Bahasa Murid Dalam Pengajaran dan Pembelajaran (P&P) Matematik

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Sinopsis

Artikel ini akan menerangkan tentang empat langkah dalam pendekatan pengajaran dan pembelajaran (P&P) matematik menggunakan Bahasa Murid. Contoh dan ilustrasi disediakan bagi membantu pemahaman anda.

 
 

Pendahuluan.

Orang dewasa selalu meniru atau menggunakan intonasi kanak-kanak bila berkomunikasi dengan mereka, Tujuan utamanya adalah untuk mudahkan berinteraksi dengan kanak-kanak berkenaan atau dengan perkataan lain kanak-kanak itu boleh memahami apa yang ingin diperkatakan oleh orang dewasa.

Perkataan seperti 'nenen', 'syusyu' dan 'mamam' selalu dimengertikan sebagai minum susu dan makan. Begitu juga dengan 'buum' boleh membawa masuk tidur dan Syyyyy... untuk membuang air kecil.

 

Pada peringkat awal, 'nenen', 'syusyu' dan 'mamam' selalu dimengertikan sebagai minum susu dan makan.

Atas dasar itu saya berpendapat adalah lebih baik seseorang guru mengajar matematik kepada murid di tahap 1 (pemulihan) menggunakan bahasa yang biasa dengan mereka. Bahasa yang difahami oleh murid itu akan memudahkan mereka mengambil bahagian dalam perbincangan dengan guru. Dengan lain perkataan, murid akan sentiasa menyertai aktiviti pembelajaran yang dijalankan oleh guru. Pada masa yang sama, guru mesti mengadakan bahan, situasi cerita yang boleh merangsang mereka bercerita dan berbincang.

Ramai pakar pendidikan berpendapat lebih baik menggunakan pengalaman sedia ada murid untuk memulakan sesuatu pengajaran dan pembelajaran yang berkesan. Bermula dengan pengalaman mereka guru boleh membimbing murid mempelajari sesuatu konsep matematik dengan baik dan berkesan.

 
     
 

Pendekatan Bahasa Murid dibahagikan kepada EMPAT langkah:

#Langkah 1: Bahasa Murid

Bahasa Murid ialah bahasa seharian yang biasa digunakan oleh setiap murid untuk menerangkan sesuatu yang mereka lihat dalam cerita atau situasi yang kita berikan. Situasi yang dibina akan boleh merangsang murid bercakap dalam bahasa mereka sendiri. Galakkan mereka bercakap dan mereka-reka cerita berdasarkan situasi. Beri mereka masa yang cukup untuk tujuan ini. Antara aktiviti yang boleh merangsang mereka untuk turut serta dalam perbincangan adalah seperti berikut:

  • Gunakan gambar yang menarik minat mereka. Umpamanya gambar budak-budak bermain di padang.
  • Adakan cerita. Adakan ilustrasi melalui gambar/grafik yang besar.
  • Main peranan berdasarkan tema yang ditetapkan guru.
  • Bermain dengan bahan manipulatif.
  • Cerita yang direka sendiri oleh murid.

#Langkah 2: Bahasa Bahan.

Pada peringkat ini, bahasa dan istilah yang digunakan adalah berkisar disekitar situasi, cerita yang diberikan oleh guru matematik. Di sinilah sepatutnya konsep matematik dimulakan. Konsep tolak dalam matematik umpamanya dikenalkan sebagai...asingkan, jatuhkan, hilang, sudah dimakan, pecah, terbang dan sebagainya. Manakala konsep tambah dalam matematik pula dimengertikan sebagai....datang lagi, dapat lagi dan disatukan. Sambil menggunakan bahasa yang sesuai seperti;

"Apa akan jadi jika semua bola ini dihimpunkan sekali"

Galakkan mereka menggunakan bahan manipulatif untuk mewakilkan aksi, situasi, keadaan bahan dalam cerita mereka. Gunakan teknik menyoal yang baik untuk merangsang mereka ke arah konsep matematik yang ditetapkan dalam objektif pengajaran dan pembelajaran. Sambil merujuk kepada gambar, situasi dan cerita, guru haruslah mencuba membuat soalan berkaitan dengan konsep tambah yang dipelajari untuk hari berkenaan. Terpulanglah kepada kreativiti seseorang guru matematik itu untuk membuat soalan-soalan matematik yang boleh membawa kepada sesuatu konsep matematik yang ingin disampaikan.

