To assess and evaluate student knowledge, the One Minute Basic Number Facts Test (Westwood, 2012) was completed by students under test conditions. The purpose of this assessment was to collect baseline data to measure progress.

Initial Investigation

‘Dice based games devised by Dr Paul Swan will improve a student’s mental computation’

**Action Research Project**

**By Lauren Black**

Hypothesis

Initial Investigation

**Improving Mental Calculation in Year 3/4**

Prior to the commencement of teaching and learning, the context for the project was defined. The following factors were identified:

The class for the project (Year 3/4)

The learning area and topic for the project (Maths- Mental Calculation)

The specific learning needs in the class

A suitable time to complete the project each week (2 20 minute sessions per week for 5 weeks)

What teaching and learning strategies am I seeking to develop?

Target Group

The project targeted a group of 8 year 3/4 students in mathematics. The group of students were identified according to their mental mathematics ability. The target group of students have higher learning needs in mental calculation and as a result they were in the lower maths group.

Teaching Strategies

In consultation with the classroom teacher, Dr Paul Swan's mathematics strategies were identified as suitable for the learning needs of the target group. Following this, a hypothesis was defined.

The One Minute Basic Number Facts Test (Westwood, 2012) was selected as "The results allow rapid identification of students whose slowness and difficulties in most areas of basic mathematics and problem solving may be due to lack of automaticity in their recall of most basic number facts" (Westwood, 2012, p.89).

Pre-Test Conclusions

The results of the pre-test concluded that students require further development with the fluency of their mental calculations. The students were lacking the ability to quickly and accurately complete sums involving addition, subtraction, multiplication and division.

Formative Assessment

Formative assessment was completed continuously throughout the project with students informally questioned at the end of each session with concept checking questions. A formal formative assessment was completed after 3 lessons. This assessed student progress, thoughts and feelings in the form of reflection and a series of 10 mental questions reviewed as a class.

The findings of the assessment concluded that most students still require improvement with the accuracy of their calculation. However, the students confidence and attitude towards mathematics had improved significantly. According to Kara (2009, p. 100) “Positive attitudes will ensure that they [students] acquire lifelong learning skills... an individual with positive attitudes toward any subject concentrates on it, is interested in it and takes all the actions necessary to succeed in learning about it. Thus, a favourable achievement in learning is to be expected”. Therefore, the ARP has had a positive impact on student learning that was perhaps not initially identified.

Where to from here?

Identify Teaching and Learning Structure

The structure for the project was identified as follows:

Pre-Test (One Minute Basic Number Facts Test)

'Connect Three' activity

'Mary's Game' activity

Formative assessment and reflection

'Add 'n' Multiply activity

Post-Test (One Minute Basic Number Facts Test)

Post-Test

A post-test was conducted using the same Basic Number Facts Test (Westwood, 2012) completed in the pre-test. The results of the pre-test and post-test were compared to measure student progress and therefore determine whether the hypothesis is supported.

Implications and Variables

Despite the hypothesis being supported, a number of variables may have effected the results. These are as follows:

The project did not have a control group to allow for the comparison of results

External influences during testing such as distractions, student focus and well-being may effect results

No repeat trials limit the accuracy of the project

Questions

Initial Investigation

Research was completed on facilitating student learning in mathematics. The use of manipulatives was identified as one strategy to assist students to move from concrete to abstract knowledge. According to White, Swan & Marshall (2009, p.2) “A manipulative material is an object(s) that can be handled by an individual in a sensory manner during which process, and conscious and unconscious thinking will be fostered”. Consequently, I intended to use dice and other manipulatives throughout my project to facilitate student learning.

What research am I focusing on?

Now your turn...

Initial Investigation

Dr Paul Swan is an Australian educator who has written a range of books and created numerous resources for primary and middle school mathematics education.

Educational purpose of Paul Swan's mathematics strategies

To facilitate student learning, activities from the book 'Dice Dilemma's' (Swan, 1997) were used. The activities in this book are designed to improve mental calculation through game based activities that use manipulatives.

According to Swan & Marshall (2008, p. 338) “... given the right conditions, games can achieve an increase in basic fact skills in a stimulating and enjoyable environment”.

An analysis of the student results reveal that 80% of the students improved their addition and subtraction scores, 50% improved their multiplication scores and 60% improved their division scores. Considering this, the hypothesis ‘Dice based games devised by Dr Paul Swan will improve a student’s mental computation’ is supported. However, the amount by which each student improved by does vary and the possible variables which may have affected the results need to be considered.

The End

Thank you!

Was the hypothesis supported?

Post-Test Conclusions

Conclusion

The action research project successfully facilitated both teaching and learning. It demonstrated the benefits of game based activities and manipulatives on mathematics by improving mental calculation and student attitudes towards mathematics. However, to provide more comprehensive and accurate results, the project would need to be completed in a more controlled environment.

References:

Australian Curriculum Links

Year 3- Number and Algebra: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055). Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) .

Sample of Basic Number Facts Test (Westwood, 2012)

Pre-Test

Westwood, P. (2012). Numeracy and Learning Difficulties: Approaches to Teaching and Assessment. [Ebook Library Version. Retrieved from http://ecu.edu.au

Swan, P., & Marshall, L. (2008). Mathematics games: Time wasters or time well spent? Joondalup, Western Australia: Edith Cowan University, Faculty of Education and Arts. Retrieved from http://ro.ecu.edu.au/ecuworks/636/

White, G., Swan, P., & Marshall, L. (2009). Hands on Heads on: A mathematics manipulatives continuum. Edith Cowan University. Retrieved from www.drpaulswan.com.au/.../index.cfm?&...mathematics%20manipulative

Kara, A. (2009) "The Effect of a ‘Learning Theories’ Unit on Students’ Attitudes Toward Learning," Australian Journal of Teacher Education: Vol. 34: Iss. 3, Article 5. DOI: 10.14221/ajte.2009v34n3.5. Available at: http://ro.ecu.edu.au/ajte/vol34/iss3/5