A major policy change in Indian education after 34 years and the first educational policy of 21st century has been approved by the union cabinet on 29 July, 2020 through the National Education Policy (NEP, 2020). The NEP provides comprehensive framework for both school and higher education across the country. The NEP 2020 clearly states that, “The very highest priority of the education system will be to achieve universal foundational literacy and numeracy in primary school and beyond by 2025. The rest of this Policy will be largely irrelevant for such a large portion of our students if this most basic learning requirement (i.e., reading, writing, and arithmetic at the foundational level) is not first achieved.”

Foundational Literacy and Numeracy: An Urgent & Necessary Prerequisite to Learning (NEP, 2020)

Foundational numeracy is making sense of numbers and ability to do basic operations like addition and subtraction of the same. One of the main objectives of the NEP, 2020 is to achieve universal foundational numeracy by grade 3 by 2025. In this context, this article throws some light on the learning levels of grade 4 and grade 5 government school students on foundational numeracy skills which they are supposed to achieve by grade 3. Without attaining foundational numeracy, students will not be ready to make sense of the number concepts covered in middle school grades. This creates a learning gap which will widen as the child progresses to the higher grades. This increases the chances of these students dropping out of the school system.

Educational Initiatives Pvt. Ltd. has been advocating the same and has conducted assessments measuring foundational literacy and numeracy of government school students of Himachal Pradesh, Rajasthan and Telangana. Students are expected to master these skills by grade 3 as per the National Curriculum Framework (NCF, 2005). But what is the current state of students of grades 4 and 5 on these skills?

The table below shows the learning levels of government school students of grades 4 and 5 in addition and subtraction problems.

Table: Average performance of grade 4 and 5 students in addition and subtraction sub-skills

   
Sub-skill   
   
Assessment item   
   
Grade 4
   (N= 1033)   
   
Grade 5
    (N= 718)   
Addition of single digit numbers with sum less than 10    
5 + 4    
   
84%   
   
91%   
Addition of single digit numbers with sum less than 20    
8 + 9   
   
73%   
   
84%   
Addition of 2-digit numbers without regrouping    
      3 4
   + 2 1   
   
85%   
   
90%   
Addition of 2-digit numbers with regrouping    
     4 9
   + 3 2   
   
64%   
   
76%   
Addition of 3-digit numbers with regrouping    
     598
   +124   
   
60%   
   
74%   
Horizontal addition (3-digit + 2-digit)    
125 + 37   
   
30%   
   
48%   
Subtraction of numbers up to 10    
9 – 5    
   
71%   
   
84%   
Subtraction of numbers up to 20    
17 – 8   
   
60%   
   
76%   
Subtraction of 2-digit numbers without regrouping    
     8 9
   – 6 5   
   
64%   
   
77%   
Subtraction of 2-digit numbers with regrouping    
     8 1
   – 4 9   
   
40%   
   
53%   
Subtraction of 3-digit numbers with regrouping    
     7 2 2
   – 5 9 8   
   
28%   
   
42%   
Subtraction of numbers when 0 is involved    
     5 0 6
   – 2 0 9   
   
13%   
   
27%   
  • Around 30% of grade 4 students cannot solve simple facts like 8 + 9 and 9 – 4.
  • Around 25% of grade 5 students cannot solve 49 + 32.
  • Only 42% of the students of grade 5 and 28% of grade 4 students can solve subtraction of 3-digit numbers with regrouping.
  • Only 40% of class 4 students can solve subtraction of 2-digit numbers. When 0 is involved in the subtraction, very few students are answering those problems correctly.

The large-scale assessments like the Annual Status of Education Report (ASER) study conducted by Pratham and the National Achievement Survey conducted by the National Council of Educational Research and Training (NCERT) also reported poor learning levels of the students on addition and subtraction. ASER, 2018 has reported that only 24% of the Indian students in grades 4,5,6 and 7 can solve the subtraction of 2-digit numbers correctly. The National Achievement Survey, 2017 has reported that 57% of grade 3 students can solve simple daily life problems involving addition and subtraction of 3-digit numbers with and without regrouping.