Ilustrasi 1: Apakah cerita matematik yang murid boleh buat tentang gambar di atas?

Sebagai sifat semulajadi seorang kanak-kanak yang suka bertanding, mereka akan berebut untuk bercerita berdasarkan pengalaman masing-masing. Guru harus menerima dan bersetuju dengan cerita mereka. Di antara perkataan yang akan kita dengar ialah 'kupu-kupu', 'rama-rama', 'katak hijau', 'katak kelabu','katak besar', 'pokok', 'jambatan', 'rumah'' dan mungkin murid nyatakan dalam dalam bahasa Inggeris seperti 'frogs' dan 'butterflies'.

Dalam situasi di atas, guru boleh membuat perbezaan bilangan katak hijau dengan katak kelabu, bilangan kupu-kupu dan lain-lain lagi. Kemahiran operasi matematik iaitu menambah dan menolak boleh dipelajari serentak.

#Langkah 3: Bahasa Matematik.

Selepas murid mengambil bahagian dengan aktif dalam perbincangan menggunakan Bahasa Murid, guru bolehlah membimbing murid menggunakan istilah atau bahasa matematik yang betul. Umpamanya, jumlah katak kelabu dengan katak hijau itu boleh dikatakan sebagai:

"Tiga katak hijau tambah dengan empat katak kelabu bersamaan dengan tujuh"

Begitu juga jika mencari perbezaan. Jumlah katak ialah tujuh dan tiga berwarna hijau dikatakan sebagai tujuh tolak tiga berbaki empat. Pada peringkat ini, guru dengan murid masih lagi secara lisan dan memanilupasi bahan konkrit yang ada bersama mereka.

#Langkah 4: Simbol (Perwakilan)

Langkah berikutnya ialah guru menggunakan perwakilan berbentuk bahan manipulatif untuk mewakilkan situasi seperti di atas. Contoh:

3 ekor katak hijau diwakilkan dengan dan ditambah dengan 4 ekor katak kelabu yang diwakilkan dengan . Jumlahnya ialah tujuh (7).

Situasi ini boleh dituliskan dengan ringkas seperti  3 + 4 = 7.

Setelah melalui EMPAT langkah tersebut, adalah diharapkan murid dapat menguasai sesuatu konsep matematik berdasarkan kemahiran mereka sendiri. Membina kefahaman melalui perincangan yang dibimbing oleh guru secara terancang dan mengamalkan prinsip pembelajaran matematik yang bermakna, berguna, seronok dan mencabar.

Langkah-langkah ini juga boleh membiasakan murid dengan masalah bercerita dan boleh membantu mereka memahami masalah bercerita dengan mudah. Kebiasaan itu nanti akan menolong mereka mahir untuk memetik maklumat dan data yang relevan untuk membuat pengiraan dan mendapat jawapan.

Hasil Kaji selidik Masalah Matematik di Malaysia

Berdasarkan kajian masalah matematik yang dibuat oleh Clements pada tahun 1970 dan 1983 di Pulau Pinang, didapati bahawa murid Tingkatan 1 di Malaysia tidak menghadapi masalah mengira yang serius. Namun demikian, didapati ada masalah yang nyata bila membaca, memahami, dan membuat trasformasi yang betul dalam penyelesaian masalah matematik. Adalah diharapkan, dengan pendekatan yang telah dibincangkan di dalam artikel ini iaitu menggunakan bahasa murid dalam pengajaran dan pembelajaran matematik sedikit sebanyak dapat membantu menyelesaikan masalah tersebut.

Beberapa orang penyelidik telah menggunakan kaedah 'Newman Error Analysis' untuk mengetahui bidang kelemahan murid dalam pendidikan matematik. Clements, dengan bantuan guru-guru yang berkursus di RESCAM telah membuat kajian tentang pengaruh bahasa dalam murid menjawab soalan yang berbentuk cerita. Semua guru bersetuju bahawa ayat yang digunakan adalah mudah difahami dan masalah yang dikemukakan juga tidaklah kompleks atau susah.

