always presented with a fraction bar (e.g., \( 1 / \% \) ), which negates these terms. In a similar way, describing a fraction as a number over a number does not help children understand that a fraction is a single quantity. Students' misunderstanding that fractions consist of two separate numbers separated by a line may lead to errors such as adding across the top number and adding across the bottom number when adding fractions. As children learn to reduce a fraction to lowest terms, some children believe this means the value of the fraction changes; a better choice is to describe determining an equivalent fraction in simplest form, which eliminates the angles and how these relate to properties of shapes and coordinate planes. Children with mathematics difficulty struggle with geometry concepts through high school (Dobbins, Gagnon, \& Ulrich, 2014); therefore, it is necessary to provide a consistent and strong geometry background to children across grade levels, Often, general vocabulary is used to describe geometric concepts, yet children are expected to interpret formal geometric vocabulary. Educators should show the connection between informal and formal terms (see Figure 4). Many of the issues around language with geometry pertain to preciseness of similar and congruent shapes, same does not help with this task. As children learn transformations in the early elementary grades, educators often describe these as flips, slides, and turns. Although these terms describe the action of a transformation, children in the later elementary and middle school grades must be familiar with the formal terms of reflection, translation, and rotation. Specificity with the term is necessary for children to have gained adequate exposure to the term for practice within textbooks and on high-stakes assessments. In a similar manner, shapes do not shrink or stretch. Instead, these are dilations of a shape. ious

The text discusses the challenges children face in understanding fractions and geometry concepts, particularly due to the language used in teaching. Here’s a breakdown of the key points: 1. **Understanding Fractions**: - Children often perceive fractions as two separate numbers rather than a single quantity. This misunderstanding can lead to errors, such as incorrectly adding fractions by summing the numerators and denominators separately. - When teaching fractions, it's important to emphasize that reducing a fraction to its lowest terms does not change its value; instead, it should be framed as finding an equivalent fraction in simplest form. 2. **Geometry Concepts**: - Students with difficulties in mathematics often struggle with geometry throughout their education. A strong foundation in geometry is essential across grade levels. - There is a gap between informal and formal vocabulary in geometry. Educators should bridge this gap by connecting everyday language with formal geometric terms. - Specific terms like "similar" and "congruent" need to be clearly defined to avoid confusion. - When teaching transformations, educators often use informal terms like "flips," "slides," and "turns." However, students must also learn the formal terms: reflection, translation, and rotation. - The concept of dilations should be introduced correctly, emphasizing that shapes do not simply shrink or stretch. ### Recommendations for Educators: - Use clear and consistent language when teaching fractions and geometry. - Provide examples that illustrate the connection between informal and formal terms. - Ensure that students have adequate exposure to formal terminology to prepare them for higher-level mathematics and assessments. - Reinforce the understanding of fractions as single quantities and transformations as specific actions to enhance comprehension. By addressing these language issues and providing a solid foundation in both fractions and geometry, educators can help students develop a better understanding of these mathematical concepts.