The above data tells us that there are students who are at grade 1 math level as well as grade 4 math level in the same class. So, it is important to have assessments that can detect exactly what a student knows so that better interventions can be planned to reduce these gaps. For example, in our assessment on addition and subtraction, the test starts with questions that cover a very basic skill like the addition of single-digit numbers. This kind of assessments is even more important to the government school students where the learning gaps are high and students of varying math abilities are present in the same grade.

Why are these students struggling in learning the very foundational number skill like addition and subtraction? There can be 2 main reasons.

  1. The students may not have attained more basic foundational skills like number recognition, number writing, ordering of numbers and place value understanding which is mainly the case with the students who are struggling to solve even single-digit addition and subtraction problems.
  2. The students might have some strong misconceptions that affect the learning of the skills under addition and subtraction. Or the students are not fluent in addition and subtraction facts.

The assessments that EI has conducted on foundational numeracy also measured grade 4 and 5 students’ learning levels on the basic number concepts like number recognition, number writing, number comparison, forming a number, missing numbers and addition and subtraction fact fluency.

Some of the insights we got are quite surprising.

  • Only 67% and 71% of grade 4 and grade 5 students can recognise 3-digit numbers and only 60% of the students can write 3-digit numbers correctly.
  • Around 30% of the students have NOT answered a single question correctly on forming the larger number with the given digits.
  • Around 45% of class 4 and 5 students cannot answer a simple item on the missing number like 258, 259, ___ 261 and only 40% and 50% of the grade 4 and 5 students have answered the missing number question, 35, 40, 45, __

 So, many of the grade 4 and 5 students are even struggling with the very basic number concepts that hinder their learning of addition and subtraction.

If not the above number concepts like number recognition, comparison, forming a number etc., what are the other areas where these students are struggling to learn addition and subtraction concepts?

Addition and subtraction fact fluency: It is the ability to compute a single-digit addition fact or the related subtraction fact in 3 seconds or less (Jordan & Montani, 1997). This can be achieved either by retrieving the fact from memory or by applying efficient strategies like doubling, decomposing the given fact to a known easier fact by converting the subtraction fact to a known addition fact, etc.

Being able to fluently recall basic addition facts is a crucial and a foundational skill without which further skills (like the addition of 2-digits numbers) cannot be mastered. If a child has not developed this skill, then when she is solving more complex problems, a major chunk of her mental processes (working memory) will be devoted to solving the basic addition facts and not solving the larger problem presented.
For example, while solving a problem like 405 + 67, the student follows an algorithm which can seem quite sophisticated for her. To successfully solve the problem, she has to hold multiple items (digits to add, the sum, carry over rule etc.) in her working memory and process it simultaneously. This working memory is limited for every learner. If she cannot retrieve the basic addition facts from memory, she will not be able to free up the already limited mental store for processing the addition algorithm and its components.

Research says that students should be able to solve at least 20 single-digit addition facts and the related subtraction facts correctly in a minute by grade 3. But the average grade 4 and 5 government school students can solve only 10 addition facts correctly in a minute and 6 to 8 subtraction facts correctly in a minute.

With such low levels of addition and subtraction fact fluency, these students are further struggling in applying the addition and subtraction algorithm correctly.

These are the learning levels of the students who might have moved to grade 5 and grade 6 now

(2020-21) as these assessments were conducted by EI in the academic year 2019-20. Though the current policy focuses on the students in primary grades achieving foundational numeracy, it is important to understand that there are many students who are moving to middle school and are still struggling with these foundational number concepts.

Though the article mentioned government school data, the insights should be looked into by the private school teachers as well. If not the same per cent as the government school, even private schools will have students of poor math ability who haven’t mastered the foundational number sense even after grade 3.

We recommend teachers to administer tests on foundational numeracy to understand these gaps. Subsequently provide some interventions on foundational number sense for the first few months of the academic year. This will help to reduce some of these learning gaps so that students will be able to make sense of the current grade math concepts.

 

References:

Jordan, N. C., & Montani, T. O. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of learning disabilities, 30(6), 624-634.

Pratham (2018). Annual Status of Education Report (ASER). Retrieved from the

World Wide Web: http://img.asercentre.org/docs/ASER%202018/Release%20Material/aserreport2018.pdf

The National Educational Policy (2020). Retrieved from http://niepid.nic.in/nep_2020.pdf

 

Praveena K

Praveena K

Praveena K is a lead educational specialist working on math pedagogy research
Praveena K