Effective teaching is defined as “teaching that is in accord with sound
principles, and which promote student learning and enhances the personal and
social development of students” (Cole & Chan, 1987, pp.303). Key points relating to effective teaching are the ability to communicate effectively,
ask effective questions, thoughtfully plan and prepare lessons, use varying
combinations of instructional modes, motivate students and use constructivist
teaching methods. These hallmarks of effective teaching will therefore be discussed
with reference to the Melcombe Primary School Year 5 Maths lesson video (Evans & Atteshlis, 2008) and Maths
Lesson Plan (appendix A).
The
basis of all effective teaching is efficient communication as most aspects of
the teacher’s role depend upon skills in communicating competently (Cole & Chan,
1987). Communicating efficiently is an important aspect of effective teaching (Cole
& Chan, 1987). The teacher in the
video (Evans & Atteshlis, 2008) demonstrated this by emphasising
important and relevant aspects of the grid method and presented coherent and
meaningful messages. The sequence of her dialogue allowed students to interpret
the intended meaning correctly. It was evident that the teacher focussed on
efficient communication skills (Cole & Chan, 1987). Competent teaching
involves developing “qualities and skills
that enhance efficient communication” (Cole & Chan, 1987, pp.26). The
teacher in the video (Evans & Atteshlis, 2008)
had personal qualities and attitudes that enhanced positive relationships with
the students. She demonstrated patience and listened carefully to student
responses. She spoke to students in language they could understand. Precise
directions were given during demonstration, and guided practice activities.
Non-verbal communication such as physical movement, hand gestures and facial
expression were effectively used when managing the classroom (Cole & Chan,
1987). Effective teachers are, “competent at formulating, encoding,
transmitting and interpreting messages” (Cole & Chan, 1987, pp.41). This
was evident in the video (Evans & Atteshlis, 2008)
where the teacher skilfully presented the lesson and listened to her students
actively. The teacher anticipated class
reactions and presented the subject matter suited to the abilities of the
students with sensitive and empathic attitude (Cole & Chan, 1987). Highly
developed communication skills and personal qualities are essential
characteristics of successful teachers (Cole & Chan, 1987).
Careful
planning and preparation allow for efficient organisation and presentation of
lessons (Cole & Chan, 1987). The foundations of effective teaching are
thoughtful, systematic planning of goals that are productive to learning
experiences (Killen, 2007). According to Killen (2007), lessons cannot be
successful if teachers do not thoroughly plan and integrate lessons into the
medium and long-term plans as the syllabus or curriculum objectives
suggest. In preparing the lesson plan
(appendix A), the Australian Curriculum, Assessment and
Reporting Authority (ACARA) objectives were taken into account. Carefully
prepared lessons help the teacher take into account individual student needs
and differences in abilities (Killen, 2007). It was evident that the teacher in
the video (Evans & Atteshlis, 2008) took individual student needs and
differences in abilities into account when planning. Not only did the teacher
divide the class into ability groups but also planned for multiplication
problems of varying difficulties. Killen (2007) states, that imaginative
planning ensures lessons are motivating, interesting and relevant to students. The
lesson plan (appendix A), demonstrates this imaginative planning with a video (Atkinson & Driscoll,
1995) at the start of the lesson, aimed to engage and motivate the students
into focussing on the lesson ahead. The use of iPad application Grid Mult
(SUMS, n.d.), is another example of imaginative planning as it is motivating,
interesting and relevant to students. In Mathematics, effective teaching
requires teachers to plan for explicit teaching procedures where the aim is to
master knowledge or learn a skill which can be taught in a step-by-step manner
(Rosenshine & Stevens, 1986). The video (Evans & Atteshlis, 2008) and
lesson plan (appendix A) show explicit teaching procedures that are effective
to teaching as identified by Rosenshine and Stevens (1986). Planning questions
to engage students at many cognitive levels based on the revised Blooms
taxonomy is another characteristic essential to effective teaching. Planning
questions in advance based on Blooms taxonomy, give students an opportunity to
think creatively and imaginatively (South Australia Department of Education,
1987). The characteristics of effective teaching are therefore, thoughtful,
imaginative and systematic planning where teachers take into consideration
curriculum goals and objectives. They have effective procedures in planning and
preparation and plan questions at various cognitive levels.
