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Showing posts with the label Math Education

Philippines' Poor Performance in Math and Science Is Much More Than Just A Language Problem

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With the dismal performance of students in the Philippines in the 2019 TIMSS, it is timely to reflect on why basic education in the Philippines is failing. Surely,  there are factors  that correlate with low scores in math and science. These are parental education, number of books available at home, availability of computers and internet, and the general attitude of students toward mathematics. These factors indeed require an Herculean effort to overcome for any educational system. Developing skills in math and science requires support from home, but this cannot be used as an excuse for the failure of a school system. One must not disregard, for instance, the fact that teachers in the Philippines themselves do not do well in exams in mathematics . There is likewise a tendency to find fault in the testing itself. Language is one excuse. When reasons are too obvious, it is not really helpful to look further. When students from the Philippines took the exam in their language...

Fourth Graders in the Philippines Score Last in Math and Science

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When this blog started back in 2012, I noted that second year high school students in the Philippines had the lowest scores in both Math and Science in both 1999 and 2003 TIMSS. The results for the 2019 TIMSS are now available. This time, fourth grade students from the Philippines participated. These students are clearly products of the new K to 12 curriculum and the scores are actually worse this time. These data suggest that the new curriculum has not addressed what really plagues Philippine basic education. The DepEd K+12 curriculum introduced in 2012 only exacerbates the problems of education in the Philippines. Above copied from Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: https://timssandpirls.bc.edu/timss2019/international-results/ The drop in scores is quite substantial. The black curve is for ma...

A Lesson on Doubling

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Exponential growth is characterized by a rate that is increasing with time. One can use a doubling time to describe such growth. For example, now that it is spring time, one can observe how fast weeds grow. If the doubling time in the area that weeds cover is 3 days, one can imagine that starting with a square foot of weed coverage, in the next three days, the weed will cover 2 square feet. In six days, it will be 4, and in nine days, it will be 8 square feet. And in just 3 weeks, that is, 21 days, the weed area would have doubled 7 times. By that time, 128 square feet will be covered by weeds. That will be a lot of work on my weed whacker. The death rate from COVID-19 behaves similarly. And right now, the doubling time for the number of COVID-19 deaths in the US is 3 days. Above copied from the New York Times Currently, the number of deaths in the US due to the novel corona virus is just a little under 6,000. If we assume that the doubling time remains constant for the next thr...

Lessons on Coronavirus

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While Princeton University has moved to virtual instruction up till April 5, Sarah Schwartz shares in EducationWeek  lesson plans for science, math, and media literacy from K-12 schools. One lesson graphs world data on Coronavirus  from the World Health Organization. Another looks at possible sparks of prejudice against Asians because of the outbreak and why such a reaction has no scientific basis. And a third one encourages not just to repeat what is seen in social media, but actually evaluate whether these are simply exaggerated or real. Above copied from EducationWeek The current outbreak is a real threat but during these times, reliable information is a must. There are a lot of numbers involved so the data do provide an opportunity to construct math lessons. Take, for instance the following graph that explains why slowing down an epidemic is helpful. The above illustrates how nonpharmaceutical interventions (frequent washing of hands, staying home if one is no...

We Voted For ONE Fairfax

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Elections unfortunately do not solve problems. What we do after the poll matters. However, we do bring what we value to the ballot box and it is crystal clear that yesterday, we, at Fairfax county, voted for equity, diversity and inclusiveness. The paths to these values are not easy. These values will challenge some of our strongly held preconceived notions. For this reason, it is imperative that we listen to what evidence tells us. The Washington Post  states that the Democratic supported candidates winning yesterday pushes the Fairfax County School Board further to the left. This is not about left versus right. The winners of yesterday's school board elections rejected elitism, intolerance and division. Our new school board embraces "education for all". Our new district representative, Ricardy Anderson, for instance, wrote this last night, "...as we work to close the achievement gap that cripples our most vulnerable." Above copied from the Washington Post...

A Standardized Exam That May Actually Be Useful In Answering Who Could Teach Algebra

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My son is taking algebra in middle school. A lot of schools across the United States provide an opportunity for students who have demonstrated good performance in elementary mathematics to enroll in an algebra course in their middle school years. These students can furnish a good set of data to evaluate what teacher characteristics correlate with student performance in algebra. A study with this goal has been recently published by Marzano Research in conjunction with the National Center for Education Evaluation and Regional Assistance. The study looks at all middle school students who have taken algebra in the year 2015 in the state of Missouri. The data surprisingly include a substantial number of underrepresented groups as well as economically disadvantaged students. And across all students, there is one characteristic of a teacher that correlates with strong student performance in algebra. Here is the shocker: It is how much algebra a teacher knows. It is not the level of certifica...

