Running head: INVESTIGATING GUIDED MATHEMATICS INSTRUCTION

PROSPECTIVE TEACHERS USINGGUIDED MATH TO DIFFERENTIATE MATHEMATICSINSTRUCTION

Yvonne J. John, Ph. D

Centre for Education Programmes

The University of Trinidad and Tobago

Old Southern Main Road, Curepe

Trinidad and Tobago

Email:

1-(868)-642-8888 Ext. 29193

Stephen Joseph, Ph. D

Avril Sampson, MSc

Centre for Education Programmes

The University of Trinidad and Tobago

ABSTRACT

In Trinidad and Tobago large numbers of children found in schools are not developing the mathematical skills needed to achieve basic numeracy (Ministry of Education, Trinidad and Tobago National Test, 2013). This study examined the effect of differentiatedmath instruction training on prospective teachers’ ability to meet students’ needs. Prospective teachers placed in primary schools of Trinidad and Tobago participated in a two-week, field-teaching practice focusing on small group instruction in mathematics. The study used a convergent, mixed-method, research design aimed at triangulating a single group pretest/posttest quasi-experiment with survey and focus group responses, and reflections from the sample group of prospective teachers. Findings of the study revealed that the ability of prospective teachers to meet students’ needs in mathematics greatly improved with differentiated instruction training in guided mathematicsframeworks.

Keywords: prospective teachers, guided math

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Running head: INVESTIGATING GUIDED MATHEMATICS INSTRUCTION

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Running head: INVESTIGATING GUIDED MATHEMATICS INSTRUCTION

1. PROSPECTIVE TEACHER USINGGUIDED MATH FRAMEWORKS TO DIFFERENTIATE MATHEMATICS

Mathematics is essential to everything that children learn in school. Understanding how children learn mathematics, apply what they learn to solve problems, and how they plan and assess that knowledge daily is fundamental to meeting their needs. Creating a classroom population of students eager and readyto apply mathematical concepts to their everyday lives presents teachers with many challenges and choices. The purpose for conducting this study stemmed from specific weaknesses analyzed in student outcomes based on the Trinidad and Tobago Primary School National Test (2013), and observations of classroom practices during practicum sessions. In Trinidad and Tobago, the National Test is a standardized test administered annually to primary school students in Standard One and Three, in basic subjects of English Language Arts and Mathematics, and Standard Two and Four in Science and Social Studies (The National Test, (n.d.). The major objectives of this examination postulated by the (Ministry Of Education, n.d.) are: (1) gathering information which enables administrators at the school, district and national levels to make decisions, (2) identifying areas of the primary school system that require further investigation, (3) identifying national norms, (4) comparing students’ performance by school and educational districts and (5) tracking students’ progress through school. The National Test, (2013) report reveals that Standard Three students in 295 of 536 primary schools (55%) are not meeting benchmarks in total mathematics (Table 1). Too many children experience mathematical literacy problems.

Table1:Mathematics Performance on National Test 2013

Status / No. of Schools / % Primary schools
Failing = (< 50%) students not meeting benchmarks / 295 / 55%
Passing = (≥50%)students meeting benchmarks / 241 / 45%
Total / 536 / 100%

Moreover, in spite the fact that so many of our children are experiencing challenges in basic mathematics skills, it was observed that teachers in the primary schools of Trinidad and Tobago continue to give whole group instruction in mathematics with little or no differentiated instruction provided, particularly for the at-risk students. Overall, the statistics show that students in some primary and special schools of Trinidad and Tobago continue to fail in basic areas of mathematics such as number/number sense, measurement and money, geometry and statistics (National Test, 2013). In response to the student data and observation of methods employed by teachers, the researchers decided to conduct a study with prospective teachers pursuing studies in special needs education in differentiating math using formative assessment data to group and match instruction to meet the needs of students in the content areas of mathematics.