The
ability to ask questions in all phases of the lesson is a vital teaching skill,
and is the key to effective teaching (Fetherston, 2007). The teacher needs to
ask key questions so that students are able to formulate an answer in order to
demonstrate the objectives of the lesson (Fetherston, 2007). These questions
provide the teacher with good feedback about the effectiveness of the lesson
(Fetherston, 2007). For instance, in the video (Evans & Atteshlis, 2008),
after guided-practice activities, the teacher asked questions relating to
lining up of digits, placing tens and units in columns, the trick about zero
and partitioning of numbers. All of these questions were related to the
objectives, thus providing the teacher with feedback about the lesson effectiveness.
Enabling questions led students into thinking about a topic from previous
lessons so that there was a smooth flow from the previous lesson (Fetherston,
2007). At the start of the lesson in the video (Evans & Atteshlis, 2008),
not only were key questions asked, but students also discussed amongst
themselves, the laws used when multiplying and dividing. This was the basis to
move on to the main body of the lesson. According to Fetherston (2007),
planning of questions should have a combination of high and low order questions.
The created lesson plan (appendix A) begins with high and low order questions
not only to introduce students to the topic but also to stimulate and challenge
the more advanced students in high quality talk (Fetherston, 2007). Learning is
enhanced when a teacher uses ‘good questions where students learn by answering
and where the teacher, learns from student’s answers (Sullivan, 1997). These
types of questions make students and teachers aware if understanding of a topic
is not complete (Sullivan, 1997). Student achievement is at a better level when
the frequency of the questions asked by teachers is high (Cole & Chan,
1987). Not only does this stimulate communication, but it also focusses student
attention, evaluates their knowledge and understanding, stimulates particular
kinds of thinking and controls student social behaviour (Cole & Chan,
1987). Effective teaching is the ability to ask questions not only to stimulate
and challenge the students but also to ensure that genuine learning occurs
(Fetherston, 2007).
Effective
teaching involves the teacher using various instructional modes such as
practice drills and direct instruction that incorporates technology, so that
student interest and abilities are accommodated (Marsh, 2004). Identifying
different types of instructional modes not only helps the teacher to focus upon
whom the lesson is for but also helps in identifying what the role of the
teacher and learner are (Whitton et al., 2010). A
wide variety of instructional modes are essential for effective teaching where
the emphasis on lesson activity should be teacher directed and student centred
(Marsh, 2004). Practice drills, is a mode of instruction involving repetition.
In mathematics, drills are necessary to master and perfect skills (Marsh,
2004). Drills
can be enjoyable especially with technological aids. Mathematics is one of the
many subjects where practice drills can be effectively used that students
enjoy, provided they are short, varied, encouraging and students understand the
reason for drills (Marsh, 2004). The lesson plan (appendix A) incorporates drills
by making use of iPad application, Grid Mult (SUMS, n.d.) as it provides students with
opportunities to practise the skills learnt in a fun way. Direct instruction is
used in the lesson plan (appendix A) to promote step-by-step process of grid
method multiplication. The purpose is to help students learn the content of the
lesson in an efficient way. These have been incorporated into the lesson plan
by explanation, demonstration, guided practice (worksheet, appendix B),
feedback and practice using the iPad. Lecturing is another instructional mode
where the teacher presents orally (Marsh, 2004). This method of instructional
mode was effectively used in the video (Evans & Atteshlis, 2008)
as it included use of technology such as interactive whiteboard and Power-Point
presentation. The teacher had good lecture characteristics such as encouraging
students to ask questions, limiting the time of the lecture, stating the key
points at the start, and allowing sufficient breaks so that it did not lead to
student boredom (Marsh, 2004). There are many instructional strategies described
by various authors and it is an essential characteristic of effective teaching
to accommodate student interests and abilities incorporating technology (Marsh,
2004).