How Do Children Learn Math

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Similar to constructing a house that starts with a foundation, the mathematical skills and knowledge of a sixth grader are influenced by what this sixth grader knew or learned during preschool and the early elementary years. Grade six pupils in the Philippines average less than 35% in the 2017 National Achievement Test. With this poor performance, it is useful to examine the relationship, if there is one, between early math knowledge in kindergarten and first grade, and later math achievement at the end of elementary school. Such a relationship, called a "math trajectory", can be useful in pinpointing which items in early math are highly predictive of math performance in sixth grade. Bethany Rittle-Johnson and coworkers have recently mapped a "math trajectory" for low-income children by following the progress in math of over 500 children in Tennessee from ages 4 to 11. Since these children come from a disadvantaged background, their path in math is likely to be sim...

Wake Up! DepEd, Philippine Schools Are Failing

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While some activists are bickering about the removal of Filipino subjects as required courses from higher education and the secretary of education Leonor Briones says "While were picking up on Science and Technology, we should not forget sports, culture, and history", we are totally missing the fact that basic education in the Philippines has recently taken a nosedive because of DepEd's K to 12 curriculum. National Achievement Test scores especially in mathematics and science have dropped drastically to 37.30% and 30.94%, respectively. These scores are not even half the passing score in these tests. The Grade 6 scores should be alarming especially when compared to years prior to the new curriculum. The dramatic drop occurs across all subjects, with marked deterioration in mathematics and science. This shows that the spiral curriculum is not working. When students do not reach grade level in these subjects, the spiral only becomes a "broken spiral". It...

Teaching Math and the Plasticity of the Brain

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Jo Boaler and her student, Tanya Lamar, recently made the following statement on Time magazine :  "A number of different studies have shown that when students are given the freedom to think in ways that make sense to them, learning disabilities are no longer a barrier to mathematical achievement. Yet many teachers have not been trained to teach in this way." This is quite a lofty statement and yet, it is difficult to find research supporting this generalization. Accepting this statement actually means that the only reason why students with disabilities are not doing well in math is the teacher. There are correct and wrong answers in mathematics and in the sciences, there are fruitful and unproductive approaches to understanding nature. For this reason, both math and science require a combination of procedural fluency and conceptual understanding. Take for instance the addition of fractions. Without the correct procedure and an understanding of fractions, one may simply ...

Inclusive Education

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I am starting this post with two quotes. The first one comes from 92 governments and 25 international organizations. This is part of the Salamanca statement : "We believe and proclaim that every child has a fundamental right to education , and must be given the opportunity to achieve and maintain an acceptable level of learning." This is inspiring. The second one comes from a former principal, Brian Butler: "...this process of measuring students based on how far they are from the norm and then sorting and labeling into bins of “gifted, high, low, special” only produce ways of seeing and acting that discriminate and privilege some students in the expense of others...." And Brian Butler is correct when he adds, "I actually don’t blame parents as much as I blame our profession because many of us are ok with sorting and selecting and we reinforce this belief." This sorting is not only unfair but is likewise ineffective based on evidence from research. As schoo...

Should We Encourage Young Children to Use Their Fingers When Doing Math?

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I was recently reminded of an article written by Boaler and Chen a couple of years ago on why math teachers should encourage their young students to use their fingers while I was browsing through Facebook.  These authors were apparently drawing their conclusion from a study published in the journal Frontiers in Psychology    by Berteletti and Booth. Unfortunately, this article is an excellent example of how the public can be misinformed by not reading properly the research article. In fact, one sentence in the summary of the research article should have forced Boaler and Chen to be more thoughtful before they write scientific findings for public consumption. Here is the sentence: "Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area." And here is the graph: Above copied from Frontiers in Psychology What is shown above is how much a certain region in the brain is activated, specifica...

