Math's BIG problem

Raise bar of Grade 4 Numeracy Mastery from paltry 50%

Use incentives to woo top teachers to inner-city, rural schools

Tamika Benjamin, Guest Columnist

Governments worldwide, in recognition of the new mathematics- and
science-driven age in which we all live and must compete, have taken
critical steps to review their mathematics education programmes to
ensure that their citizens are able to participate in, and contribute
to, national growth and development.

The decision of the previous
minister of education, Andrew Holness, to make the Grade Four Numeracy
Test a nationally administered test and publish the results is one which
must be applauded, as it has played a significant role in putting
mathematics education at the primary level back in focus in Jamaica. The
level of attention the subject matter has received as a result of the
publication of the 2011 Grade Four Numeracy Test results is, therefore,
not surprising.

The data show that while we have seen some
improvement in the performance of our students, the average Jamaican
primary-school student continues to struggle with critical but basic
mathematics ideas.

The Grade Four Numeracy Test is administered in
the last term of each school year to students registered in private and
public primary educational institutions across the island. According to
the Ministry of Education (MOE), in 2011, 45,654 students sat the test
with 49.2 per cent (22,469) attaining overall mastery - i.e., being able
to master all three of the combined curriculum strands. These are:

Number (number representation and operation)

Geometry and measurement

Algebra and statistics

Students
deemed to have attained 'almost mastery' (29 per cent) would have
mastered one or two of these strands, and students attaining
'non-mastery' (21.8 per cent) would have failed to master any of the
strands. To attain mastery of any of the strands, students would need to
attain at least 50 per cent of the available marks for items relevant
to the strand.

A closer look at the data presents several grounds for concern:

78.9 per cent of private-school students were able to attain mastery, compared with only 45.2 per cent of public-school students.

23.3
per cent of public-school students were classified as 'non- mastery',
compared with only 4.6 per cent of private-school students.

74
(nine per cent) of the 790 public schools had less than 20 per cent of
their students attaining mastery, with 19 of these schools attaining 0
per cent mastery.

Only 33 (four per cent) primary schools were able to attain levels of mastery exceeding 80 per cent of their grade-four cohort.

poor most vulnerable

A
review of the data suggests that our inner-city and deep-rural schools
are most vulnerable to significantly low levels of performance. Consider
the data in Region 1, for example: 47 schools were placed in Tiers 1 or
2 (see Table 1). Of this number, 64 per cent (30) are located in
inner-city communities and 23 per cent (11) are located in deep-rural
communities. This trend has serious implications for our nation, on the
social, educational and economic fronts.

Having closely examined
the data generated by the Ministry of Education (MOE), I believe that
issues relating to the manner in which student performance is evaluated
and reported require some consideration, interrogation and action. From a
professional standpoint, it is my opinion that the 50 per cent mark
established for mastery is a very low standard (a viewpoint shared by
other mathematics educators, curriculum and assessment specialists who
were consulted).

However, having examined such instruments and
systems in other educational jurisdictions, this approach is not
particularly unique. It must be noted that in some of these instances,
policy decisions were eventually taken to raise the bar as one of the
measures implemented to improve student-attainment levels, as it was
found that students deemed to have mastered at the stated levels were
not able to compete in other jurisdictions.

Raising the bar was
one step taken to stem complacency and ensure that students were not
only able to pass the test, but had indeed acquired the level of
knowledge needed to successfully apply mathematical ideas to the
solution of problems.

In our context, the reality is that students
whose mastery levels are between 50 and 65 per cent - maybe even as
high as 70 per cent - will face challenges learning more complex
concepts if the gaps in their learning are not identified and addressed
at the earliest time. This raises valid concerns about classifying their
performance as at the mastery level.

If the MOE chooses to keep
its cut score/pass mark at the current level, I would recommend that
serious consideration be given to taking two critical steps to adjust
the reporting format - particularly if the primary purpose for
administering the test is to be satisfied - '... to provide a profile of
individual students for targeted interventions ... .' (MOE, 2012)

redefine mastery bands

The
first recommendation in this regard is that the mastery band be divided
into smaller bands, qualifying the level of mastery attained and
outlining the level of additional support or remediation that the
student will require so that he/she is able to progress to the next
educational level successfully.

A proposal for consideration is
outlined in Table 2. Here, the actual level of mastery is outlined, and
the actions of the school are proposed. In addition to making these
adjustments, it is also being recommended that critical steps be taken
to ensure that schools receive the data in a timely manner so that
intervention can be implemented in the shortest possible time, improving
the chances of its impact being meaningful and successful.

Taking
this reporting approach will also lead to the elimination of the need
to categorise student performance as overall mastery, an approach which
is unreliable. Currently, overall mastery is attained when a student is
able to master all three of the combined bands. This approach is not a
reliable one, since to master a combined band, a student must just
attain 50 per cent of the available marks for the combined band.
Therefore, a student could master one of the strands in the combination
but still be determined to have mastered the combined band.