In
motivating students effectively, teachers regulate and deliver “information that is important to students” (Cole
& Chan, 1987, pp.10). Motivational
goals influence students in the quality of learning (Whitton et al., 2000).
They engage in learning for different goals and purposes, therefore, teachers
should become knowledgeable in methods of motivation to be effective (Whitton et al., 2010).
Intrinsic motivation is when “learning comes entirely from performing a particular task” (Marsh, 2004). In the
video (Evans & Atteshlis, 2008), the teacher intrinsically
motivated students by not only making the lesson and activity interesting, but
also enjoyable. It was evident that the green group were strongly motivated “to work on challenging tasks” on their
own with confidence and showed a strong interest in mathematics (Marsh, 2004,
pp. 36). Extrinsic
motivation is when students are rewarded for a particular behaviour (Marsh,
2004). In the video (Evans & Atteshlis, 2008),
the teacher showed evidence of this form of motivation by awarding points to
students at the end of the lesson. There is conflicting research on tangible
extrinsic rewards but it is likely that the teacher, in this video (Evans &
Atteshlis, 2008), believes in the positive effects
of extrinsic rewards such as the research of Cameron (2001), Hidi and
Harackiewicz (2000). Following general principles for motivating students such
as those suggested by Marsh (2000) will avoid brining about low levels of
motivation. The lesson plan (appendix A) takes into consideration the list of
principles for motivating students by creating interest with use of
entertaining video (Atkinson
& Driscoll, 1995) at the beginning of the lesson (Whitton et al., 2010), creating goals and objectives
which are achievable, creating clear outcomes that students will be informed
about and finally creating challenging and varied learning activities that
maintains interest. Effective teachers are knowledgeable in methods of
motivation and follow general principles in motivating students to provide and
present information using constructivist approaches that will enable the
student to learn.
A
dominant teaching paradigm in Australia is using constructivist approaches to
learning and using constructivist teaching strategies (Fetherston, 2007). One
constructivist teaching strategy is to link new material to what the student
already knows (Fetherston, 2007). In the video (Evans & Atteshlis, 2008),
the teacher takes a constructivist approach by asking students questions on
what they already know about multiplying and then linking this information to
the lesson on grid multiplication. Utilising the advantages of group work such
as collaborative and cooperative learning is another constructivist approach to
learning, which is an essential characteristic of effective teaching (Fetherston,
2007). Both constructivist strategies are effectively utilised in the video (Evans &
Atteshlis, 2008) and lesson plan (appendix A). Students
are grouped and throughout the lesson, participate in discussion (chatterbox)
where the teacher either deals with the group or scaffold’s individual learner
understanding. Establishing these groups allows students to work effectively in
the classroom (Fetherston, 2007). Clements and Battisa (1990) state, that when
a teacher demands students to
use set mathematical procedures, students are seriously curtailed in making
sense of the activity. It further states, that students mimic the procedures by
rote that makes little sense to them (Clements & Battisa, 1990). In the
video (Evans & Atteshlis, 2008), the teacher, in prior lessons,
taught the formal method of multiplication followed by grid multiplication of
two-digits by one digit. The lesson plan (appendix A), follows on from this
lesson to show how to multiply two-digits by two-digits Future lessons could be
followed on from the created lesson plan, showing students how to multiply
using other informal methods and then finally planning a lesson where students
can discover their own method of working, reflecting on previous lessons. These
various methods of multiplication can be shown to the students so they can learn
to weave a connection for themselves (Palmer, 1998). They can be guided to choose a method that works
best for them without demanding them
to use a particular method (Clements & Battisa, 1990). Allowing students to
construct their own knowledge, taking advantage of group work both cooperative
and collaborative, and using teaching strategies that do not demand a
particular method of working are just a few constructivist approaches that is
the dominant teaching approach in Australia (Fetherston, 2007).
