80 percent of the time; receive a low final grade from their teachers in behavior; and fail either math or English. Eighth-graders who miss five weeks of school or fail math or English have at least a 75 percent chance of dropping out of high school." While the factors expand beyond a failure in math class, the fact that students who struggle with math may be more likely to drop out of high school implies an urgent need to help students succeed in elementary and middle school mathematics.
The report includes a plethora of strategies to prevent future high-school students from dropping out. Some of these suggestions include establishing a data system that tracks individual grades and monitoring grades in core academic subjects early on. Upon identifying at-risk students, the report offers suggestions for interventions such as offering tutoring sessions, establishing learning communities, and providing opportunities for catching up on missed content.
As math educators, we recognize the importance of helping students succeed in early math classes so that they may find success in higher-level math. However, this report indicates that there is a far more important reason to ensure that all students have the support and tools for success in elementary and middle-school math. Knowing that we can help prevent students from dropping out of high-school gives me even more motivation to do all I can for my students.
Here’s a little vignette from last spring. I was in a group of parents waiting to collect kids from a “new school” visit. The teacher was wrapping up the day with an outdoor game where kids left and rejoined a circle based on some algorithm. Physical math in the sunshine, with lots of happy noise and an improbable amount of focus.
I exchanged who’s, where’s and how old’s with the parent next to me and we talked briefly about work. She then said, “You know, I think I’ve done it all wrong. I have an MBA in marketing, I worked for a major hospital group, and I had my own company for a while. But I really wish I had been a teacher.”
Now those of you in the trenches may say that was the spring weather talking. Who wouldn’t feel that teaching was blessed work, when the task was an outdoor number game on a gorgeous day?
But teachers: know that the meaning underlying your work is envied by many, MANY ordinary civilians. Your most mundane everyday activities have the potential for purpose that few jobs can offer.
We are in awe of you – your endurance, your attention to the details that matter, your endless patience when asked to handle the same problem over and over and over again. All in the same day.
But in that same day, something or several somethings may have happened that have lasting significance. And that is what we find most awe-inspiring of all.
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I admit...I’ve said it to my colleagues, “That kid is so lazy!” I’m guilty of looking at some of my former students and wondering how they could be so lazy, or how they could lose or simply forget about an assignment. Then, a few weeks ago, I came across an article explaining that many “lazy” students are actually lacking executive skills – the ability to organize materials and break down assignments. While not all students’ apparent lack of effort can be attributed to this issue, many students may be lacking the executive skills necessary to succeed.
The article states that students in elementary schools tend not to feel the effects of lacking these skills because they often have greater support from teachers and parents. As students enter middle school, the level of adult support is weaned and students who have not acquired executive skills begin to suffer. The author uses the RTI 3-tier model to provide suggestions for how to help students in this area:
- Tier 1 (whole-class) Interventions
- Establish classroom routines and rules and review them frequently.
- Develop a method for communicating information to parents.
- Integrate study-skills lessons.
- Plan fun activities as incentives for students to meet certain goals.
- Tier 2 (small-group) Interventions
- Break tasks into small parts – give students suggestions about where to start.
- Establish after-school homework clubs.
- Provide progress reports to parents and involve parents in incentive plans.
- Initiate small-group coaching sessions to teach students how to manage assignments.
- Allow students to use free-time to complete assignments.
- Tier 3 (individual) Interventions
- Define target behavior and criteria for success.
- Establish environmental modifications such as a quiet, distraction-free space to do work.
- Explicitly teach executive skills.
- Provide visual reminders of expectations.
- Monitor student’s use of independent time.
These suggestions aren’t likely to be the magic solution for getting all students to do their work. However, it might be helpful to consider which of your students have the ability but may lack the executive skills to be successful. Then, try some of these tips and let us know how they work for your students!
Dawson, P. (2010). Lazy – or Not? Educational Leadership, volume 68 (Issue 2). 35 – 38.
http://www.flickr.com/photos/mrehan00/ / CC BY 2.0
Now that I've settled into the school year and reviewed last year's test results, it's time for me to really dig into my role as a "consultant" to the teachers and students. As always, our goal is to ensure that all students are met at their current level and moved forward on their educational path. Thankfully, guidelines have been put in place to support this process. In my last entry, I discussed the basics of the Response to Intervention (RTI) model, and now I'm going to help you implement it.
Tier 1 of the model suggests that all students be supported through consistent monitoring and subsequent curriculum adjustments. This involves screening all students at the beginning of the year and monitoring progress throughout the year. The initial screening can give you a good idea about the "buckets" your students are likely to fall into. However, it's the consistent monitoring that is essential to track the progress of each student. As students are monitored, you might see some systematic issues with the majority of students. Oftentimes, these issues are with the curriculum and how this content is being taught. At this point, you should take a look at your curriculum and adjust teaching strategies to better meet the needs of all students.
You might also see some students doing very well on the assessment and others who appear to be struggling just a bit. This could indicate the need for more differentiated instruction within the classroom setting. It is important that students are given the opportunity to remain in the standard classroom setting, and many times this can be achieved by providing more challenging assignments to some and less intense assignments and support tools to others. Once these strategies are in place, give it a few weeks and reassess all students to determine if improvements have been made. If a small group of students are still struggling, they are likely to be candidates for Tier 2 interventions. Stay tuned for tips on how to help those students succeed in your math class!
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Most teachers have an understanding of the term Response to Intervention (RTI) when it comes to Language Arts. Over the past several years, however, there has been an increased emphasis on RTI in the mathematics classroom. In upcoming blog entries, I'll be offering tips on how to successfully implement RTI in your classroom, so I thought I'd start first by refreshing everyone's memory about the purpose of RTI.
The goal of RTI is to promote continuous monitoring and intervention to prevent students from falling behind. Implementing RTI effectively can help differentiate between students who have specific learning disabilities and those who are struggling in a particular area but can be brought up to level with some intervention. The three tiers of the RTI model are meant to be flexible so that students can receive the appropriate level of support based on their needs at a particular time. Students who do not respond after moving through the RTI framework may receive additional services for a specific learning disability.
TIER 1 is the most comprehensive tier that covers standard classroom instruction and review for all students. In Tier 1, students are screened, monitored and should receive research-based instruction. This instruction may include some remediation, but students receiving only Tier 1 instruction are considered to be working on grade level.
TIER 2 interventions are designed for students who have been identified as struggling with a particular content area.
TIER 3 interventions include specific, intensive support for students who may be working several years below grade level. Tier 3 students often receive one-on-one help and are closely monitored to determine if improvements are being made. If interventions offered in Tier 3 are unsuccessful, students should be afforded the opportunity to receive additional services through the school's special education department.
Now that we've reviewed the Response to Intervention framework, look for future posts about how to deliver math instruction at each level. In the meantime, share your school's sucess stories with implementing the RTI framework for math instruction.