Consider
the data presented in Table 3 and outlined for the number strands here.
While 58.2 per cent of students attained mastery in number
representation and 45.3 per cent for number operation, significantly
more students - 68.5 per cent - were deemed to have mastered the
combined number strand. In future, individual strands should be
considered on their own merit and the overall score used to determine
the level of mastery. This will give a more accurate national picture of
the performance of our children.

In addition to making these
necessary adjustments to the reporting system for the Grade Four
Numeracy Test, I am also recommending that serious consideration be
given to implementing some additional strategic activities aimed at
producing sustained improvements in student performance in the medium
and long terms.

training where necessary

Identify and
provide additional training for primary-level teachers who can function
with mathematics specialists at the local primary-school level - taking
responsibility for the management and delivery of the primary
mathematics curriculum. This is not a proposal that, if properly
implemented, should see an increase in the number of teachers employed,
but redeployment may be necessary. In this instance, priority should be
given to those performing at Tiers 1 and 2. To qualify, these teachers
should display a sound understanding of mathematics content (as assessed
through a specially designed test) before they are allowed to
participate in professional development activities designed to develop
their pedagogical content knowledge (PCK) and equip them with the
knowledge, skills and competences that they will need to take on the
task.

Training of these individuals should be outsourced to
established teacher-education institutions across the island and should
be guided by a standardised curriculum designed to equip the specialists
according to international standards. Serious consideration should be
given to compensating these individuals through a special allowance -
particularly those who will be employed in inner-city and rural schools.

Bodies
such as the National Council of Teachers of Mathematics and the
Association of Mathematics Teacher Educators have recognised the
significant role that persons trained to function as mathematics
specialists have played, and can play, in improving student performance
in mathematics at the primary level of education systems worldwide.

Establish
a National Comprehensive Numeracy Policy which would outline standards
for teacher education and the teaching and learning of mathematics at
the primary and secondary levels. Standards should:

Address minimum mathematics contact hours;

Describe the methodology to be employed in teaching mathematics;

Address quality of intake (designed to increase minimum requirement for entry to primary programmes over time);

Mandate the administration of diagnostic testing on entry and the use of results to address content gaps and misconceptions;

Outline
the philosophy and structure of the programme design with particular
focus on the knowledge base for teaching, which should be developed
during the programme - PCK - knowledge of content, pedagogy appropriate
to content and context and knowledge of the curriculum;

Provide
opportunities for student teachers to identify and confront their
beliefs about, and attitudes towards, the teaching and learning of
mathematics.

By addressing teacher education through
accountability-driven policy, we have the potential to break the current
cycle of underperformance which is being fuelled by the fact that our
teacher-education institutions receive student teachers with significant
content gaps and misconceptions. With more effective teachers entering
the classroom equipped to contribute to the sound mathematics education
of future generations, certainly within the next five to 10 years we
should begin to see incremental improvements in student performance.

Review
the primary curriculum, and in so doing rationalise the objectives and
eliminate those developed at grade seven and eight. Our primary
mathematics curriculum contains several concepts and ideas that are
often deemed too advanced for students in the age group and which, as a
result, require more time for students to master.

In
rationalising these anomalies, teachers should have additional time to
effectively explore and develop critical foundation concepts by engaging
students in discussions and activities which are aimed at facilitating
the development of their problem-solving and critical-thinking skills.

These strategies must be implemented and supported with adequate accountability systems.

We
must work with a great sense of urgency. We have lost too much time.
Our children and our future are depending on the actions we take today.

Dr
Tamika Benjamin is director of the Caribbean Centre of Excellence in
Mathematics Teaching. Email feedback to columns@gleanerjm.com and
tamikabenjamin@hotmail.com.

Table 1 - School Performance Bands by Tier

Tier	% of Students Attaining Masterry
1	0-19
2	20-39
3	40-59
4	60-79
5	80-100

National math programme not adding up ...

Table 2 - Proposed Revised Reporting Structure

CUT SCORE	PERFORMANCE	DESCRIPTION AND RECOMMENDED
		LEVEL OF SUPPORT REQUIRED
0 - 29	Non-mastery	Student performing significantly below
		grade level, re-teaching required -
		individual and small group (maximum
		5) intervention
30 - 49	Near Mastery	Student performing below grade level,
		intense remediation required - small
		group (maximum 5 students)
50 - 64	Inconsistent Mastery	Student performing at Grade level,
		gaps in content identified.Support
		required in two to three strands
70 - 85	Proficient	Student performing at Grade level,
		support required in one strand
86 - 100	Full Mastery	Student performing at Grade level -
		has mastered all strands

Table 3 Comparison of Mastery in Individual versus Combined Strands

INDIVIDUAL STRAND	PERCENTAGE	PERCENTAGE
	MASTERY	COMBINED MASTERY
Number Representation	58.2	68.5
Number Operation	45.3
Geometry	75.3	70.7
Measurement	69.3
Algebra	54.5	54.6
Statistics	47