While teachers may teach the fundamental concepts of math in school, parents have a critical role in helping their children become successful math students. From very early childhood, the interactions of parents with their children impact the child’s later math achievement. A study by Susan Levine, et al. found that the more interactions that parents had with their toddler in which they used and discussed numbers, the greater the child’s understanding of the cardinal meaning of numbers at 46 months. Other studies show that math knowledge at the time of school entry predicts later math achievement through at least 5th grade.
Here is a list of some of the most interesting findings from two studies on the development of number sense among young children:
- Children exhibit marked differences in mathematical knowledge by the time they enter preschool.
- Math knowledge at the time of school entry predicts later math achievement through at least 5th grade.
- A child’s knowledge level is highly related to the complexity of early childhood parental instruction.
- Findings show that children learn to recite the number sequence before they understand the cardinal meanings of the number words.
- Parents who talked more about number with their toddlers had children with a better grasp of the cardinal meaning of numbers at 46 months.
- Researchers found a correlation between cardinal number knowledge at 46 months and performance on vocabulary comprehension task at 54 months.
- The use of number words with small children includes some unique challenges:
- Cardinal number does not refer to an object or a characteristic of an object but rather a property of sets.
- Number words describe sets that vary widely.
- Number words are used in counting as well as to describe sets.
- Number talk that references present objects was more predictive of children’s later number knowledge, especially when talking about large sets.
Read the full studies here:
Providing the best parental support from early childhood through grade-school is not always intuitive. Parents themselves often need some instruction. Several resources are available to help parents develop the skills to engage their children in mathematical thinking at home and become involved in the learning process:
Math Is Everywhere is an initiative from Sesame Workshop™, the producers of Sesame Street, which provides fun and easy math activities and applications in everyday life. See the video available online.
CollegeBound is a free, online parent education program that offers simple ways for parents to help their children perform better in school.
The National Parental Information and Resource Center offers studies about the role of parent involvement in education and strategies for developing partnerships between parents and educators.
Parents can help their children become more successful math students by encouraging them to be active during out-of-school time. Physical activity has been shown to improve academic performance due to the effect it has on the brain. According to John Ratey, a clinical associate professor of psychiatry at Harvard Medical School, exercise stimulates the brain, sustains attention, and promotes people’s ability to sort through information and take it in. Furthermore, physical activity may reduce the symptoms of oppositional defiance disorder and ADHD, which reduce many students’ focus in the classroom. Dr. Ratey describes exercise as “Miracle-Gro for the brain” because it preserves nerve cells and even makes them stronger.
In his book Spark, Dr. Ratey profiles the Learning Readiness Physical Education program in Naperville, IL. The difference in achievement between students who participated in the program and those who didn’t is significant. The addition of exercise to students’ schedules was associated with an especially large jump in science and mathematics performance. Notably, after the program was introduced, eighth grade students from the Naperville schools finished first in the world in science and sixth in math on the TIMSS (Trends in International Mathematics and Science Study) international standards test.
City Park Collegiate School in Saskatchewan, Canada has experienced similar success by implementing strenuous physical activity as part of the math and language arts curricula. Students were more focused and attentive after 20 minutes of cardio exercise and found it much easier to apply themselves to their schoolwork. You can view a documentary, Brain Gains, about the school’s program on Dr. Ratey’s website.
Parents can encourage their children to experience the positive effects of exercise by modeling an active lifestyle. One mother from Natick, Massachusetts, inspired by Dr. Ratey’s book, established a before-school exercise program for students at a local elementary school. The program, called Build Our Kids’ Success (BOKS), has since expanded to 25 schools in the Boston area. It is important, especially in an age of technology, to get kids moving. We’d love to hear about similar physical activity initiatives in your district. Are they working?
Most children are familiar with “Head, Shoulders, Knees, and Toes,” an interactive song that teaches different parts of the body. But Megan McClelland, an associate professor of child development and family science at Oregon State University, has developed a similar, Simon Says-like task, called Head-Toes-Knees-Shoulders that may actually improve academic achievement. The task helps preschool-aged children increase their self-regulation. Self-regulation affects people’s ability to listen, pay attention, follow instructions, and complete tasks. Greater self-regulation has been shown to improve children’s math and early literacy achievement. Self-regulation is especially important to develop early on because children tend to enter school at varying levels, and those with low self-regulation often give up on school and learning early on.