The
characteristics of effective teaching are being able to communicate effectively
so that coherent and meaningful messages are presented, combined with personal
qualities that enhance communication. Imaginative planning and preparing of
thoughtful lessons, considering ACARA objectives and taking into account
individual students needs and differences are essential to effective teaching.
It was emphasised that key to effective teaching is the ability to ask
stimulating and challenging questions in order for genuine learning to occur.
Drills and direct teaching are some instructional modes that may incorporate
technology that are characteristics of effective teaching. The principles of motivation
were discussed and finally, constructivist approaches and teaching strategies
were discussed as the characteristics of effective teaching.
REFERENCES
Atkinson, R., Driscoll, R. (Writers), & Birkin, J.
(Director). (1995). Mr. Bean: Goodnight Mr. Bean [Motion Picture].
United Kingdom. Retrieved from http://www.youtube.com/watch?v=FmbmNp1RDCE
The Australian Curriculum. (2012). Retrieved from Australian Curriculum Assessment and
Reporting Authority (ACARA): http://www.australiancurriculum.edu.au/Elements/ACMNA100Cameron,
J. (2001). Negative effects of reward on instrinsic motivation - a limited
phenomenon. Review of Educational Research, 71(1), 29-42.
Chan, Peter G. Cole and Lorna K.S. (1987). Teaching
Principles and Practice. New York: Prentice Hall.
Clements, D.H. & Battisa, M.T. (1990). Constructivist
learning and teaching. Arithmetic Teacher, 38(1).
Crouch, R. H. (1996). School Sport and the Law. The
Practising Administrator, 3.
Education, S. A. (1987). Listening and Speaking - K-7
teacher notes. 53-60.
Evans, P., & Atteshlis, C. (Producers). (MMVIII). Uncut
Classrooms: Melcombe Primary School, Year 5, Mathsl [Motion Picture].
Fetherston, T. (2007). Becoming an effective teacher.
South Melbourne: Cengage Learning.
Hidi, S., & Harackiewicz, J. M. (2000). Motivating
the academically unmotivated: A critical issue for the 21st century. Review
of Educational Research, 70(2), 151-80.
Killen, R. (2007). Effective Teaching Strategies.
Melbourne: Thomson Social Science Press.
Marsh, C. (2008). Becoming a teacher: knowledge skills
and issues. Australia: Pearson Education .
Marsh, C. J. (2004). Becoming a Teacher (3 ed.).
Frenchs Forest, NSW: Pearson Education Australia.
Palmer, P. J. (1998). The Courage to Teach: Exploring
the inner landscape of a teacher's life. San Francisco, California:
Jossey-Bass.
Rosenshine, B. and Stevens, R. (1986). Teaching
Functions in M.C. Wittrock (ed.), Handbook of research on teaching. New
York: Macmillan.
SUMS. (n.d.). Grid Mult Version 1.1. Retrieved
from http://itunes.apple.com
Whitton, D., Barker, K., Nosworthy, Sinclair, C.,
Nanlohy, P. (2010). Learning for teaching: Teaching for learning.
Melbourne: Cengage Learning.
APPENDIX
A: MATHS LESSON PLAN (Melcombe Primary School)
Learning
Area
|
Year
|
Time/Session
|
Date
|
Mathematics
|
5
|
9am-10am
|
26/10/12
|
Topic/Lesson Title:
Grid Method Multiplication – multiplying
two-digits by two-digits
PREPARATION
|
Follow
up lesson for
|
Melcombe Primary School, Year 5, Maths (Evans & Atteshlis, 2008)
|
Rationale
/ Goal
|
·
To use an
informal method to multiply two-digits by two-digits.
