What exactly are the causes of

students’ learning difficulties

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— An in-depth discussion on “reducing students’ burdens while

improving the quality of education” (One)

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         The ongoing educational reform is themed “reducing students’ burdens while improving the quality of education”. As can be seen, it is imperative to have a correct understanding of “reducing students’ burdens”. What does “overburdened” mean? Being overburdened is actually one of the learning difficulties. So why do students have difficulty learning? Any misunderstanding in this could lead to the misaligned implementation of the education reform. Therefore, the question as to what the root causes of students’ learning difficulties are well worth an in-depth discussion. 

 

         To my mind, the causes of students’ learning difficulties lie in instructors and the suitability of classroom teaching. 

 

         This is because a masterly instructor would clarify each concept in classroom teaching to allow every student thoroughly understand each new piece of knowledge. He will also find the aptest examples and analyze and teach them for students to master new knowledge in the shortest time possible. He will make an appropriate amount of well-targeted homework so that students are able to consolidate what they’ve learned during the day. Such a teacher will also combine textbook knowledge to be taught with prior knowledge, and in the meantime, properly bring in the knowledge that will be learned in the future in an ingenious way as an extension, thereby arousing students’ interest and provoking them to leverage their imagination to understand new knowledge scientifically and actively carry out their learning activities. 

 

         Do students learning in such an environment still need to go to catch-up classes? Will they still be overwhelmed by assignments that seem impossible to finish? Therefore, the cause of students’ learning burdens is instructors, which is manifested in the important stage of classroom teaching. Importance should be attached to scientific teaching. 

 

         A Chinese high school educational expert in mathematics once visited the Mathematics Department of Teachers College, Columbia University, and gave a lecture. This expert had decades’ worth of experience in helping students get full marks in math in the College Entrance Exam and get admitted into top-notch universities. In his lecture based on the ongoing reform in mathematics teaching at the time and his own experience in math teaching, he mentioned that the key to solving students’ learning difficulties and helping them achieve exceptional academic performance lies in the fulfillment of teachers’ leading role in education and teaching. 

 

         Here, allow me to present a detailed summary of the expert’s lecture. 

 

         Take mathematics, for example. Today, many students enter high school gates with high-strung nerves - the 45-minute classes are filled with teachers’ instructions and constant notetaking. The result is filling one notebook after another. Some teachers even hold a competition over students’ notebooks and praise those who have kept the most stunning notebooks. All equations, theorems, and definitions must be memorized. Students stand in queues in teachers’ offices waiting to be checked and those who cannot perfectly recite them will be penalized, usually in the form of writing them down repeatedly. Year after year, this has been the routine of our mathematics class. They also take such a routine for mathematics class for granted. They attribute poor test results to a failure to take good notes or recite equations. Amid endless lecturing, homework correcting, recitation checking, catch-up classes, repeated tests, and training, they feel that the classes that they have to attend and the exercises they must finish will never come to an end. School leaders also emphasize the diligence of teachers and always pick up the most hard-working faculty members as candidates for commendation. The cycle simply repeats itself year after year. 

 

         Do students need to take notes in math classes? Is queuing to recite mathematical theorems and equations necessary? Isn’t such teaching and learning problematic? 

 

         How much is high school math knowledge put all together? From sets, functions, inequalities, and triangles to permutation and combination, binomial theorem to preliminary statistics, this is a limited scope of knowledge. 

 

         How many definitions, equations, and theorems are there altogether in high school math? This is also a limited scope of knowledge. 

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         How many knowledge points and mathematical methodologies have to be mastered in high school math? This is still a limited scope of knowledge. 

 

         The questions as to which examples should be adopted to clarify each piece of content, knowledge point, or methodology in high school math and which exercises should be assigned in order for them to consolidate these knowledge points can also be a limited concept. 

 

         Teachers are reflecting over and summarizing these questions in their practices. 

 

         The senior academic year of high school starts from September 1 to May 30 of the next year (before the college entrance exam). So, the question goes: How many class hours are there altogether? How many should be assigned to the dual-foundation revision for the first round of revision of different chapters? How many go to the second round of revision for comprehensive enhancement? And how many go to the final home stretch stage? The answers are obviously of another limited scope. 

 

         According to the syllabus of high school mathematics, controlling the difficulty and quantity of the first cycle is necessary. The same also is true for the control of those of the second and final cycles. This way, both the vertical sequence based on knowledge characteristics and the horizontal layers of difficulty coefficients are well arranged, making the entire mathematical revision process in the senior year properly organized and easy to navigate. This is something that we can accomplish. 

