First-grade Latino English language learners' performance on story problems in spanish versus english

To explore whether teaching English Language Learners (ELLs) with an emphasis on English story problem is appropriate, we compared the performance of a group of Latino first graders when working in Spanish and in English on two equivalent sets of story problems. The students’ performance was slightly higher in English than in Spanish, but lower than monolingual students from other studies. ELLs’ success in English indicated that the children’s knowledge of conversational English was sufficient to comprehend story problems, leading us to conclude that teaching through story problems is a viable approach with ELLs

Fostering relational thinking while negotiating the meaning of the equal sign

In this article, we relate an experience in which we have used number sentences to begin to develop algebraic thinking. Working with third-graders during six sessions, we set out to explore the following questions: How do students’ conceptions of the equal sign evolve when considering and discussing varied True/False number sentences? Do students develop relational thinking while we negotiate the meaning of the equal sign? Do students retain the new interpretation of the equal sign over time? We successfully helped the students to broaden their conceptions through the different tasks but were only partially successful at initiating relational thinking. The particularities of both developments are here described

English-language learners’ problem solving in Spanish versus English

To explore the role of language in English Language Learners (ELLs)´ problem solving, we compare the performance of a group of Latino first graders when working in Spanish and in English on two equivalent sets of story problems. We contrast our results with others from previous studies with bilingual and monolinguals children by focusing on students´ performance in problems with the same semantic structure. This comparison leads us to discuss some factors influencing students´ problem solving. The findings support the use of problem solving in teaching ELLs. Students’ performance was slightly higher in English, even in problems of higher language complexity, but lower than monolingual students from other studies

Breaking the addition addiction: creating the conditions for knowing-to act in early algebra

We use data from a teaching experiment with a group of eight years old students to explore the potential of examining number sentences to promote relational thinking. This type of thinking requires attention to mathematical structure through consideration of relationships between terms contained in the sentence and not just on computation and comparison of the numeric values of each side. We show that children came to “know-to act” in the context of written activities and orchestrated discussions about number sentences, overcoming some of their computational habits and developing new ways to see and more flexibly approach the sentences. The results help to advance the study of young students´ emergent algebraic modes of thinking

El papel del lenguaje en la resolución de problemas verbales aritméticos. Un estudio con alumnos bilingües

Para explorar el papel del lenguaje en la resolución de problemas por alumnos que están aprendiendo el idioma del aula, comparamos el rendimiento de un grupo de alumnos latinos de primero de primaria en la resolución de dos conjuntos equivalentes de problemas verbales en español e inglés. Contrastamos nuestros resultados con los de otros estudios con alumnos bilingües y monolingües, centrándonos en la resolución de problemas con la misma estructura semántica. Los resultados muestran que el rendimiento de los alumnos fue ligeramente superior en inglés, incluso en problemas de alta complejidad lingüística, pero menor que el rendimiento de alumnos monolingües en otros estudios. Estos resultados apoyan el uso de problemas verbales en la enseñanza de las matemáticas en inglés cuando los alumnos están aprendiendo dicho idioma

Spanish/English bilingual students’ comprehension of arithmetic story problem texts.

In this paper we explore some of factors that affect bilingual students’ comprehension of story problems: vocabulary, syntax, cultural relevance and understanding of the word problem genre. In an effort to determine how these factors interact, we asked 18 Spanish/English bilingual children to retell and solve arithmetic story problems in their first and second language in one-on-one interviews. We found that students attempted to build meaningful representations with coherence among events and actions and manipulated the quantities according to their interpretation. Occasional unfamiliar vocabulary tended not to be an issue. Children made inferences drawing on their personal experiences to make the texts more coherent. It was not so much the surface features of the text including syntax and vocabulary that interfered with children’s interpreting them successfully, rather it was the situations and the limited information provided about them that affected comprehension. We conclude with implications for teachers and textbook writers

From an operational to a relational conception of the equal sign. Thirds graders' developing algebraic thinking

We describe a teaching experiment about third grade students« understanding of the equal sign and their initial forays into analyzing expressions. We used true/false and open number sentences in forms unfamiliar to the students to cause students to reconsider their conceptions of the equal sign. Our results suggest a sequence of three stages in the evolution of students' understanding of the equal sign with students progressing from a procedural/computational perspective to an analytic perspective. Our data show that as students deepened their conceptions about the equal sign they began to analyze expressions in ways that promoted algebraic thinking. We describe the essential elements of instruction that advanced this learning

Trabajo con igualdades numéricas para promover pensamiento relacional

En este documento presentamos algunos de los resultados de un estudio que aporta evidencias de la capacidad de los alumnos de tercer grado para desarrollar pensamiento relacional y para comprender el significado del signo igual trabajando en un contexto de igualdades numéricas

In the transition from arithmetic to algebra: Misconceptions of the equal sign

This paper describes an ongoing study where we analyze elementary students' misconceptions of the equal sign. Considering the proposal of many researchers of fostering algebraic thinking in arithmetic settings, numeric open sentences were proposed to 3rd and 5th/6th grade students in order to analyze their understanding of the equal sign and their ways of thinking of and solving equal sign arithmetic expressions. Different misconceptions and solving approaches were detected in both groups