·
Solve problems
involving multiplication of two-digit numbers using mental, written
strategies, and digital technology (ACARA, 2012, ACMNA 100).
·
Skills and
concepts targeted are multiplication, division, addition, inverse operations,
place values and partitioning of numbers.
·
Students should
be able to multiply two-digits by two-digits using the grid method.
|
Learning
area links as per Australian Curriculum
|
Australian Curriculum, Assessment and Reporting
Authority (ACARA)
Mathematics – Year 5 – Number and Algebra
“Solve problems involving multiplication of large
numbers by one- or two-digit numbers using efficient mental, written
strategies and appropriate digital technologies (ACMNA100)” (ACARA,
2012).
|
Children’s
prior knowledge/experience
|
The year 5 students at Melcombe Primary School:
·
Know their times
table from previous year levels and previous lessons this year.
·
Know how to
perform addition and understand meaning of inverse operations.
·
Have prior
knowledge of place values and partitioning of numbers.
·
Have prior
knowledge of multiplying two-digits by one-digit using the grid method.
|
Objectives
|
At the end of the lesson, the
students will be able to, multiply two-digits by two-digits, using the grid
method and:
·
Demonstrate
neatness and accuracy in lining up of digits (place value).
·
Remember the
trick about the zero (remembering to put the zero/s back).
·
Partition numbers
accurately by splitting the numbers into tens and units.
Students will demonstrate
learning by working collaboratively in groups.
Students will complete
worksheets, with number and/or word problems, involving two-digit by
two-digit multiplication, using the grid method, and with 90% or higher
accuracy.
Students will use iPad, Grid
Mult (SUMS, n.d.) application, to solve multiplication problems involving two-digits by
two digits without the use of writing aids.
|
Preparation
/ Resources (Consumables &
Non-consumables)
|
·
Teacher Aide or
adult helper
·
5 iPads fully
charged with Grid Mult Application (SUMS, n.d.)
·
Interactive
whiteboard /1 teacher iPad connected to interactive whiteboard
·
PPT presentation of
complete lesson
·
Whiteboard markers
for teacher
·
Mini whiteboards,
whiteboard markers, and erasers for each student
·
Colour coded worksheets
for each group (Appendix B)
·
Copy of times
table for each student
·
Number fans for each student
Students to be divided into
mixed-ability groups:
Yellow (low-medium ability) Red (low-high ability) Green
(medium-high ability)
The room layout to be
re-configured. Carpet area: where all students can clearly see the
interactive whiteboard. Desks to be arranged so that groups can complete worksheets.
Worksheets to be placed on desks for individual students. Copy of the times
table for each student.
|
PROCEDURE
|
Introduction/Motivation
|
|
Show the class the above video to engage the
children in learning about multiplication. At the end of the video, ask
students to chat amongst themselves (chatterbox time) to discuss:
1. What was Mr Bean doing?
2. What does it have to do with our lesson today?
3. Do you think you can teach Mr Bean how to count
the sheep on the poster without using a calculator?
4. What function did Mr Bean press on his
calculator, between the two numbers? Plus, minus, times, or divide symbol?
Gain students attention by clapping a rhythm to
focus student’s attention for the main body of the lesson.
Quiz:
Mental Math problems (times tables). Students use number fans to
display answer to teacher.
|
Main
Body of the lesson
|
1. Display and read out aloud the objective of
lesson on the interactive whiteboard. (To use the grid method to multiply
two-digits by two-digits)
Chatterbox: What can you tell me about the Grid
method?
Teacher: Discuss answers with whole class.
2. Display and read out aloud the Grid method
success criteria on the interactive whiteboard. (Stated in objectives)
General
Capabilities: Literacy
“Invite
students who see any words whose meaning they don’t know to come up and
overwrite the word(s) concerned” (Brooks & Grundy, 1998, pp.22). Explain
meanings of these words.