Previous studies had shown that the Head-Toes-Knees-Shoulders task, in which children must listen carefully and follow instructions, was associated with significant improvement in self-regulation. Furthermore, these students also made gains in academic achievement. McClelland’s most recent study reveals that even children with initially higher levels of self-regulation (in this case children in Asian countries where children are known to have stronger self-regulation than in the U.S.) benefitted from the Head-Toes-Knees-Shoulders task. Students who performed well on the task scored significantly better in math, reading, and early literacy. Most notably, Chinese students who did well on the task performed 4 months ahead of their classmates in math.
Head-Toes-Knees-Shoulders and other similar tasks could be used in early-learning classrooms to develop children’s self-regulation and measure whether children are ready for kindergarten. Children who enter school without strong self-regulation are often inattentive, disruptive, and disengaged from the start. McClelland hopes to further develop Head-Toes-Knees-Shoulders and other tasks designed to improve and assess self-regulation, and thereby, academic achievement. She is currently performing a 4-year study to evaluate and refine Head-Toes-Knees-Shoulders. If the study proves successful, the task could be adopted by teachers across the country to measure kindergarten readiness. Who would have thought that a game similar to Simon Says could have such important implications for learning?
http://www.flickr.com/photos/neff/ / CC BY 2.0
I recently wrote about Fibonacci numbers and how they occur in nature, but did you know that you can also find this in poetry?
Fibonacci poetry is a poetic form that follows the Fibonacci sequence and can manifest by applying it to either words or syllables. In April 2006, Author Gregory Pincus introduced his version of Fibonacci poetry, “Fib”, on his blog. It’s a six-line, twenty-syllable (or word) poem with the following breakdown:
1 (syllable or word)
Let’s see a Fib that uses syllables in action:
A lullaby song.
The best song of spring has arrived.
Beginning poets will have an easier time creating this type of poem with words as it’s a challenge to get the flow of the poem and count out syllables simultaneously. No matter which way you apply the structure, Fibs are a fun way to fire up your brain while celebrating math.
As the new school year begins, teachers will be given a new class roster and begin the task of getting to know those pupils they will be teaching for the next 10 months. For me, this was always an exciting time of year – a fresh start with fresh faces and new expectations. Typically, it doesn’t take long to learn enough about your students to be able to predict which students will be shining stars and which students are likely to struggle throughout the year. Undoubtedly, you will have some students that will leave you wondering, how did he get this far?
Recently, I’ve come across several articles describing how districts are opting to move students along their educational path according to their ability level, not their age. In other words, students won’t automatically move to 4th grade simply because they passed 3rd grade. Instead, students will have to show mastery on the majority of topics covered in 3rd grade before advancing. We all know that passing does not imply mastery; therefore some educators are wondering if mastery of skills should be a requirement for advancing students a grade level.
Because this is a relatively new philosophy, there is not a lot of longitudinal research that supports or refutes this type of structure. My initial thoughts are that it would be a logistical nightmare. Students would be “moving” at all different rates, and because students may master skills at various points throughout the school year, it would be difficult to determine when a student is ready for the subsequent level. In addition, some students who fail to master a subject (whether it is because of a learning disability or disinterest in the topic) may be stuck at a level for far too long. And, what about those students who excel in English but just don’t understand math? Do they move forward? I think there’s potential in this type of thinking that is closely linked to individualized instruction and prescriptive learning paths. I don’t think the vast majority of schools are ready yet to take on this type of learning structure; however I do think a version of this will be the future of education. In the meantime, I’m truly curious about your thoughts on this topic.
Cognitive science research has shown that using comparison to teach algebra is a good thing. What has remained a question mark, however, is how to best train teachers to use such methods. A new study found that using comparison instructionally during professional development impacts teacher flexibility in teaching algebra.
The researchers – Christopher Yakes at California State University Chico, and Jon Star at Harvard University – piloted a one-day professional development activity to make teachers aware of comparison techniques. To impact implementation, they also sought to make the teachers more flexible themselves by helping them understand the nuances of different solution methods and problems.
Teachers engaged in a series of group problem-solving activities in which they were given two similar problems with two suggested strategies for solving a math problem (The full problem set is available online). The group then created and presented a poster with all four combinations of problem and strategy, allowing them to practice three research-based teaching techniques for using comparisons:
1. To-be-compared solution strategies should be presented to students side-by-side, rather than sequentially. A side-by-side comparison helps students notice and remember the features that are important to each or both solution strategies.
2. Discussion of and comparison of multiple strategies helps students justify why a particular solution strategy or solution step is acceptable and helps students make sense of why certain strategies are more efficient than others for particular problems.
3. Provide students with the opportunity to generate multiple solution methods to the same problem, either by investigating multiple solution methods of the same equation or by creating new equations to solve by a given method. In general, knowledge of multiple solution strategies seems to help students more readily consider efficiency and accuracy when solving problems.