2. LITERATURE REVIEW

Limited research is being done concerning the role of prospective teachers’ ability to use a framework in mathematics to meet the needs of at-risk students in Trinidad and Tobago and the Caribbean. However, a review of the literature for the use of guided math has producedsome informative articles. Sammons (2006) postulates that teachers are finding it difficult to use methods they have used successfully in the past since these no longer are working for the children that they teach. The demands of the new curriculum standards (MOE, 2014) require new ways of teaching mathematics in schools. Sammons states that it is important to develop a model that offers students the opportunities to develop their mathematical skills and be able to apply that knowledge to function independently in the world of mathematics.Sammons (2006)suggests a model which comprises the following components:a classroom environment of numeracy, morning math warm-ups and calendar board activities, whole-class instruction, guided math instruction with small grops of students, math workshop, individual conferencing and an ongoing system of assessment. These components, Sammons proposes, will allow the teacher to support student’s needs.

2.1. Assessment and analysis of data

National Council for Teachers of Mathematics (NCTM), 2000) stressed the Assessment Principle in the Principle and Standards for School Mathematics.The two main ideas of the principle areassessment to enhance students’ learning, and assessment as a valuable tool for making instructional decisions.

2.2. Making instructional decisions

On-going assessment provides teachers with timely information about class and individual needs,hence effective teachers are constantly engaged in formative assessment. Van de Walle, et al., (2014) point out that (TheCouncil of Chief State School Officers(CCSSO), 2010; and NCTM, 2000) reiterate that assessment is not separate from instruction, but that it should include the critical mathematical practice and processes that occur in effective problem-based instructional approaches.

2.3 The classroom environment of numeracy

Numeracy skills are fundamental in order for children to reach their maximum potential. The Ministry of Education of Trinidad and Tobago has made raising numeracy and literacy skills a priority across the new primary schools’ curriculum.Sammons states that the creation of a classroom environment which supports numeracy enables students to build on their acquired knowledge of numbers. Van de Walle claims that the logistics, physical environment and tone of the classroom must be addresed to meet the needs of the students. He further states, that in attending to the needs of the students the seating arrangement, grouping strategies and access to materials must be considered.

2.4. Effective math instruction

What are the characteristics of effective math instruction? Research has indicated that it takes more than a good teacher, in fact, it involves good teachers, a numeracy rich classroom environment and a curriculum that has depth and breadth (Protheroe, 2007).Trinidad and Tobago. MOE curriculum guide points out that teachers should emphasize numeracy across the curriculum. In the classroom, that means making consistent connection between Math and real life situations. It also emphasizes a focus on problem solving, communication, and representation, critical thinking and reasoning. Students should be exposed to daily opportunities to read, write and speak Math (MOE, 2013).

Many teachers are moving away from the traditional, teacher-centered approach, however, it is an excellent method for presenting strategies or for making connections at the beginning of the lessons and for ongoing review of mastered skills (Sammons, 2007). (Murray & Jorgensen, 2007; Small, 2009) state that though it is challenging to plan a lesson that focuses on a target mathematical concept or skill that is suitable for whole-group instruction while meeting the needs of a variety of students, teachers should consider parellel tasks and open questions.

2.5. Principles and standards of school mathematics

The Equity Principles and Standards for School Mathematics states: “Excellence in mathematics education requires equity --- high expectations and strong support for all students. All students, regardless of their personal characteristics, backgrounds, or physical challenges must have opportunities to study--- and support to learn mathematics” (NCTM, 2000, p. 12). Teaching for equity is much more than providing children with an equal opportunity to learn mathematics, instead, it is the ability to attain equal outcomes for all students by being perceptive to their individual needs (Van de Walle, 2014). Planning, teaching and assessing students with exceptionalities, including students who are gifted pose challenges for many teachers. Baroody, (1987) points to the fact that students who struggle with math may continue to do so because they are ‘instructionally disabled’. The equity principle points to the fact that there are students who must be considered if teachers are to address and maintain equal results – high expectations while providing for individual differences (Van de Walle, 2014). This can only be achieved through small-group instruction, and frameworks such as guided math.

