Predicting phenotypes from genetic crosses: a mathematical concept to help struggling biology students.

Abstract:

Predicting phenotypic outcomes from genetic crosses is often very difficult for biology students, especially those with learning disabilities. With our mathematical concept, struggling students in inclusive biology classrooms are now better equipped to solve genetic problems and predict phenotypes, because of improved understanding of dominance and recessiveness. Furthermore, this new concept has gained popularity among our dyslexic biology students who usually have difficulty in conceptualizing alleles and genes with alphabetical letters. In addition to giving these students the option of using numerical representations, this method minimizes confusion that is often caused by alphabetical representations.

Key Words: Phenotypic outcomes; mathematical concept; alleles; dominance; recessiveness; biology students.

Article Type:

Report

Subject:

Sciences education (Methods)
Allelomorphism (Properties)
Phenotype (Study and teaching)
Special education (Methods)

Authors:

Baurhoo, Neerusha
Darwish, Shireef

Pub Date:

05/01/2012

Publication:

Name: The American Biology Teacher Publisher: National Association of Biology Teachers Audience: Academic; Professional Format: Magazine/Journal Subject: Biological sciences; Education Copyright: COPYRIGHT 2012 National Association of Biology Teachers ISSN: 0002-7685

Issue:

Date: May, 2012 Source Volume: 74 Source Issue: 5

Product:

Product Code: 8294000 Education of Handicapped; 9105115 Special Education Programs NAICS Code: 61111 Elementary and Secondary Schools; 92311 Administration of Education Programs

Geographic:

Geographic Scope: United States Geographic Code: 1USA United States

Accession Number:

288628475

Full Text:

Many biology students struggle to understand key terms such as gene and allele even after classroom and laboratory instruction (Yilmaz et al., 2010). These students face difficulties in comprehending related concepts such as dominance and recessiveness (Browning & Lehmen, 1988; Freidenreich et al., 2010), thus impeding their knowledge-building process in fundamental genetics. Consequently, they tend to wrongly predict phenotypic outcomes from genetic crosses (Browning & Lehmen, 1988). Among our struggling college-level biology students, we commonly find that slow learners and those diagnosed with dyslexia express confusion in interpreting phenotypes from genetic crosses. To help struggling students in inclusive biology classrooms, we have developed a mathematical concept to predict phenotypes from genetic crosses.

* Mathematical Concept in Monohybrid & Dihybrid Crosses

From Mendel's pea experiments, we formulated the following story problem. Rita crosses pea plants as a hobby Rita decides to cross a pea plant that is homozygous for the purple allele with a pea plant that is homozygous for the white allele. Purple is the dominant trait for color of flowers. Predict the genotypic and phenotypic outcomes for the [F.sub.1] and [F.sub.2] generations for Rita.

First, students are asked to build a key table (Table 1) to list all alleles and genes involved in the monohybrid cross. Using Table 1, they proceed to build a Punnett square to show genotypic outcomes. Because the main problem for our students is in predicting the phenotype for heterozygotes (the gene Pp), the mathematical concept we developed specifically addresses this issue. We ask students to use 100 as the number to represent the dominant purple allele P and 0 to represent p, the recessive white allele. The next step is to add 100 to 0, and the resulting total can be matched to the phenotype (Table 2), which is then used to complete the Punnett square and conclude whether the genotype yields white or purple flowers (Table 3). The mathematical concept can also be extended to predict homozygous dominant traits such as purple flowers, which is represented by the numerical value of 200 because the dominant purple allele P has been given a numerical value of 100 (Table 3). Similarly, homozygous recessive traits can be numerically predicted by a value of zero (Table 3).

For a dihybrid cross, we ask students to predict the [F.sub.1] genetic outcomes when two homozygous pea plants with yellow round seeds and green wrinkled seeds are crossed. Following the same procedure as the monohybrid test, students build the Punnett square using the mathematical concept in Table 4.

* Conclusion

With our new mathematical concept, biology students can better understand that, in the case of heterozygous traits, a dominant allele determines appearance by contributing 100% to the overall phenotype, whereas the recessive allele has no observable effects on the organism and, hence, contributes 0%. Furthermore, using numerical representations of alleles in addition to alphabetical letters can be less confusing and provide a better understanding of allelic effects for dyslexic students and slow learners. We believe that this technique might be beneficial for inclusive biology classrooms as well as special-education settings.

DOI: 10.1525/abt.2012.74.5.11

References

Browning, M.E. & Lehman, J.D. (1988). Identification of student misconceptions in genetics problem solving via computer program. Journal of Research in Science Teaching, 25, 747-761.