Achievement Gaps in Elementary Mathematics

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Children from low income families do poorly in standardized math exams. Children who are either Hispanic or Black in the United States also do poorly compared to Asian Americans and Whites. There is an achievement gap that can be traced to race and socioeconomic status. The  Integration Project at the Center for New York City Affairs  has now provided us a tool to see these gaps for its 220,000 pupils in grades 3-5 in one graph: Courtesy of the New School’s Center for New York City Affairs On the vertical scale of the axis are the scores in the 2016 State math test (a score of 3 means the student is performing at grade level), and on the horizontal scale are the estimated income of the student's family. We see mostly purple and orange (Asians and Whites) with both high math scores and high family income. Blacks and Hispanics, represented by yellow and green circles are mostly in the lower left side of the graph characterized by low scores and low family income. Students...

Those Who Can, Should Teach

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Although factors outside the classroom greatly influence basic education, inside the classroom, the teacher still plays a major role. Improving basic education therefore entails better teacher preparation. Asking the question what makes a better teacher is therefore important in addressing the present challenges schools face. With this in mind, the following quote posted in MindShift  and the Hechinger Report  from Yoon Jeon Kim, a research scientist at the MIT Teaching Systems Lab, deserves our attention. At the heart of the Teaching Systems Lab is the Woodrow Wilson Academy of Teaching and Learning where scientists and engineers are trained to become educators in their field. The academy clearly works on the principle that excellence in teaching comes from content knowledge, as stated in of its web pages . Your STEM content knowledge is what will make you an excellent teacher   The WW Academy only focuses on the preparation of STEM teachers. We recognize the ...

How Do We Produce Innovators

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Innovation is important for progress. To be competitive, we need to become more efficient and make what we produce more valued. Breakthroughs are primarily driven by individuals who can innovate. But how exactly can a society increase its number of innovators. Researchers at the Equality of Opportunity Project have examined the lives of about a million inventors in the United States of America to tease out the necessary ingredients for a country to produce innovators. They find that inventors are more likely to come from those who score high in third grade math and from wealthy families. Above copied from Bell et al. (2017). Who Becomes an Inventor in America?The Importance of Exposure to Innovation. The graph above reminds us of what mathematician Alfred North Whitehead said in The Aims of Education, and other essays : "…inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. ‘Necessity is the mother of invention’ is a silly prov...

The Children Are in School, But Are They Learning?

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There remains the serious concern that about 60 million children in the world are out of school . Both former and current secretaries of education in the Philippines have raised the importance of addressing out-of-school youth. There is, however, an equally serious plague in basic education. " More than 617 million children and adolescents are not achieving minimum proficiency levels (MPLs) in reading and mathematics, according to new estimates from the UNESCO Institute for Statistics (UIS). " That is 6 out of 10 children who are in school and yet, are not learning. And in every region of the world, most children who are not learning are actually in school and not out of school. Above copied from UNESCO's Fact Sheet No. 46, September 2017, UIS/FS/2017/ED/46 There are about 75 million children from Eastern and South-Eastern Asia who fail to reach proficiency levels in math and reading. More than sixty percent of children in school in this region fail in math and re...

Deeper Learning Through Worked Examples

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Nowadays, one can search in YouTube  to find how a specific do-it-yourself task is done. From fixing appliances to minor renovations, homeowners need not learn by trial and error, saving money and time, and avoiding costly mistakes and grief. Learning through worked examples likewise demands a lower cognitive load than inquiry but objections against this learning method remain. One common complaint is that students only learn superficially through worked examples. Worked examples can indeed appear as mere recipes that one can simply follow without real understanding.  Thus, when facing another task that is not exactly identical to the one illustrated, a transfer of knowledge often fails. Learning through worked examples, however, can drive deeper learning, but this requires proper implementation. Showing someones how a task is done is effective in learning that specific task. Providing worked examples, that is, demonstrating to students how a particular problem is solved, co...

No More Algebra?

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Math is beautiful. Algebra will help you with developing critical thinking skills. You will use it in the future. These are some reasons often provided to justfy making algebra as a required course. One can say the same thing about art. Art is likewise beautiful. You may likewise use what you learn in an art course in your job. Besides, our planet "earth" is simply "eh" without "art". However, there may be a slight difference between art and algebra. Students find algebra as a major hindrance to obtaining higher education. In community colleges, passing algebra has become a barrier to graduation. Removing algebra as a required course in community colleges has recently gained momentum in Calufornia. Jude Thaddeus Socrates, a professor of mathematics at Pasadein posted the following on Facebook : Above copied from Facebook But before arriving quickly at such a conclusion, we may need to pause. First, the challenges of algebra in both high school a...