Teachers reported that the activity made them question why they taught a certain solution method over another, made them more aware of student flexibility, and helped them see flexibility as a more valuable instructional goal.
Source: Journal of Mathematics Teacher Education
A recent report from the National Science Foundation (NSF) reveals the six factors that distinguish successful STEM (Science, Technology, Engineering and Math) education programs. eSchoolNews highlighted the report, which specifically assessed specialized schools with a STEM focus, but the recommendations provide food for thought to all educators interested in STEM. Adam Gamoran, chair of the committee that authored the report, emphasized the importance of implementing all six factors because they are interdependent in creating a successful STEM learning environment:
- A coherent set of standards and curriculum
- Highly qualified teachers
- A supportive system of assessment and accountability
- Adequate instructional time
- Equal access
- A school culture that encourages learning
Teacher training opportunities and sufficient instructional time to focus on STEM subjects were repeatedly lacking in schools. But when schools support these goals collectively, STEM can become an integral and valuable part of the curriculum. “Some people may have expected to see effective STEM instruction mostly in the selective STEM schools, but we found that effective STEM instruction may occur [...] even in regular schools,” Gamoran said.
Do you think advancing STEM is an achievable goal for all schools? What STEM initiatives has your school taken?
A few weeks ago I wrote a blog post about how the Fibonacci sequence appears frequently in nature. Fibonacci’s greatest and most useful achievement, though, may have been initiating the widespread use of the Arabic number system. Leonardo da Pisa, better known as Fibonacci, was the father of arithmetic as we know it. A story on NPR discusses the 13th century mathematician’s Liber Abaci, which means “book of calculations.” The book introduced the Arabic numerals from 0 to 9 and the ideas of basic arithmetic.
Before Leonardo da Pisa, people had to use a physical abacus to perform any calculations, so commerce, banking, as well as other everyday tasks were much more time-consuming. The only people familiar with the Hindu-Arabic number system, the one we use to perform calculations today, were scholars who studied mathematics. Leonardo wrote Liber Abaci so that ordinary people, not just mathematicians, could understand this system. His book revolutionized the way people thought about numbers and led to rapid and widespread advances in commerce, banking, science and technology.
Can you imagine a world before basic math? From the moment we wake up and look at the clock, we are dependent on numbers. Math is truly an integral part of our everyday lives. The NPR “Math Guy” Keith Devlin recently published a book about Fibonacci called The Man of Numbers. Read an excerpt from the book and let us know what you think!
Sometimes when I work with upper elementary or middle-school students, I wonder what (if anything) could have been done to better prepare these students for their current math challenges. Recently, the results of a longitudinal study were released detailing specific skills that first-graders need to master in order to meet with success in 5th grade math. According to the article describing the study, students need to master numbers, counting, and low-level operations early on in their math career.
The study was completed in an effort to learn what skills must be taught in order to produce successful students who can tackle math-related careers. Researchers monitored students from first through fifth grade and found that those who understood the number line and basic math facts showed more progress as they entered their 5th grade math class. Additionally, while the study did not extend to later mathematical courses, it is implied that students who do well in 5th grade math are far more likely to do well in subsequent, more-difficult math courses.
In my opinion, the challenge with this information is that a student who can count and recognize numbers is often thought to have mastery of basic number concepts. Unfortunately, this is not always the case. Young students need to be fluent with counting, should understand what the numbers represent, and must be flexible with their numbers so that they can operate with the numbers in a variety of ways. Such mastery requires students to be able to decompose numbers and identify different forms of numbers. These skills should be covered in schools, but it is important that teachers suggest that parents engage with number activities at home as well. Students need to be given as many opportunities as possible to help them succeed throughout their math career. When research highlights specific skills that are essential for future success, it is the duty of educators to utilize such information.
You might recognize the name Conrad Wolfram. He’s the founder of Wolfram Research and a big proponent for math reform.
In his 2010 TED Talk, Wolfram shared his thoughts on how today's math should be taught, and sees computer programming as the key. He believes that currently there is not enough focus on real world math and asking the right questions. Instead, there is too much focus on hand computation. If computers were used to focus on the computation part it would leave instructors and students more time to focus on the way math can be applied.
One of the main arguments against this method is students should know math basics before using the computer for computation. Wolfram argues that “basics” is hard to define and varies person to person. He turns the argument into a choice between “how it gets done” versus “what you’re trying to do.” When this is the question, Wolfram believes the answer is simple: Computer programming.
