There was a paper in Nature Neuroscience not too long ago, that showed transgenerational transmission of a specific olfactory memory in mice. The authors showed that, remarkably, the olfactory memory of acetophenone can be passed down to the offspring and grand-offspring. They showed DNA methylation changes in the gene encoding the olfactory receptor for acetophenone, suggesting that DNA methylation (or perhaps another epigenetic process) could be the molecular mechanism for transgenerational transmission of this memory. They also showed that the memory is not being transmitted between generations by behaviour: IVF and cross-fostering experiments revealed that the memory was being transmitted through the germline, via the sperm/egg. So, there is at least some evidence that behavioural memories can be transmitted to the next generation by epigenetic mechanisms.

Dias & Ressler (2014) http://www.nature.com/neuro/journal/v17/n1/abs/nn.3594.html

Article Parental olfactory experience influences behavior and neural...

Experiences during gestation are actually a hotbed of controversy, especially when they might be non-obvious to prying, expecting scientists' eyes.  Consider the attached article on the once-supposedly innate response to the maternal warning call in ducklings.

But see also the recent literature on the rather explicit interaction of experience with genetics in terms of RNA up-regulation during training. E.g., http://www.ncbi.nlm.nih.gov/pubmed/23083740

Best wishes,

Damian

First you have to delineate what you indicate by the offspring’s ‘cognitive processes’ and the metrics being used to assess it. Then you have to examine the components underlying the emergence of cognition, if you agree with the hypothesis that cognition is not a “thing” but an emergent process incorporating non-linear patterns involving multiple acts (Rachlin, 2014; Staddon, 2014).

Consider that the human organism begins its journey typically through the genetic coupling of its two parents – yet, even from this primordial stage the effect of epigenetic influences arising appear quite significant (Teh et al., 2014). By the time the child has exited the womb, “maternal smoking, maternal depression, maternal BMI, infant birth weight, gestational age, and (even) birth order”, among others, predisposes the infant’s sensitivities to certain features of the forthcoming novel environment outside the womb (Marr, 2008).

Now consider the role of memory - to remember (and eventually reason, imagine, create and so on) is to demonstrate a specific type of transitivity (known in some circles as ‘mutual and combinatorial entailment’) and relational coherency which, once learned, can generalize to encompass the impressive repertoire that comprises of symbolic and verbal (human) activity (Wilson et al., 2014; Hayes et al., 2014). Infant tests for memory infer the a priori existence of numerous “capacities” which themselves are quite troublesome to de-construct and analyze when/if such attempts come about. But examining the development of such “capacities”, rather then looking at the scientifically shaky notion of ‘memory’, can help delineate the processes required for “doing” cognition (e.g., Lipkens, 1993).

Coming from a biological perspective, one question you may first ask is “what are the processes I am looking for” followed by “what are the behavioral building blocks underlying the emergence of these processes”. It is useful to keep in mind that "cognition” is dependent on behavior, not the other way round. Of course, the easy way out has been to refer to “working memory” or “memory capacity” as the variables of interest but doing so, while an enjoyable philosophical exercise, has little bearing on biology and/or behavioral dynamics (Uttal, 2001). Extrapolating meaningful patterns from the never-ceasing non-linear interactions between ribosomes and experience is a daunting task (hence why the notion of “memory” becomes so intuitively appealing), but it is a path you should at least consider.

Hayes & Sanford (2014) Cooperation came first: Evolution and human cognition.

Lipkens et al., (1993) Longitudinal Study of the Development of Derived Relations in an Infant

Marr (2008). Damasio's Error: A Bio-Behavioral Explanation of the Somatic Marker

Rachlin (2014). The escape of the mind. Oxford University Press.

SEP -> Stanford Encyclopaedia of Philosophy (2005). Epistemological Problems of Memory

Staddon (2014). The new behaviorism. Psychology press

Teh et al., (2014). The effect of genotype and in utero environment on interindividual variation in neonate DNA methylomes. Genome Research.

Uttal (2001). The New Phrenology: The Limits of Localizing Cognitive Processes in the Brain. MIT Press

Wilson et al., (2013) Evolving the future: Toward a science of intentional change

It is very hard to tease apart genetic and maternal care effects on behavior.  In rodent models we use "cross fostering" experiments to attempt to account for the maternal care effects. The design is to take pups from one genetic background at the day of birth and foster them to lactating dams of another genetic background, and vice versa depending on experimental design.  If the behavior of the adult offspring is more similar to the genetic mother than the foster mother, than the phenotype is determined to be genetic.  If the behavior of the adult offspring is more similar to the foster mother than the genetic mother, than the behavior is determined to be inherited through maternal care experience.

There was a paper in Nature Neuroscience not too long ago, that showed transgenerational transmission of a specific olfactory memory in mice. The authors showed that, remarkably, the olfactory memory of acetophenone can be passed down to the offspring and grand-offspring. They showed DNA methylation changes in the gene encoding the olfactory receptor for acetophenone, suggesting that DNA methylation (or perhaps another epigenetic process) could be the molecular mechanism for transgenerational transmission of this memory. They also showed that the memory is not being transmitted between generations by behaviour: IVF and cross-fostering experiments revealed that the memory was being transmitted through the germline, via the sperm/egg. So, there is at least some evidence that behavioural memories can be transmitted to the next generation by epigenetic mechanisms.

Dias & Ressler (2014) http://www.nature.com/neuro/journal/v17/n1/abs/nn.3594.html

Article Parental olfactory experience influences behavior and neural...

thank so much for all your suggestion and ideas..

There is some more to say, even for oviparous animals (e.g fish and amphibians) where the mother never sees her offspring, development of the CNS is controlled by maternal effect genes and their proteins laid in the egg. For example, the flow within the node during gastrulation (which is dominated by the maternal effect) is controlling Left/Right asymmetries in the embryos and, consequently, LR brain asymmetries and thus, personalities. 

I agree with the previous answers. The question is very interesting. In fact it is the so called Nature vs Nurture problem. Nowadays many scientists focus their attention in epigenetic factors that contribute to CNS development. We know that genes are essential for that development and these genes come from both parents. However, during pregnancy and after delivery, there are several factors that modify gene expression. For example, stress. High cortisol levels in the mother during pregnancy affect brain features of the offspring (they can be more sensitive to stress). The same happens with other hormones. Hence, a male with a low level of testosterone keeps the brain with a female-like structure (and this could be detected in spatial memory tasks). These are just two examples. I’m afraid that the answer to this question involves many factors and it’s not so simple (but we’re trying ;-)

Related to the answer above, it may be helpful to look at Rachel Yehuda's work on epigenetics, the transmission of trauma, and exposure to traumatic events among pregnant women.  

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2891396/

This is part of the broader study on epigenetics and stress during pregnancy, such as http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0056967