Freidenreich, H.B., Duncan, R.G. & Shea, N. (2011). Exploring middle school students' understanding of three conceptual models in genetics. International Journal of Science Education, 33, 2323-2349.

Yilmaz, D., Tekkaya, C. & Sungur, S. (2011). The comparative effects of prediction/discussion-based learning cycle, conceptual change text, and traditional instructions on student understanding of genetics. International Journal of Science Education, 33, 607-628.

NEERUSHA BAURHOO is a doctoral student in Educational Studies at McGill University, 3700 McTavish Street, Montreal, Quebec H3A 1Y2, Canada; e-mail: neerusha.baurhoo@mail.mcgill.ca. SHIREEF DARWISH is Faculty of Biology at John Abbott College, 21 275 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec H9X 3L9, Canada.

Table 1. Key table for alleles and genotypes.

                            Letter
From Question           Representation       Definition

Purple is dominant            P           Allele for
                                          purple flowers

White is recessive            p           Allele for white
                                          flowers

Dominant homozygous           PP          Genotype for
purple gametes               (P)          purple flowers

Recessive homozygous          pp          Genotype for
white gametes                 (p)         white flowers

Table 2. Mathematical concept in monohybrid tests
for predicting phenotypes of flowers.

Alleles &    Mathematical     Phenotypic
Genotypes      Concept      Interpretation

P                100+           Purple
p                 0             White
Pp               100            Purple

Table 3. Mathematical concept in Punnett squares for
predicting flower color in F1 and F2 generations.

 Monohybrid Cross [F.sub.1] Generation

              [female]          [male]

[female]        (P)              (P)

                 Pp               Pp
  (p)        100 + 0 = 100    100 + 0 = 100
               Purple           Purple

                 Pp               Pp
  (p)       100 + 0 = 100    100 + 0 = 100
               Purple           Purple

 Monohybrid Cross [F.sub.2] Generation

              [female]          [male]

[female]        (P)              (p)

                 PP               Pp
 (P)       100 + 100 = 200   100 + 0 = 100
               Purple           Purple

                 Pp               pp
 (P)      100 + 0 = 100      0 + 0 = 0
               Purple            white

Table 4. Mathematical concept in dihybrid tests for
predicting phenotypes of seeds.

Alleles &   Mathematical     Phenotypic
Genotypes     Concept      Interpretation

Y              100 +           Yellow
y                0             Green
Yy              100            Yellow
R              100 +           Round
r                0            Wrinkled
Rr              100            Round

Gale Copyright:

Predicting phenotypes from genetic crosses: a mathematical concept to help struggling biology students.

Abstract:	Predicting phenotypic outcomes from genetic crosses is often very difficult for biology students, especially those with learning disabilities. With our mathematical concept, struggling students in inclusive biology classrooms are now better equipped to solve genetic problems and predict phenotypes, because of improved understanding of dominance and recessiveness. Furthermore, this new concept has gained popularity among our dyslexic biology students who usually have difficulty in conceptualizing alleles and genes with alphabetical letters. In addition to giving these students the option of using numerical representations, this method minimizes confusion that is often caused by alphabetical representations. Key Words: Phenotypic outcomes; mathematical concept; alleles; dominance; recessiveness; biology students.