2.6. Guided math

Guided math according to Newton, (2013) allows teachers to address students at their instructional level so that you can take them to their potential. He reiterates that guided math allows the teacher to support learning by grouping students in small instructional groups to teach them in their zone of proximal development (Vygotsky, 1978). Newton (2013) states that the goals of guided math are for students to become proficient mathematicians who have conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and mathematical confidence. Guided math aims at getting students comfortable with numbers, operations and mathematical concepts so that they can work independently with new and different contexts. Cobb County School, (n.d.) describes guided math as an environment in which some students are given the opportunity to work independent of teacher guidance to building student’s skills, concepts and strategies through the use of teacher directed tasks and/or Math Learning Centers. The teacher pre-selects a group to observe and conference with for the purpose of assessing student growth and development, while noting areas where additional support is needed. Ideally, Guided Math should take place daily for at least 15 minutes, but as little as once per week, has a significant benefit in building student self-reliance, independence and critical thinking skills (Newton (2013).

2.6. Guided Math groups

Students should be grouped by instructional level, that is, the level at which instruction is not too easy or difficult but “just right” for students to work in their zone of proximal development. Sammons recommends that guided math groups should be homogeneous, according to performance on a variety of mathematical assessment, but should also be flexible.

2.7. ‘How To’ Differentiate Mathematics Instruction

The problem most teachers face when differentiating instruction to meet the needs of students in small-group teacher-led activity is ‘how to’ get everything done and increase student achievement (Gibson, 2008). There is no explicit guide to systematic and explicit instruction in ‘how to’ deliver differentiated instruction. In fact, it is reported that scientific research has not provided procedural models to differentiation, mainly because of the uncertainty surrounding what differentiation is and the limited research surrounding how to implement it in classrooms.

Even though there is no current standard step-by-step procedure to give teachers a guideline in order to differentiate math instruction, the consensus in the literature is that the particulars of ‘how-to' deliver that instruction should be left to the teacher, yet, there are core skills, which make up any differentiated math instruction methodology. The researchers’ position in this study was to give prospective teachers the core skills necessary to differentiate math instruction, and evaluate the success of an individual teacher's math instruction on the basis of fulfilling students' needs.

3. METHODOLOGY AND DESIGN

3.1. Purpose of the Study

The purpose of this study was to investigate whether training in guided math frameworkswill increase the ability of prospective teachers to better meet the needs of students. These prospective teachers were exposed to the primary school new curriculum prior to practicum placement in nine primary schools in Trinidad and Tobago.

3.2. Hypothesis and Research Questions

The hypothesis for this study was as follows: Prospective teachers receiving systematic and explicit training using differentiated mathematics instruction ---guided math frameworks --- will be better able to meet students’ needs in mathematics.

Additionally, the following three research questions were investigated.

  1. What are prospective teachers’ perceptionsabout training in diagnostic math assessment and analysis to meet the needs of students?
  2. What are prospective teachers’ perceptions about training in developmental math pedagogy aimed at increasing their ability to meet the needs of students?
  3. To what extent do prospective teachers understand that the instruction in guided math frameworks will improve their ability to meet the needs of students?

3.3. Population and sample

The population for the study comprised all prospective year-3 and year-4 teachers (in-service and pre-service) completing a Bachelor of Education degree in Special Needs, Early Childhood Care Education (ECCE) and Primary Education at the University of Trinidad and Tobago (UTT).

Participants for this study, 31 prospective teachers (29 females and two males), were purposively selected from a larger sample of 49 prospective teachers (46 females and three males).These participants were registered for the courses Teaching Mathematics II To Students With Mild To Moderate Disabilities, and Engaging In Classroom Practice/Enhancing And Improving Classroom Practices for Semester 2.They must also have successfully completed the courses of Teaching Mathematics I To Students With Mild To Moderate Disabilities and Deepening the Field Teaching Experience for Semester 1. Selection criteria for these participants required that they participated in a prior study on differentiating instruction varying content, process and product to meet the needs of their students based on students’ interest (Joseph & John, 2014).

