**Teaching Math Through Inquiry** Lindsey Serrano March 2012

**Introduction** • Research Question • What is the effect of Using Inquiry Based Teaching in Mathematics on Student Retention of Math Concepts and Attitude?

**Why Is This Important?** • To learn new math concepts students need to be able to retain basic math operations taught in previous grades. • When the teacher must re-teach previously taught topics fewer new concepts are learned. • Students are better able to apply math formulas to new types of problems when the formula is understood and not simply memorized.

**Review of Literature** • IMPROVING BASIC MATH SKILLS USING TECHNOLOGY (Siobhan Hudson, Sarah Kadan, Karen Lavin, Tylita Vasquez, Dec. 2010) • Researchers tested the use of manipulatives, cooperative learning, and technology on the retention of basic math skills among various students from 4th, 5th, 6th and 9th grade classes. • Student scores increased significantly on a test of basic math skills after receiving instruction using using different forms of technology.

**Review of Literature** • Making Connections in Mathematics Conceptual Mathematics Intervention For Low-Performing Students (LeaneR. Ketterlin-Geller, David J. Chard, Hank Fien, Jan/ Feb 2008) • A group of fifth grade students who received an inquiry based math curriculum scored significantly higher on an inquiry based application assessment than the groups who received a different type of instruction. • There was no significant difference between the groups on statewide accountability tests or district math tests.

**Review of Literature** • Passive or Passionate Participation in Mathematics: Diagnosing and Improving Student Participation in Mathematics (Rose M. Gottler, August 2010) • Participation in mathematics was measured in a group of fifth grade students who received lecture based instruction and inquiry based instruction. Results showed that when students received inquiry based instruction, their levels of participation increased in discussion and class activities. • Additional research is needed to determine if there is a link between student participation and understanding of material.

**Review of Literature ** • The Use of Inquiry in the Development of Preservice Teacher Efficacy in Mathematics and Science (Greer M. Richardson and Ling L. Liang 2008) • “The NCTM and NRC standards clearly state that students must engage in doing mathematics (i.e., via inquiry) to understand mathematics”. • Students who learn math through inquiry are learning concepts and processes in the same way as mathematicians.

**Review of Literature** • Inquiry-Based Learning: An Educational Reform Based Upon Content-Centered Teaching (M. Padraig M. M. McLoughlin Ph.D. Presented January, 2009) • Inquiry based instruction is centered around the content being taught. “Without the content there is no inquiry; without inquiry no learning; and, without learning no reason for a class…” • “Students must learn mathematics by doing, not simply discussing, seeing or reading it”.

**Summary** • Inquiry has shown to have positive results in student learning on inquiry tasks vs traditional teaching. No negative impact on traditional state tests. (Leane R. Ketterlin-Geller, David J. Chard, Hank Fien, Jan/ Feb 2008) • Standards call for inquiry based practices in math (Greer M. Richardson and Ling L. Liang 2008)

**Research Design ** • To measure levels of retention a two group replication study post/post-test replication design was used. • Post-test design was used to obtain differences in attitude under each condition.

**Intervention** • The use of an inquiry based approach to teach math concepts. This was used with different students acting as a control for each other on two units—integers and metric system.

**Sample** • 68 sixth grade math students • 4 math classes of mixed ability levels

**Instrumentation and Data Collection ** • Teacher observed student engagement during both types of approaches • Likert Scale, Serrano’s Attitude Towards Math (confidence and enjoyment) Scale • Unit tests on content

**Threats to Validity** • Researcher Bias • Subject History • Testing threat

**Results: Attitude** • The two-tailed t test showed no significant change in student attitudes after receiving an inquiry based teaching approach or a teacher centered approach ( t= 0.0210, df = 67, P = 0.9833)

**Attitude Experimental/ Control **

**Student Attitude**

**Results: Retention Unit 1** • The two-tailed t test showed Asignificant difference between the retention scores of students who received inquiry based instruction compared to the control group in test 1 (t = 3.3515, df = 66, P = 0.0013)

**Retention Test 1**

**Retention Test 1**

**Results: Unit 2** • The two-tailed t test results showed extremely significant difference between the retention scores of students who received inquiry based instruction compared to the control group in test 2 (t = 4.0709, df = 66, P = 0.0001)

**Retention Results Test 2**

**Retention Test 2**

**Results: Across units** • The two-tailed t test result showed extremely significant difference when comparing individual student retention scores after receiving inquiry based teaching compared to non-inquiry based teaching across both units (t = 5.1010, df = 67, P < 0.0001)

**Individual Student Retention Results**

**Individual Student Retention**

**Discussion** • Student attitudes: No difference between Inquiry and Non-Inquiry teaching. • Retention: Student scores increased over time with Inquiry based teaching and decreased over time with Non-Inquiry based teaching. Several reasons may explain result: engagement, staying in the struggle, explicit conversations.

**Action ** • Share information with colleagues. • Create more opportunities for Inquiry Based teaching activities in my math classes.

**References** • Chard, David, J. Feind, Hank, Ketterlin-Geller, Leane, (2008), Making Connections in Mathematics Conceptual Mathematics Intervention For Low-Performing Students, Remedial and Special Education Journal Vol 29 Number 1, Jan/Feb 2008, Retrieved October 23rd, 2011 from http://dx.doi.org/10.1177/0741932507309711 • Gottler, Rose M., (2010), Passive or Passionate Participation in Mathematics: Diagnosing and Improving Student Participation in Mathematics. Marygrove College. Retrieved March 24th, 2012 from http://www.eric.ed.gov/PDFS/ED511318.pdf • Hudson, Siobhan, Kadan, Sarah, Lavin, Karen, Vasquez, Tylita, (2010) Improving Basic Math Skills Using Technology, Saint Xavier University. Retreived March 26th, 2012 from http://www.eric.ed.gov/PDFS/ED512698.pdf • Liang, Ling, L., Richardson, Greer, M. (2008), The Use of Inquiry in theDevelopment of PreserviceTeacherEfficacy in Mathematics and Science, Journal of Elementary Science Education, Vol. 20, No. 1 (Winter 2008), pp. 1-16. Retrieved March 24th 2012 from http://www.eric.ed.gov/PDFS/EJ798565.pdf • McLoughlin, M., Padraig M, (2009), Inquiry-Based Learning:An Educational Reform Based Upon Content-Centred Teaching. Paper presented at the Annual Meeting of the American Mathematical Society Washington, DC. Retrieved on March 24th, 2012 from http://www.eric.ed.gov/PDFS/ED506295.pdf