Chatterbox: What can you tell me about the lining
up of the digits? What happens if you don’t line up the digits? What can you
tell me about the trick of the zero? What can you tell me about the partition
of the numbers?
Teacher: Discuss answers with whole class.
Main Body of the lesson continue …
3. Explain to students
(step-by-step) how to set out their work using two-digits multiplied by
two-digits. For example: 24x36 =_____ (Use interactive whiteboard to display
PPT of example Math problem)
Step 1: Show how the numbers
are placed on the grid, lined and partitioned in tens, and units.
Step 2: Multiply numbers
ignoring the zero and then remembering to add the zero back.
Step 3: Add the numbers in
each column.
Step 4. Add the two numbers
in both columns to get final answer.
4. Demonstrate another
example as in step 3 followed by a short “Brain Break” activity.
5. Adult helpers to hand out
mini whiteboards, markers and erasers to students. Students to arrange
themselves into their groups as previous lesson (yellow, red and green). Give
the following multiplication problems:
Yellow:
21x11
Red: 51x16 Green: 96x48
6. Ask class to put their boards and pens down and
look at the interactive whiteboard. Each group’s multiplication problem to be
solved using the steps shown earlier. Emphasize neatness of grid. Follow this
by a short “Brain Break” activity.
7. Display key teaching points on the whiteboard
and discuss with class. (See dot points in objectives)
GUIDED
PRACTICE ACTIVITIES:
8. Send red group
to their tables to do multiplication problems on the iPad using Grid Mult (SUMS, n.d.) application.
Send yellow
group to their tables to do worksheets that are ready on their tables with a
copy each of the times tables.
Yellow group to
use iPad when they finish their worksheet and red
group to commence worksheets.
Green group to
remain on the floor with teacher to do more challenging problems involving
three-digits multiplied by two-digits. Demonstrate 235x64. Complete
worksheets (green sheet).
10. Provide evaluative and/or non-evaluative
feedback to red and yellow groups. Move around the room to
provide intrinsic feedback, correct and quiz students on the
steps.
11. Once red
group finishes their worksheets, ask the yellow
and red groups to move to carpet area
while green group goes to their desks
and works on the iPad. Discuss with the group on the carpet area how they
feel about today’s lesson and revise steps.
|
Closure/
Student reflection
|
Green group to return to the carpet area. All students
participate in quick revision of random times -tables. Ask students the
following questions:
1. What
have you learnt in today’s lesson that you did not know before?
2. How can
you prove that you have learnt something?
3. How
will you use it in another subject or somewhere?
4. Do you
think you can help Mr Bean to multiply without using a calculator?
|
Assessment
|
Assessment of student
achievement – check worksheet answers
General evaluation of lesson:
·
Have objectives
been achieved?
·
Were students
interested?
·
Did the students
require a lot of individual help on the worksheet?
·
Did the students
benefit from using the iPad? Were there any issues?
|
REFERENCES – LESSON PLAN
The Australian Curriculum. (2012). Retrieved from Australian Curriculum Assessment and Reporting
Authority (ACARA): http://www.australiancurriculum.edu.au/Elements/ACMNA100
Atkinson, R., Driscoll, R. (Writers), & Birkin, J.
(Director). (1995). Mr. Bean: Goodnight Mr. Bean [Motion Picture].
United Kingdom. Retrieved from http://www.youtube.com/watch?v=FmbmNp1RDCE
Brooks, A., & Grundy, P. (1998). Beginning to Write:
writing activities for elementary and intermediate learners. United
Kingdom: Cambridge University Press.
Evans, P., & Atteshlis, C. (Producers). (MMVIII). Uncut
Classrooms: Melcombe Primary School, Year 5, Maths. Retrieved from http://www.schoolsworld.tv/node/2051?terms=644
Sheep Image Source: http://www.fun-with-pictures.com/image-files/sheep.gif
SUMS. (n.d.). Grid Mult Version 1.1. Retrieved from
http://itunes.apple.com
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