Sebanyak 40 soalan diberikan kepada 18 orang murid di tingkatan 1. Ujian ini dijalankan pada bulan Februari yang memberikan gambaran kepada kita bahawa kemahiran sedia ada murid adalah setakat kemahiran dan pengetahuan di tahun 6 sahaja.

Temubual dijalankan keatas semua murid sebaik sahaja keputusan ujian itu diperolehi. Di bawah adalah statistik yang diperolehi daripada temubual tersebut.

Murid Skor Membaca Pemahaman Transformasi K/proses Cuai
1 28 - 3 2 - 7
2 28 - 6 2 2 1
3 27 - 5 3 2 1
4 26 - 4 5 - 5
5 23 - 5 2 6 4
6 21 - 14 2 3 -
7 21 - 9 5 - 5
8 17 - 12 6 4 1
9 17 - 8 11 4 -
10 17 - 9 5 - 9
11 16 - 1 10 1 2
12 16 - 12 9 3 -
13 15 - 14 8 2 -
14 14 - 5 11 - 10
15 13 - 13 10 - 4
16 13 - 20 - 1 6
17 13 - 8 5 2 12
18 13 - 22 3 2 -
JUMLAH %            

Daripada data di atas, jelas kepada kita bahawa peratus yang tinggi dilihat pada masalah memahami soalan dan membuat transformasi daripada ayat matematik kepada operasi yang betul. Manakala hanya 18 peratus sahaja yang melibatkan kemahiran proses pengiraan.

Dengan itu, langkah lebih awal perlu dilakukan bagi melatih murid-murid sejak dibangku sekolah rendah lagi  mengenai kemahiran memahami soalan dan membuat transformasi daripada ayat matematik kepada operasi yang betul. Gunakanlah kaedah dan pendekatan Bahasa Murid yang telah dibincangkan dalam P&P matematik anda mulai sekarang. Semoga berjaya!

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Students’ Perception On Teaching And Learning Mathematics In English

Abstract

 

Students use language to communicate and to understand mathematics concepts. Language influences students’ thought by molding perception and structuring ideas. However, in recent years, science and mathematics in lower secondary subjects have been taught in English. This may create problems in learning these subjects. Therefore, this research was carried out to gather information and to get the clearer picture on what have happened regarding the teaching and learning science and mathematics in schools. The research instrument was a set of 16-item questionnaire that was designed to identify students’ perception on teaching and learning mathematics. The respondents consist of 279 lower secondary school students from three schools in rural area of Johor, Malaysia. The research found out that the respondents agreed to the importance of English Language in everyday life as well as career opportunity however they felt that learning science and mathematics was very difficult and demanding. This is due to the lack of ability in understanding of the subject matters and the instruction language. The result also showed that learning science is more difficult than learning mathematics. Finally, the findings revealed that there are challenges for the science and mathematics teachers to work wisely in order to overcome students’ learning difficulties and to promote effective learning among students.

 

Introduction

 

In learning mathematics, students frequently encounter mathematics problems involving calculations, understanding of concepts, principles and mathematical relationship with others subjects. Study on engineering students’ perceptions in learning mathematics at Universiti Teknologi Malaysia and some schools in Johor has been carried out and the results showed that mathematics subject was one of the interesting and important subject to learn but it was difficult one to learn (Aziz, 1992). The reasons why mathematics subject are difficult to learn is that the concepts in mathematics are abstract and difficult to understand, and also the students have alternative meaning of certain mathematical words before any mathematics teaching takes place. According to Ihejieto (1995), there are factors other than academic standing on the students’ side which could explain the performance trend. These factors are;

i.                    Students’ dislike for mathematics that may stem from psychological incidences such as fear, endurance, perseverance and associated factors.

ii.                   The mathematics curriculum may have not much relevance to real life situation.

iii.                 Mathematics teachers were not interested in the subject and did not help their students by way of catering for individual differences.

iv.                iv. Other resources material such as text books seemed lacking in both in school and at home.

 

Since the mathematical knowledge and skills can only be delivered through language therefore this study will only focus on students’ understanding in mathematics that experience English medium of instruction. This is necessary because language plays an important role in communication, thinking and is a tool for exchanging ideas and concepts between individuals (Aziz, 2003). However, recently science and mathematics have been taught in English. This may create unfamiliarity to those concepts taught to them and may slow down or retard their science and mathematics learning. Sudden change to the current science and mathematic medium of instruction may also cause cultural shock to the students. Normally, students’ conceptions of prior experience and knowledge influence students’ learning in science and mathematics. Students prior knowledge and experience can be amazingly tenacious and resistance to change (Gilbert, 1982). It is therefore essential for this research to explore student’s viewpoints and perceptions on teaching and learning mathematics in English in order to gather information and to get the clearer picture on what have happening in schools.