Article Type:	Report
Subject:	Sciences education (Methods) Allelomorphism (Properties) Phenotype (Study and teaching) Special education (Methods)
Authors:	Baurhoo, Neerusha Darwish, Shireef
Pub Date:	05/01/2012
Publication:	Name: The American Biology Teacher Publisher: National Association of Biology Teachers Audience: Academic; Professional Format: Magazine/Journal Subject: Biological sciences; Education Copyright: COPYRIGHT 2012 National Association of Biology Teachers ISSN: 0002-7685
Issue:	Date: May, 2012 Source Volume: 74 Source Issue: 5
Product:	Product Code: 8294000 Education of Handicapped; 9105115 Special Education Programs NAICS Code: 61111 Elementary and Secondary Schools; 92311 Administration of Education Programs
Geographic:	Geographic Scope: United States Geographic Code: 1USA United States
Accession Number:	288628475
Full Text:	Many biology students struggle to understand key terms such as gene and allele even after classroom and laboratory instruction (Yilmaz et al., 2010). These students face difficulties in comprehending related concepts such as dominance and recessiveness (Browning & Lehmen, 1988; Freidenreich et al., 2010), thus impeding their knowledge-building process in fundamental genetics. Consequently, they tend to wrongly predict phenotypic outcomes from genetic crosses (Browning & Lehmen, 1988). Among our struggling college-level biology students, we commonly find that slow learners and those diagnosed with dyslexia express confusion in interpreting phenotypes from genetic crosses. To help struggling students in inclusive biology classrooms, we have developed a mathematical concept to predict phenotypes from genetic crosses. * Mathematical Concept in Monohybrid & Dihybrid Crosses From Mendel's pea experiments, we formulated the following story problem. Rita crosses pea plants as a hobby Rita decides to cross a pea plant that is homozygous for the purple allele with a pea plant that is homozygous for the white allele. Purple is the dominant trait for color of flowers. Predict the genotypic and phenotypic outcomes for the [F.sub.1] and [F.sub.2] generations for Rita. First, students are asked to build a key table (Table 1) to list all alleles and genes involved in the monohybrid cross. Using Table 1, they proceed to build a Punnett square to show genotypic outcomes. Because the main problem for our students is in predicting the phenotype for heterozygotes (the gene Pp), the mathematical concept we developed specifically addresses this issue. We ask students to use 100 as the number to represent the dominant purple allele P and 0 to represent p, the recessive white allele. The next step is to add 100 to 0, and the resulting total can be matched to the phenotype (Table 2), which is then used to complete the Punnett square and conclude whether the genotype yields white or purple flowers (Table 3). The mathematical concept can also be extended to predict homozygous dominant traits such as purple flowers, which is represented by the numerical value of 200 because the dominant purple allele P has been given a numerical value of 100 (Table 3). Similarly, homozygous recessive traits can be numerically predicted by a value of zero (Table 3). For a dihybrid cross, we ask students to predict the [F.sub.1] genetic outcomes when two homozygous pea plants with yellow round seeds and green wrinkled seeds are crossed. Following the same procedure as the monohybrid test, students build the Punnett square using the mathematical concept in Table 4. * Conclusion With our new mathematical concept, biology students can better understand that, in the case of heterozygous traits, a dominant allele determines appearance by contributing 100% to the overall phenotype, whereas the recessive allele has no observable effects on the organism and, hence, contributes 0%. Furthermore, using numerical representations of alleles in addition to alphabetical letters can be less confusing and provide a better understanding of allelic effects for dyslexic students and slow learners. We believe that this technique might be beneficial for inclusive biology classrooms as well as special-education settings. DOI: 10.1525/abt.2012.74.5.11 References Browning, M.E. & Lehman, J.D. (1988). Identification of student misconceptions in genetics problem solving via computer program. Journal of Research in Science Teaching, 25, 747-761. Freidenreich, H.B., Duncan, R.G. & Shea, N. (2011). Exploring middle school students' understanding of three conceptual models in genetics. International Journal of Science Education, 33, 2323-2349. Yilmaz, D., Tekkaya, C. & Sungur, S. (2011). The comparative effects of prediction/discussion-based learning cycle, conceptual change text, and traditional instructions on student understanding of genetics. International Journal of Science Education, 33, 607-628. NEERUSHA BAURHOO is a doctoral student in Educational Studies at McGill University, 3700 McTavish Street, Montreal, Quebec H3A 1Y2, Canada; e-mail: neerusha.baurhoo@mail.mcgill.ca. SHIREEF DARWISH is Faculty of Biology at John Abbott College, 21 275 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec H9X 3L9, Canada. Table 1. Key table for alleles and genotypes. Letter From Question Representation Definition Purple is dominant P Allele for purple flowers White is recessive p Allele for white flowers Dominant homozygous PP Genotype for purple gametes (P) purple flowers Recessive homozygous pp Genotype for white gametes (p) white flowers Table 2. Mathematical concept in monohybrid tests for predicting phenotypes of flowers. Alleles & Mathematical Phenotypic Genotypes Concept Interpretation P 100+ Purple p 0 White Pp 100 Purple Table 3. Mathematical concept in Punnett squares for predicting flower color in F1 and F2 generations. Monohybrid Cross [F.sub.1] Generation [female] [male] [female] (P) (P) Pp Pp (p) 100 + 0 = 100 100 + 0 = 100 Purple Purple Pp Pp (p) 100 + 0 = 100 100 + 0 = 100 Purple Purple Monohybrid Cross [F.sub.2] Generation [female] [male] [female] (P) (p) PP Pp (P) 100 + 100 = 200 100 + 0 = 100 Purple Purple Pp pp (P) 100 + 0 = 100 0 + 0 = 0 Purple white Table 4. Mathematical concept in dihybrid tests for predicting phenotypes of seeds. Alleles & Mathematical Phenotypic Genotypes Concept Interpretation Y 100 + Yellow y 0 Green Yy 100 Yellow R 100 + Round r 0 Wrinkled Rr 100 Round
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