Family mediation of mathematically based concepts while engaged in a problem-solving activity with their young deaf children

Dr. Karen Kritzer/Kent State University, OH was available from 09/1/08 until 09/21/08 to answer questions and share ideas concerning her research and its implications for parents of children who are deaf/hard of hearing, their teachers and other professionals who work with them.

You are encouraged to read the research summary below and review the attached discussion.

Abstract: This study examined the relationship between young deaf children’s level of mathematics ability (“high” and “low”, as defined by test score on the Test of Early Mathematics Ability-3) and opportunities available for the construction of early mathematics knowledge during a problem-solving task implemented by their parents.Findings indicate that the manner in which mathematically based concepts (number/counting, quantity, time/sequence, and categorization) were incorporated into the activity was more meaningful for children who demonstrated high levels of mathematical ability.In addition, children who demonstrated high levels of mathematical ability experienced a more purposeful use of mediation during activity implementation; however, overall use of mediated learning experiences was limited for children from both ability groups. Paragraph 1: Hearing children begin formal schooling already knowing a great deal of mathematics.It is likely that they develop this knowledge through informal experiences within their home environment. Cooking with mom for example, helping to set the table at mealtimes, and/or playing simple counting and number games with family members can all contribute to young hearing children’s development of early mathematics concepts. Perhaps the most salient characteristic of young hearing children’s early environment is the fact that they are constantly surrounded by mathematical language. The young hearing child experiences vocabulary related to size for example, as grandma comments on how big the child has grown, or sequencing as dad mentions that a bath and story will occur before bedtime. Paragraph 2: For young deaf children, early informal knowledge of mathematics may not be so readily developed. Given the ramifications of hearing loss, deaf children, those with hearing parents in particular, are not likely to be exposed to linguistically-presented mathematics concepts quite as pervasively as their hearing peers. Some hearing parents with deaf children may find communication with their children challenging for a variety of reasons, including lack of knowledge of sign vocabulary that can be used to express mathematical concepts, inexperience with the process of gaining visual attention prior to communicating with the child, and language delays on the part of the child. Furthermore, rather than engage in the time-consuming task of explaining a task such as sorting laundry to the deaf child, a parent might find it easier to complete the task him/herself. Given these challenges, young deaf children, may begin kindergarten with a foundation of early mathematics concept knowledge that differs from their hearing peers.The purpose of this study was to assess the early mathematics knowledge of young deaf children and factors within the home that contribute to this knowledge. Paragraph 3: Twenty-nine children between the ages of 4 and 6 years, from schools for the deaf nationwide, participated in the study upon which the findings presented in this article are based. The Test of Early Mathematical Ability (TEMA-3) was administered to the children and the scores were used to select participants for the portion of the study described in this article. Participants were selected as follows: scores within 1 standard deviation of the mean formed the “average” group; scores 2 standard deviations above and below the mean formed the “high” and “low” ability groups respectively.Three participants from each the “high” and “low” groups were randomly selected and invited to participate in the second level of the study.The three selected participants in the “high” group all had deaf parents and lived in homes in which American Sign Language was the primary means of communication. The three participants in the “low” group all had hearing parents and spoken English, with some sign support, was the primary language spoken in the home. Paragraph 4: To examine the opportunities available for early mathematics learning for each child under similar conditions, data for the portion of the study described in this article were collected through use of a planned problem-solving activity, “This is In, This is Not,” from the book “Family Math for Young Children” (Coates & Stenmark, 1997), that parents were asked to conduct with their deaf children.The mathematical purpose of the activity was to observe, describe, and sort into categories.The written description of the activity suggests that parents collect a variety of items (i.e., toys, kitchen utensils, food products) to be used during the activity and then designate a sorting space.The activity takes place as children take turns sorting items into the sorting space.The parent might begin, for example, by picking up a blue car and saying, “This is in (the sorting space) because it is blue.”According to activity directions, all items are sorted as either belonging to the category or not. Paragraph 5: Videotape data from parents’ implementation of the activity, were coded for incorporation of mathematically-based concepts in the following areas: numbers and/or counting; quantity; time and/or sequence; and categorization.Findings indicated that parents of children with “high” mathematical ability incorporated these mathematics concepts into the activity substantially more frequently than parents of children with “low” mathematical ability. More critical however, is that these concepts were purposely incorporated into the activity in a manner that made them meaningful to the children.For example, after separating a specific category of objects, children with “high” mathematical ability were asked “how many” items were in that group.In contrast, children with “low” mathematics ability were asked to give the parent a specified number of items with a particular characteristic, (e.g., “two red”). Paragraph 6: Videotaped data from parents’ implementation of the activity were also coded for quality of mediation; the manner in which parents set up the activity and interacted with their children.Parents of children with “high” mathematical ability were found to organize the activity using materials that were more varied (e.g., toys, tools, etc.) in nature allowing for more opportunities for sorting.They also used more open-ended techniques such as humor (e.g., suggesting the child put on Mr. Potato Head glasses to help her “look carefully”) and questions (e.g., “how many are small?”) to keep the children on task. Parents of children with “low” mathematical ability were more likely to be directive in their attempts to get and maintain their children’s attention, using language such as, “pay attention,” and, “look.” In general however, incorporation of explanations, question-asking, and specific praise (i.e., praising what the child did well, rather than simply saying “good” in response to the child’s actions) were limited in both groups. Paragraph 7: In general, the opportunities available for young deaf children who participated in this study to construct early knowledge of mathematics varied in both quantity and quality.This variation was evident in both the mathematically-based concepts that the children were exposed to as well as the mediated learning experiences that were used to guide their learning.Children with “high” mathematics ability were exposed to mathematically-based concepts in a manner that was more purposeful and meaningful than that experienced by the three children with low mathematics ability. In terms of mediation however, while children with “high” mathematics ability experienced an overall higher quality of mediated learning experiences, critical aspects of mediation were lacking for all children resulting in limited opportunities to engage in high levels of thinking. Paragraph 8: Findings from this study indicate a possibility that young deaf children may be lacking opportunities within their home environments to engage in high levels of thinking.This being the case, it is likely that when these children encounter learning situations in school that require them to use more than concrete information, they will experience difficulty.The following are suggestions for stimulating young deaf children’s early mathematical awareness, first in terms of increasing quality of mediation, then in terms of bringing mathematics into the home or other early childhood environment: Mediation:

Regardless of communication modality used, obtain the child’s visual attention before initiating communication.

Draw the child’s attention to interesting events or meaningful stimuli in the surrounding environment; for example, pointing out a caterpillar outside and asking the child how it compares to the caterpillar in the story you just read.

Incorporate opportunities for the child to engage in problem solving and critical thinking by asking questions that require the child to think about the world around him/her; for example, where do you think the sun goes when the moon comes out at night?

Encourage the child to slow down and think before acting.

Mathematics:

Incorporate mathematical language and vocabulary into everyday events whenever possible; for example, by counting steps while climbing them, discussing measuring cups used while cooking, or calculating what time it will be when the cookies you are baking come out of the oven.

Discuss daily routines with the child; for example, the sequence of the day’s events, activities that must be accomplished before leaving the house, or steps in preparation for bedtime.

Encourage the child to participate in natural opportunities for problem solving; for example, by sharing snacks with a sibling, setting enough places at the table at mealtimes, or deciding which toys would be best to bring on vacation.

Provide opportunities for your child to participate in games and activities that are mathematically meaningful; for example, puzzles, matching games, or building meaningful structures out of building blocks.

Involve your child in daily chores and their mathematical implications; for example, matching as laundry is sorted, categorization as food is put away after shopping, or one-to-one correspondence as the child sets the table in preparation for mealtimes.

Reference: Kritzer, K.L. (2008). Family mediation of mathematically based concepts while engaged in a problem-solving activity with their young deaf children. Journal of Deaf Studies and Deaf Education. 13 (4)Doi:10.1093/deafed/enn007