 

RESEARCH PROBLEMS

 

Language influences students’ thought by molding perception and structuring ideas. In learning mathematics students use language to communicate and to understand mathematical facts, concepts, principles and problem solving. However these knowledge and skills are new, unfamiliar and different from the language used in everyday life (Osborne, et al., 1983). This may cause a problem in the understanding of the mathematics concepts. To investigate this problem, the following questions are raised:

  1. Do the students have problems in learning mathematics in English?

  2. What are the factors that contribute to the learning problems?

  3. Is that any relationship between the factors that contribute to the learning problems?

 

RESEARCH METHODOLOGY

 

A survey was conducted in several secondary schools in rural area of one district in Johor to gather information regarding students’ perception on teaching and learning mathematics in English. The instrument used for this study was a set of questionnaire that comprised of two parts. Part one elicited information on the students’ background. Part two of the questionnaire comprised sixteen items regarding students perception on teaching and learning science and mathematic in English. The questionnaire was administered to 279 form one and two students of several secondary schools. The respondents were given 40 minutes to complete the questionnaire. The data were analyzed statistically by using SPSSPC software program. The statistical analyses used are frequency, percentage, reliability index and correlation coefficient. The reliability index (Cronbach α) of the study for all the 279 respondents was 0.70. For the qualitative analysis, written responses of the students were analysed by listing the problems encountered by each students in his explanation.

 

RESULTS OF THE STUDY

 

Malay language previously has been used as a medium of instruction for learning science and mathematics in schools. However with the changes of a medium of instruction to English, the study revealed that some students do have problems in learning mathematics. For the purpose of this paper the findings on students’ performance and background that may contribute to the problems in learning mathematics, students’ understanding of English language used in teaching mathematics and the correlations among factors that related to the learning problems will be discussed. The general picture will be presented first, and this will be followed by more detailed discussion of data.

 

1. Students background and problem in learning mathematics in English.

 

The findings of this study indicated that students have encountered problems in understanding of the teachers’ teaching in English language. Table 1 showed that students performance in English language can be categorized as satisfactory because only 9.4% of the respondents have an A grade in UPSR examination while most of them (40%) are in a C grade group. It is also very clear that the distribution patterns of the science, mathematics and English results in Primary School Assessment Test (UPSR) are differently distributed. However, the most interesting part in this finding is the drastic drop of science monthly test results when compared to UPSR science result, where 19.9 respondents obtained an A grade in UPSR but only 4.6% of the respondents obtained an A grade in their monthly test. This is probably due to the science contents which are more advanced than before or the respondents do not understand the lesson which is conducted in English.

 

Table 1: Students’ result of UPSR and Monthly Test in English, Mathematics and Science subjects in percentage.

 

2. Students interest in Science, Mathematics and English subjects.

 

Interest closely related to motivation, and motivation is one the learning factors that influences and stimulates students to learn (Bloom, 1976). As a result motivation leads someone to learn effectively and successfully. Table 2 shows that mathematics is one of the most interesting subjects to learn compared to science and English subjects, where 55.2% of the respondents rated mathematics as high interesting subject to learn. This finding seems to be consistent with the mathematics’ monthly test result as illustrated in Table 1 where high percentage of respondent scores grade A in monthly mathematics test. Table 1 and 2 are also indicated that mathematics is less influenced by the used of English language as a medium of instruction compared to science subject.

 

Table 2: The distribution of students’ interest in English, Mathematics and Science.