Computer programming allows math to become more practical and conceptual simultaneously. It allows the student to play and interact with math in a way they wouldn’t normally because the computer is focused on the calculations. This gives the student more time to learn core concepts in math and develop a better understanding. Be sure to watch Conrad Wolfram's full talk on this subject.
What do you think about Wolfram’s support of computer programming in math education?
My district offers a study skills class to all 5th grade students to assist with their attainment of strong study habits. While managing this course’s curriculum doesn’t fall under my math-related responsibilities, I do assist other teachers as they prepare to teach the class. I feel strongly that many students are capable of attaining better grades; they just don’t know how to go about doing it. Many students haven’t learned how to take notes or how to study, and I can’t tell you how many times I’ve heard the comment, “You can’t study for math!” The challenge teachers have with teaching an entire study skills course is the need to gather enough materials to teach a year’s worth of lessons.
As a jumping-off point for teachers, I have shared an article by Cossondra George that provides three suggestions for teaching students how to learn. In the article, George suggests that teachers often know how to teach content but may not know how to help students learn the content. According to the article, there are three common pitfalls that prevent teachers from ensuring student success:
- The first pitfall is assuming that students know how to identify important information and take good notes. To combat this pitfall, teachers should help students outline important information and provide tips for how best to capture the information - perhaps by using a Venn diagram or chart. Also, requiring students to have specific note-taking tools such as designated notebooks and highlighters may also be helpful.
- The second pitfall is making the assumption that students know how to study. Teachers can overcome this pitfall by setting time aside each day to help students study and review notes from previous classes. Teachers can demonstrate study techniques such as creating note cards, identifying important vocabulary, or developing practice test questions.
- The third pitfall is assuming that students understand the link between studying and academic achievement. Help students by asking that they set goals and reflect on their studying and note-taking techniques. Guide them to recognize how their habits lead them to their final result.
When students understand that they can learn to learn, they possess one more tool to help them meet success. The provided suggestions won’t change students’ educational path overnight, but they can go a long way towards helping students achieve their goals.
Confronting the complexity of the federal budget is an engaging way to get kids thinking about the importance of numbers. In light of the budget crisis, American Public Media and 360KID have developed Budget Hero, an online game in which players try their best to balance the federal budget. Players can make policy changes by playing a variety of policy cards. The results of these changes are reflected by the budget deficit/surplus, the size of government as a percentage of GDP, the national debt as a percentage of GDP, and the projected year in which the budget “busts.”
The game uses data from the Congressional Budget Office (CBO) to assess the impact of various policy changes. Players can choose up to three badges that reflect their budget priorities, such as defense, health and wellness, green initiatives, or several others. The fun, interactive game allows participants to experiment with government investments and budget cuts and then compare their results to others’.
Students can get a sense of the financial scale of some initiatives versus others, and they can learn about the difficulties of balancing the federal budget by reviewing the numbers involved. Classes can compare their solutions and debate the best measures for successful fiscal policy. At a time when the government’s budget has grabbed the public’s attention, why not take the opportunity to teach students about math with this highly relevant topic?
It seems that every time I have a conversation with another educator about best practices, the words differentiated instruction come up. This term has certainly become a popular one in education and most teachers recognize the benefits of teaching to individual students' strengths. What follows from instruction, however, is assessment, and rarely have I heard (or used) the term differentiated assessment. In the urgency for educators to master the technique of differentiated instruction, there has been little focus on assessing students in a more individualized manner.
Douglas Reeves recently authored an article providing some suggestions for integrating differentiated assessment into classroom practices. At the heart of his suggestions is the idea of creating a “menu” from which students can choose. This idea is most easily started with homework assignments. Reeves suggests offering different levels of problems in 3 separate columns. Students have to choose a certain number of problems from any of the columns. In doing this, all of the students complete the same number of problems but not necessarily the same level of problems. Some students will start with easy problems and stick with them because they need more practice. Others will move on to more challenging problems at various points throughout the assignment. The idea is that students work to their ability level, and by seeing which problems students complete each evening the teacher gets a quick snapshot of each student’s comfort level.
Reeves extends this idea into other areas of assessment by suggesting that teachers offer different assignments with the same available point values. For example, one student may choose an assignment worth 100 points, while another student may choose to complete 2 smaller 50-point assignments. Students are completing the same amount of work but each student can choose an activity that is configured to best meet his or her needs.
These are just a few suggestions to get your brain churning about how to integrate differentiated assessment. Just as differentiated instruction took teachers years to research and master, it is likely that this skill will require the same amount of time. So, let’s get started…let’s take our instruction to the next level with powerful assessments that meet student needs.