 

         Questions like how many example questions are needed to clarify a knowledge point should be brought to the table for discussion among teachers. Both teachers and students can also validate their answers to these questions in practice and analyze further problems from the perspectives of quality and quantity in order to reach a consensus. The quantity of example questions and the mastery of knowledge points are not in a monotone-increasing relationship. 

 

         Based on my (the educator's) years of experience in high school mathematical teaching, I compiled three books, namely, 100 revision Notes for High School Mathematics, 30 Sets of Revision Test Papers for High School Mathematics, and 20 Lectures on Revision of High School Mathematics, to steer students at the senior year through their mathematics revision. 

 

         The first book is dedicated to the first round of cyclic revision, allowing students to get a full glimpse of the general knowledge that they have to master from the book. In return, I give instructions about each key content and knowledge point based on the example questions presented in the book. The question as to whether these example questions are enough to clarify a knowledge point is open for discussion. Notably, all example questions in the book are carefully examined and selected and can stand practical tests. The solution to each example question is optimal and logically presented in a standardized format, and in a novel way. 

 

         The second and third books are for the second round and final home stretch stages. Unit test papers cover all knowledge points of a unit. The weight and difficulty levels of different content are determined based on the syllabus. Students’ test results adequately tell how well they have mastered certain knowledge. The third book, namely, lectures, highlights the most important knowledge, methodologies, and question types in high school math in the form of special topics. It represents a complement to the first book of teaching notes. What has already been emphasized in the Teaching Notes is omitted in the Special Lectures. The compilation logic of the first book means that it cannot address all content. Then the third book comes to serve as a complement as well as enhancement and consolidation. For example, knowledge about abstract functions and fixed points cannot be explained in a chapter-wise order in the first book. It is more appropriate to place it in the third book. Other examples are symmetric and classification discussion problems. These mathematical ideologies involve algebraic, triangular, and geometrical knowledge, and thus are very suitable to place in the third book as special topics. However, as mathematical induction is addressed in detail in a chapter in the first book, the third book simply omits it. 

 

         New lessons and revisions about high school mathematics should be quantified to establish a functional relationship between time and progress. Ideally, on teachers’ computers, calendar dates and the numbers of teaching notes should be matched right from the school start date on September 1 to the eve of the College Entrance Examination. Such a teaching approach keeps the school, teachers, and students (including parents) informed of the progress of teaching during the entire senior year. The result is that they will have peace of mind without being panicked or psychologically burdened. 

 

         For high school mathematics, we come up with the slogan of “refined compilation, teaching, and exercise”. Of course, these are dynamic processes. No one can be confident enough to say which book is the best. On the one hand, a book in itself may not be the best. Teachers consult and negotiate with each other to modify their approaches when problems arise in order to achieve improvement. On the other hand, what seems to be the best may cease to be so as textbook requirements and the syllabus change over time. Hence, our instructional book must also change to address these needs. 

 

         With respect to teaching for the freshman and sophomore years, especially for high-performing students, we should stress A&E (Accelerate & Enrichment): 1. we should provide appropriately more advanced content; 2. the content should be more deepened, heightened, or extended based on the newly released policies about the College Entrance Exam and school textbooks. However, it should be noted that teaching basic concepts should be highlighted and each knowledge point should be adequately clarified for students to master them and skillfully apply them. This is a necessary condition for getting a grade higher than 140 or even the full mark, as well as a guarantee for students to step into higher knowledge fields after they go to college. 

 

         So, if we want to evaluate whether such a teaching approach is scientific, whether students have learning difficulties or whether they are overburdened, we simply need to put all teaching notes onto the table and go through them page by page, followed by discussion among all of us. Nothing is clearer than that given the fact that all evidence is on the table. Our daily teaching activities are in strict accordance with the teaching notes we have formulated. 

 

         Hence, the regulatory administrations of education, teachers, students, and parents should all be aware that classroom teaching is the main battlefield for the reform of education and teaching. Here, teachers’ quality is the key. To improve the quality of education, solve students’ learning difficulties and reduce their learning burdens, the first battle we should fight is to ensure the quality of classroom teaching and achieve great results in stages of “refined compilation, teaching, and exercise”. 

 

         The special lecture provided by this Chinese mathematical educator is of great implication for us. Qualitatively and quantitatively analyzing our courses, textbooks, disciplinary content, and knowledge points and ensuring our teaching notes are matched with teaching dates are all effective methodologies for scientific teaching. Teachers are the key to successful educational reforms. With these methodologies in mind, we are strongly confident about the prospects of mathematical teaching in the future. 

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