3.4.Research Site

This study was conducted in nine (9) of 537 primary schools in Trinidad and Tobago. The nine primary school sites were assigned on a quota-sampling basis and contained eight ‘inclusive’ schools (students with/without mild to moderate exceptionalities) and one of the 16 special schools. The assignment was representative of the population of failing (<50% of the students meeting benchmark on the Mathematics test of the National Test) and passing schools (≥50% of the students meeting benchmark on the total Mathematics test). The site included nine (9) principals, thirty-one (31) directing teachers, one hundred and twenty-four (124) students in thirty-one (31) targeted primary classes from Infants One to Standard Three (Table 2).

Table2: School Assignment for sample group

School 1
School 2
School 3
School 4
School 5
School 6
School 7
School 8
School 9 / Percentage of students / Total Schools / # P.T
Fail (< 50%) / Pass (≥50%)
0 / 1 / 1 / 4
1 / 0 / 1 / 5
1 / 0 / 1 / 5
1 / 0 / 1 / 3
1 / 0 / 1 / 5
1 / 0 / 1 / 2
1 / 0 / 1 / 2
0 / 1 / 1 / 1
0 / 0 / 1 / 4
6 / 2 / 9 / 31

P.T = Prospective-Teachers

3.5. Research design

The researchersset out to support or refute the hypothesis, and answer the aforementioned questions, by utilizing a convergent, mixed-method design that triangulates teacher reflections and survey responses with a single-group, pretest-posttest, quasi-experiment.

3.6.Single-group, pretest-posttest, quasi-experiment

The dependent variable in this study was prospective teachers ability to meet student needs in mathematics, operationalized by three student scores in prospective teacher performance obtained from presentations/demonstration, ongoing preparation, and examined field teaching in math, triangulated with data from prospective teacher perceptions of themselves shown in surveys and reflection notes.

3.6.1.presentation/demonstration

The lecturer in practice assessed prospective teachers ability to choose, create, modify and use appropriate resources to match curriculum content being delivered in classrooms based on the choice of a teaching strategy to be demonstrated in front of peers. This assessment was based on the ability to discuss how and why the strategy was useful, and to provide justification that it was the best decision in the circumstances for meeting the needs of their children. This assessment was completed using the Demonstration of an Instructional Strategy Rubric, adapted from UTT Practicum course content, (2013), (Table 3).

Table 3: Rubic for demonstration/presentation

Outstanding [4] / The prospective teacher consistently demonstrates the accomplishment of the criteria and surpasses the knowledge, skills, disposition and/or performance skills of an initial educator
Proficient [3] / The prospective teacher adequately demonstrates the accomplishment of the criteria and meets the knowledge, skills, disposition and/or performance skills of an initial educator
Developing [2] / The prospective teacher demonstrates some accomplishment of the criteria and meets the knowledge, skills, disposition and/or performance skills of an initial educator
Beginning [1] / The prospective teacher demonstrates limited accomplishment of the criteria. There is much room for improvement on the knowledge, skills, disposition and/or performance skills of an initial educator.
Not observed [0] / The prospective teacher did not demonstrate the criteria.
OBSERVED / 0 / 1 / 2 / 3 / 4
Relevance of the strategy
  • to lesson/context in which it is used
  • to subject area
  • to learners’ level and abilities
  • theoretical underpinnings: Differentiated instruction etc

Suitability of explanation re: use in delivery
  • Diction / clarity of speaker
  • Content presented: name of strategy, purpose, targeted learners characteristics; construction; other uses etc.
  • Time period for presentation maximized
  • Benefits and challenges

Creativity re design of the strategy
  • Originality of ideas used/ Innovation
  • Selection of materials used to create resource
  • Repeatable design

Technical quality
  • Visual/tactile stimulation; size of print, etc.
  • Durability (can be reused in other lessons on other occasions, other subject areas, etc.
  • Can be used for classroom display (as a learning tool)
  • Adaptability: can be used for teacher demonstration/student discovery and manipulation; with/without teacher supervision.
  • Intricate details

Effectiveness/Overall impact
  • Aesthetically pleasing; general visual impact
  • Comprehensiveness of presentation

3.6.2.on-going preparation