Family mediation of mathematically based concepts while engaged in a problem-solving activity with their young deaf childrenKaren Kritzer/Kent State University, OHfrom 09/1/08 until 09/21/08 to answer questions and share ideas concerning her research and its implications for parents of children who are deaf/hard of hearing, their teachers and other professionals who work with them.was availableAbstract:This study examined the relationship between young deaf children’s level of mathematics ability (“high” and “low”, as defined by test score on the Test of Early Mathematics Ability-3) and opportunities available for the construction of early mathematics knowledge during a problem-solving task implemented by their parents. Findings indicate that the manner in which mathematically based concepts (number/counting, quantity, time/sequence, and categorization) were incorporated into the activity was more meaningful for children who demonstrated high levels of mathematical ability. In addition, children who demonstrated high levels of mathematical ability experienced a more purposeful use of mediation during activity implementation; however, overall use of mediated learning experiences was limited for children from both ability groups.Paragraph 1:Hearing children begin formal schooling already knowing a great deal of mathematics. It is likely that they develop this knowledge through informal experiences within their home environment. Cooking with mom for example, helping to set the table at mealtimes, and/or playing simple counting and number games with family members can all contribute to young hearing children’s development of early mathematics concepts. Perhaps the most salient characteristic of young hearing children’s early environment is the fact that they are constantly surrounded by mathematical language. The young hearing child experiences vocabulary related to size for example, as grandma comments on howbigthe child has grown, or sequencing as dad mentions that a bath and story will occurbeforebedtime.Paragraph 2:For young deaf children, early informal knowledge of mathematics may not be so readily developed. Given the ramifications of hearing loss, deaf children, those with hearing parents in particular, are not likely to be exposed to linguistically-presented mathematics concepts quite as pervasively as their hearing peers. Some hearing parents with deaf children may find communication with their children challenging for a variety of reasons, including lack of knowledge of sign vocabulary that can be used to express mathematical concepts, inexperience with the process of gaining visual attention prior to communicating with the child, and language delays on the part of the child. Furthermore, rather than engage in the time-consuming task of explaining a task such as sorting laundry to the deaf child, a parent might find it easier to complete the task him/herself. Given these challenges, young deaf children, may begin kindergarten with a foundation of early mathematics concept knowledge that differs from their hearing peers. The purpose of this study was to assess the early mathematics knowledge of young deaf children and factors within the home that contribute to this knowledge.Paragraph 3:Twenty-nine children between the ages of 4 and 6 years, from schools for the deaf nationwide, participated in the study upon which the findings presented in this article are based. The Test of Early Mathematical Ability (TEMA-3) was administered to the children and the scores were used to select participants for the portion of the study described in this article. Participants were selected as follows: scores within 1 standard deviation of the mean formed the “average” group; scores 2 standard deviations above and below the mean formed the “high” and “low” ability groups respectively. Three participants from each the “high” and “low” groups were randomly selected and invited to participate in the second level of the study. The three selected participants in the “high” group all had deaf parents and lived in homes in which American Sign Language was the primary means of communication. The three participants in the “low” group all had hearing parents and spoken English, with some sign support, was the primary language spoken in the home.Paragraph 4:To examine the opportunities available for early mathematics learning for each child under similar conditions, data for the portion of the study described in this article were collected through use of a planned problem-solving activity, “This is In, This is Not,” from the book “Family Math for Young Children” (Coates & Stenmark, 1997), that parents were asked to conduct with their deaf children. The mathematical purpose of the activity was to observe, describe, and sort into categories. The written description of the activity suggests that parents collect a variety of items (i.e., toys, kitchen utensils, food products) to be used during the activity and then designate a sorting space. The activity takes place as children take turns sorting items into the sorting space. The parent might begin, for example, by picking up a blue car and saying, “This is in (the sorting space) because it is blue.” According to activity directions, all items are sorted as either belonging to the category or not.Paragraph 5:Videotape data from parents’ implementation of the activity, were coded for incorporation of mathematically-based concepts in the following areas: numbers and/or counting; quantity; time and/or sequence; and categorization. Findings indicated that parents of children with “high” mathematical ability incorporated these mathematics concepts into the activity substantially more frequently than parents of children with “low” mathematical ability. More critical however, is that these concepts were purposely incorporated into the activity in a manner that made them meaningful to the children. For example, after separating a specific category of objects, children with “high” mathematical ability were asked “how many” items were in that group. In contrast, children with “low” mathematics ability were asked to give the parent a specified number of items with a particular characteristic, (e.g., “two red”).Paragraph 6:Videotaped data from parents’ implementation of the activity were also coded for quality of mediation; the manner in which parents set up the activity and interacted with their children. Parents of children with “high” mathematical ability were found to organize the activity using materials that were more varied (e.g., toys, tools, etc.) in nature allowing for more opportunities for sorting. They also used more open-ended techniques such as humor (e.g., suggesting the child put on Mr. Potato Head glasses to help her “look carefully”) and questions (e.g., “how many are small?”) to keep the children on task. Parents of children with “low” mathematical ability were more likely to be directive in their attempts to get and maintain their children’s attention, using language such as, “pay attention,” and, “look.” In general however, incorporation of explanations, question-asking, and specific praise (i.e., praising what the child did well, rather than simply saying “good” in response to the child’s actions) were limited in both groups.Paragraph 7:In general, the opportunities available for young deaf children who participated in this study to construct early knowledge of mathematics varied in both quantity and quality. This variation was evident in both the mathematically-based concepts that the children were exposed to as well as the mediated learning experiences that were used to guide their learning. Children with “high” mathematics ability were exposed to mathematically-based concepts in a manner that was more purposeful and meaningful than that experienced by the three children with low mathematics ability. In terms of mediation however, while children with “high” mathematics ability experienced an overall higher quality of mediated learning experiences, critical aspects of mediation were lacking for all children resulting in limited opportunities to engage in high levels of thinking.Paragraph 8:Findings from this study indicate a possibility that young deaf children may be lacking opportunities within their home environments to engage in high levels of thinking. This being the case, it is likely that when these children encounter learning situations in school that require them to use more than concrete information, they will experience difficulty. The following are suggestions for stimulating young deaf children’s early mathematical awareness, first in terms of increasing quality of mediation, then in terms of bringing mathematics into the home or other early childhood environment:Mediation:Mathematics:Reference:Kritzer, K.L. (2008). Family mediation of mathematically based concepts while engaged in a problem-solving activity with their young deaf children.

Journal of Deaf Studies and Deaf Education.13 (4) Doi:10.1093/deafed/enn007