 

 

3. Understanding of science and mathematics in English language.

 

According to the Psychology Dictionary, understand is defined as the process of becoming aware of the relationship between thing or their meaning (Evans, 1978). To learn effectively, someone has to understand what he/she had learned. Nevertheless, the study has found that the respondents were really having problems in learning science and mathematics but the problems were more obvious in learning science. This was possibly due to the nature of science that comprises a lot of factors, concepts and principles as well as problem solving processes in its content. When English language has been used as a medium of instruction in schools, the proficiency of English language is a must for respondents to understand what their teacher’s teach. Unfortunately, the findings showed that students’ competency in English are at low level as only 6.5% agreed that they could speak English very well and fluently (Item S1), majority of them could not speak very well. The findings also revealed that majority of the respondents have not taken part in many learning activities, such as questions and answers activities with their teachers and fellow friends (Item S2 and S8), teacher teaching activities (Item S5), and to speak English with teacher and friend in classroom (Item S4 and S6), and these are among several reasons why they could not improve their English language and so forth related to their problems in understanding science and mathematics in English.

 

Table 3: Students’ opinion of understanding science and mathematics in English language.

 

 

The respondents were also likely influenced by their daily spoken language as majority of them will think in Malay language before giving the answer in English (Item S8). This could be the reason why their teachers do not fully teach science and mathematics in English (Item S5).

 

4. Students attitude towards the usage of English language

 

Table 4: Students’ opinion of English usage in everyday life

 

 

 

Language is an important part of social culture (Lawton, 1989). Learning process will be effective if teachers know how to make use and describe appropriate examples of everyday life phenomena in their teaching. Simple and appropriate level of language should be used to explain the everyday life phenomena which related to scientific and mathematical concepts, in order to motivate students to understand better. However, as indicated in Table 4 revealed that majority of the respondents either hardly or seldom use English language at home (Item S3) and they used to speak their mother tongue language at home. This was supported by the facts that they like to read the Malay subtitle when watching television of English program to understand better (Item S13) and they also like to read the Malay story books rather than English story books (Item S14). From the above examples, it is clear that the respondents prefer to use Malay language as a medium of instruction. These practices may become obstacles to the respondents in learning and understanding the contents of science and mathematics in English language. Students attitude towards an academic discipline are recognized as being significant in determining success in learning. Table 5 indicates a statement of students’ motivation with regards to the important of English language in learning and in everyday life. Majority of the students felt that English language is very important for their future careers (Item S12), however they still preferred to learn science and mathematics in Malay language (Item S9) as majority of the respondents agreed to the statement that learning science and mathematics in Malay language is easier and more likely to be understood (Item S16). The choice of Malay as a medium of instruction in learning science probably due to their own everyday language that make them easier to understand better of the subjects. In spite of preferring to learn science and mathematics in Malay, they showed positive attitude towards the important of English language as majority of the respondents (83.9% of Item S15) agreed to the statement that they will refer to dictionary if they do not understand English words or terms.

 

Table 5: Students’ felt needs for English

 

 

Correlations among students’ test performance of English, Mathematics and Science subjects

 

Table 6: Correlation of students examination results for English, Mathematics and Science subjects

 

 

The results in Table 6 show that the correlations between UPSR English language and English, Mathematics and Science monthly test are 0.62, 0.48 and 0.35 respectively, while the correlations between English monthly test results and Mathematics and Science monthly test are 0.52 and 0.42 respectively. These results seem to indicate that respondents who were high in English were more likely to achieve high scores in their English, Mathematics and Science tests. In other words, the findings reveal that English language is one of several factors that contribute to the respondents’ performance of science and mathematics.

 

CONCLUSION

 

The study has established the following:

i.                    The students considered English as an important subject to learn and it was useful for everyday communications and as a tool for learning science and mathematics.

ii.                  The students felt that learning science and mathematics in English were difficult, however to learn science was more difficult compared to learn mathematics in English

iii.                 The study showed that there was a significant correlation between UPSR English result and other subjects monthly test results, such as English, Mathematics and Science.

iv.                Science subject has been found to be more affected by the implementing of teaching science and mathematics in English.

 

The results of this study described what have happening in the schools regarding the implementation of English language in learning science and mathematics. Students have encountered language problems as well as contents’ problems and to overcome these problems they need help and guidance from the teachers. Emphasized should be given more on building up students proficiency in English before they could learn science and mathematics effectively.

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Understanding Math Learning Problems

What are they?

Students who experience significant problems learning and applying mathematics manifest their math learning problems in a variety of ways. Research indicates that there are a number of reasons these students experience difficulty learning mathematics (Mercer, Jordan, & Miller, 1996; Mercer, Lane, Jordan, Allsopp, & Eisele, 1996; Mercer & Mercer, 1998; Miller & Mercer, 1997.) The following list includes these research-based math disability characteristics.

Characteristics of Students Who Have Learning Problems

Learned Helplessness - Students who experience continuous failure in math expect to fail. Their lack of confidence compels them to rely on assistance from others to complete tasks such as worksheets. Assistance that only helps the student "get through" the current set of problems or tasks and does not include re-teaching the concept/skill, only reinforces the student's belief that he cannot learn math.


Passive Learners - Students who have learning problems often are not "active" learners. They do not actively make connections between what they already know and what they are presently learning. When presented with a problem-solving situation, they do not employ strategies or activate prior knowledge to solve the problem. For example, students may learn that 8 x 4 = 32, but when presented with 8 x 5 = ___, they do not actively connect the process of multiplication to that of repeated addition. They do not think to add eight more to thirty-two in order to solve the problem. Students that have learning problems often believe that students who are successful in math just know the answers. They do not understand that students who are successful in math are good at employing strategies to solve problems.


Memory Problems - Memory deficits play a significant role in these students' math learning problems. Memory problems are most evident when students demonstrate difficulty remembering their basic addition, subtraction, multiplication, & division facts. Memory deficits also play a significant role when students are solving multi-step problems and when problem-solving situations require the use of particular problem solving strategies. A common misconception about the memory problems of these students is that it is an information storage problem; that somehow, these students just never get it stored properly. This belief probably arises because one day the student can do a math task but then the next day they can't. Teachers then re-teach the skill only to have the same experience repeated. In contrast to an information storage problem, these memory deficits are often a result of an information retrieval problem. For these students, instruction should include teaching students strategies for accessing and retrieving the information they have stored.


Attention Problems - Math requires a great deal of attention, particularly when multiple steps are involved in the problem solving process. During instruction, students who have attention problems often "miss" important pieces of information. Without these important pieces of information, students have difficulty trying to implement the problem solving process they have just learned. For example, when learning long division, students may miss the "subtract" step in the "divide, multiply, subtract, bring down" long division process. Without subtracting in the proper place, the student will be unable to solve long division problems accurately. Additionally, these students may be unable to focus on the important features that make a mathematical concept distinct. For example, when teaching geometric shapes, these students may attend to features not relevant to identifying shapes. Instead of counting the number of sides to distinguish triangles from rectangles, the student may focus on size or color. Using visual, auditory, tactile (touch), and kinesthetic (movement) cues to highlight the relevant features of a concept is helpful for these students.


Cognitive/Metacognitive Thinking Deficits - Metacognition has to do with students' ability to monitor their learning: 1.) Evaluating whether they are learning; 2.) Employing strategies when needed; 3.) Knowing whether a strategy is successful; and, 4.) Making changes when needed. These are essential skills for any problem solving situation. Because math is problem solving, students who are not metacognitively adept will have great difficulty being successful with mathematics. These students need to be explicitly taught how to be metacognitive learners. Teachers who model this process, who teach students problem solving strategies, who reinforce students' use of these strategies, and who teach students to organize themselves so they can access strategies, will help students who have metacognitive deficits become metacognitive learners.


Low Level of Academic Achievement - Students who experience math failure often lack basic math skills. Because it takes students with math disabilities a longer time to process visual and auditory information than typical learners, they often never have enough time or opportunity to master the foundational concepts/skills that make learning higher level mathematics possible. Providing these students many opportunities to respond to math tasks and providing these practice opportunities in a variety of ways is essential if these students are to ever master the math concepts/skills we teach. Additionally, teachers need to plan periodic review and practice of concepts/skills that students have previously mastered.


Math Anxiety - These students often approach math with trepidation. Because math is difficult for them, "math time" is often an anxiety-ridden experience. The best cure for math anxiety is success. Providing success starts first with the teacher. By understanding why students are having the difficulties they are having, we are less inclined to place "blame" on the students for their lack of math success. These students already feel they are not capable. The attitude with which we approach these students can be a crucial first step in rectifying the math problems they are having. Providing these students with non-threatening, risk-free opportunities to learn and practice math skills is greatly encouraged. Celebrating both small and great advances is also important. Last, if we provide instruction that is effective for these students, we will help them learn math, thereby helping them to experience the success they deserve.

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